Wikipedia talk:WikiProject Mathematics/Archive/2013/Feb

Triangular rule

I fear this is a hoax. Comments would be welcome. Deltahedron (talk) 07:40, 1 February 2013 (UTC)

After [1] it looks more as a poorly sourced stub rather than a hoax. My first impulse was also to wipe them out, all of them. But the observation of 1/2 b_i h_i under <math> suggested just an extreme incompetence in exposition of the idea, initially valid. IMHO such primitive numerical integration method may exist; but the article is not written yet. Incnis Mrsi (talk) 10:18, 1 February 2013 (UTC)

I've noted on the talk page I can't find the term in the index of the book on Amazon which even if it is something else badly put it is not notable. Dmcq (talk) 13:38, 1 February 2013 (UTC)

Now at Wikipedia:Articles for deletion/Triangular rule. Deltahedron (talk) 20:10, 1 February 2013 (UTC)

"Unregistered" appearance of <math> and latex to html

There are two distinct problems, but the latter is a consequence of the former.

Since the trimming of texvc a year ago, the default look of <math> (even for simplest cases) became, as another IP recently said, “like it's been photocopied out of a text book”. Could anybody propose an idea to make <math> in Wikipedia more accessible?

The main problem with Special:Contributions/99.241.86.114 is that he tries to make better look of Wikipedia for unregistered users, a thing which we neglect. But he apparently does not understand that he frequently makes articles worse for us. Sometimes complaints appear at his user_talk, the most recent being user talk: 99.241.86.114 #Methods of contour integration, but it's the time to develop a permanent solution. I propose: let us make a typography quality scale such that its quality in any mathematics-related article could be assessed. Then, let IPs "improve" articles which are anyway poorly formatted, but they should be barred from "improvements" in articles with a good typography. Incnis Mrsi (talk) 07:30, 2 February 2013 (UTC)

Today he replaces the standard notation for Sⁿ with a boldface perversion. How long will we await this shadow person in front of the negotiation table? Incnis Mrsi (talk) 17:03, 3 February 2013 (UTC)

Earlier they replaced some of the \oplus and \otimes symbols at gyrovector space with a unicode character, but not all of them and not the \ominus symbols. This has nothing to do with looking better for unregistered users. It is just latex to html for the sake of it. And it's not even anything to do with html - it's just pasted unicode characters. Admittedly the article does use these symbols inline in the middle of standard text so the symbols do look large. 78.144.197.99 (talk) 18:06, 3 February 2013 (UTC)

Well, most of the edits are actually fine with me. But sometimes the editor includes drastic changes to notation or formatting, such as replacing $S^{n}$ with $\mathbf {S} ^{n}$ as you noticed, or awkwardly stuffing theorems into blockquotes. Unfortunately, the edit summaries are not sufficiently detailed to decide whether an edit is potentially controversial or not, and individual edits sometimes account for fairly substantial changes without much indication of the nature of those changes. Sławomir Biały (talk) 18:11, 3 February 2013 (UTC)

For example, I just noticed that this sequence of edits introduced the notation of a bold face H to denote the upper half plane, apparently without actually saying what the notation is supposed to mean, and also opted to spell "half plane" in the germanized manner "halfplane". This is just below the threshold of me caring enough to do something about though... Sławomir Biały (talk) 18:29, 3 February 2013 (UTC)

Tropical geometry

Some other eyes would be helpful at Tropical geometry. Deltahedron (talk) 18:50, 3 February 2013 (UTC)

typography of (typographical) ellipses

In this edit, WP:ELLIPSES was cited as justification. Whoever wrote that manual page section never contemplated the use of ellipses in mathematical notation. In TeX is it commonplace to write

$a+b+c+\cdots \,$

$a+\cdots +z\,$

Notice that

$a+\ldots +z\,$

looks different from

$a+...+z\,$

and the latter is not standard in TeX. Donald Knuth obviously thought more deeply and insightfully about typography than did whoever wrote that Wikiepdia manual page.

I think the manual page should note that it is not intended to apply to mathematical notation, whose conventions may be different. That may seem obvious, but apparently it wasn't obvious to whoever did the linked edit. Michael Hardy (talk) 17:42, 2 February 2013 (UTC)

I would like to be clearer too on mathematical notation there. I moved the pages because it was impossible to type ellipses. I believe that the manual is correct when it writes that ellipses "is harder to input and edit" but I don't have strong opinion on the matter as soon as we have redirects to cover both writing styles. -- Magioladitis (talk) 17:55, 2 February 2013 (UTC)

You are apparently preoccupied with typography, but there is also a semantic aspect. Although a dedicated character U+22EF ⋯ MIDLINE HORIZONTAL ELLIPSIS exists, the former article's title ended with interpuncts and spaces, which have enough typographic appeal, but are rather nonsensical. Now someone replaced a finely-looking nonsense with a roughly-looking semantically substantial character. The former was bad and the result is not good, too. Incnis Mrsi (talk) 18:02, 2 February 2013 (UTC)

I regard ellipses as a symbols under WP:TITLE#Special characters, and as such, should be avoided in article titles. If there must be an ellipses in the title (hard to imagine), there must be a redirect containing three unspaced dots. So IAFAIC, any title with an ellipses should be moved to a title with dots. — Edokter (talk) — 18:28, 2 February 2013 (UTC)

"IFAIC"? --JBL (talk) 18:47, 2 February 2013 (UTC)

Corrected. — Edokter (talk) — 09:48, 3 February 2013 (UTC)

Instrument for Assessing Identity Confusion [2] Deltahedron (talk) 09:51, 3 February 2013 (UTC)

Ellipses are punctuation, and punctuation is not forbidden in article titles. I've moved the series articles in Template:Series (mathematics) to titles with the ⋯ character, and I've created or updated redirects from titles with three unspaced periods. (The lone exception is 1 − 2 + 3 − 4 + · · ·, which I lack the ability to move.) Ozob (talk) 16:32, 5 February 2013 (UTC)

I noticed that 3.14... does not have a page. Should the redirect be created? Tkuvho (talk) 16:41, 5 February 2013 (UTC)

Yes. Obviously to τ/2. Sławomir Biały (talk) 22:05, 5 February 2013 (UTC)

I'd like to add my supporting opinion to Ozob. We should use the correct symbol in the article title, unless there is some way (and clearcut reason) for avoiding symbols altogether. The usual arguments about people with screen readers clearly don't jibe if we are going to use an incorrect symbol as a substitute (like using three periods instead of a centered ellipsis). So what if the screen reader knows how to pronounce it? it's not the correct symbol. Sławomir Biały (talk) 22:05, 5 February 2013 (UTC)

Linear or affine?

I have noticed some folks (not very systematically) going around elementary mathematics articles and changing instances of "linear function" to "affine function": [3] and [4]. While this is perhaps technically correct terminology in higher mathematics, is this usage really very common in grade school mathematics? Also, I don't think it is helpful in an article like function (mathematics) to link to the article affine transformation in the caption of a simple affine function of one real variable (i.e., a grade-school "linear function"). Do we have a better place to link to such a notion? Sławomir Biały (talk) 01:10, 5 February 2013 (UTC)

I had just been considering this exact same problem and wondering what should be done about it. In the artricle here on linear function I'd normally call the first use of linear function an additive function and I'd call the vector one a linear transformation. I've never said affine function for affine transformation and what they are calling an affine function I'd normally call a linear relation. Over and above all that though is the main problem that the articles this is being applied to are supposed to be accessible to schoolchildren and I really think 'affine' is a blocker word in that context. Dmcq (talk) 01:48, 5 February 2013 (UTC)

The word "linear function" actually means that its graph is a line, and does not refer to the meaning from linear algebra. Because of confusion, Wikipedia currently has articles on degree-2, -3, -4, and -5 polynomials, but lacks an article (or even a section) on ax + b functions. The {{Polynomials}} navbox links to linear equation instead. IMHO a separate article must be created (possibly, by splitting of linear equation) – it is an important class of functions far beyond its rôle as endomorphisms and the automorphism group (for a ≠ 0) of the affine line. Incnis Mrsi (talk) 08:02, 5 February 2013 (UTC)

For one thing, it's what one tries to construct when one does linear regression. See for instance Linear predictor function, which has a link to the wrong kind of linear function in its lead. —David Eppstein (talk) 08:20, 5 February 2013 (UTC)

Sorry, David, you're wrong. You're making the usual clumsy mistake of thinking that the reason why linear regression is called linear is that one is fitting a line. But if you fit a parabola by least squares, that's still linear regression. And the reason for calling it that makes sense. Nonlinear regression is something else. The article on linear predictor functions has the right link. You're neglecting the fact that a column whose every entry is the number 1 may be one of the predictors, so you're taking a linear combination of that and the others. See this question and its answers. Michael Hardy (talk) 15:40, 5 February 2013 (UTC)

Ok, fine, I should have said simple linear regression. My point was not about what the "linear" in linear regression means, but rather that these functions are important in this role. —David Eppstein (talk) 16:49, 5 February 2013 (UTC)

"Affine function" smacks of the "New math" approach, and (I should hardly add) that is not the direction where we want to take Wikipedia. This is also more popular in French textbooks (Berge's Geometry, unless I am mistaken, makes a big deal out of "affine spaces" in general). I am reminded of David Mumford's story about his daughter's textbook's definition of the plane, in a French school in late 1960's, as a "torseur", a concept then very popular among mathematicians at IHES. Arcfrk (talk) 22:52, 5 February 2013 (UTC)

Maybe we can follow the approach of the German wikipedia, which distinguishes explicitly between the "highschool use" (ax + b ) of term and its meaning otherwise (linearity of operations) and has separate articles for it. We could change linear function into a disambiguation page linking to the appropriate articles, though the article for the "highschool" variant still needs to be written. --Kmhkmh (talk) 09:54, 5 February 2013 (UTC)

I agree. [5]. --El Caro (talk) 11:59, 5 February 2013 (UTC)

This seems very simple: calling an affine function linear is wrong. Isn't it? Like a grammar mistake, just because many people make the same mistake, that doesn't make it right. We have to use the "correct definition", regardless of the sophistication of mathematics. -- Taku (talk) 01:54, 6 February 2013 (UTC)

No it is actually not that simple since is about common naming conventions and a name as such is neither right nor wrong it is just name. You may argue whether particular name a misnomer and not very helpful, but that's a separate question. Moreover WP should describe mathematical terms and names as they are used and resists pushing its own naming conventions. As that name is common in "highschool" math literature (and probably some other areas) WP should explain it (and of course point out that it is not a linear function in terms operations or the usual usage of the term linear). Moreover we can combine that with (highschool oriented) article on the ax + b function, which we currently seem to lack anyhow.--Kmhkmh (talk) 02:29, 6 February 2013 (UTC)

It's not as if the definitions of linear and affine were handed down on stone tablets. Probably 99.9% of people have never heard of an affine function—a figure that even includes most scientifically literate individuals—but I'd wager a fair number have heard of a linear function (and think it means a function whose graph is a line). And anyway, regardless of terminology, it's a useless perversity to link to the article affine transformation in a context that means a linear function of a single real variable. Sławomir Biały (talk) 03:41, 6 February 2013 (UTC)

Yes, the link to affine transformation would be very unhelpful, especially when a reader is not mathematically minded. -- Taku (talk) 12:47, 6 February 2013 (UTC)

It's completely and utterly common to call any degree 1 (or constant) polynomial "linear", in the context of elementary algebra and calculus, at least in the United States. In particular, this terminology is used in both Spivak's Calculus and Stewart's Calculus (the former is a well-regarded rigorous calculus textbook; the latter is probably the most used calculus textbook in the U.S.). This is not the same meaning as in linear algebra, and it is very hard to claim that both Spivak and Stewart are "incorrect". It is completely uncommon to call these functions "affine". We should not use a word that nobody else uses in these contexts. Nobody calls them "cosets", either, even if that's what they are. — Carl (CBM · talk) 02:39, 6 February 2013 (UTC)

I suppose I stand corrected. (I didn't go to high school in US. On the other hand, Stewart is the textbook we're using to teach calculus, so maybe I should have known better.) Ok, how about degree 1 polynomial or polynomial of degree at most 1, because it's what it is? To use "linear function" to refer to such a polynomial in the context beyond elementary calculus would be very confusing. -- Taku (talk) 12:47, 6 February 2013 (UTC)

As a name for the future article that's ok with me. However linear function needs to become disambiguation and link to this article and the name linear function needs to be mentioned in that article as well because it is the under which highschool students or college freshmen are likely to look for it. The article itself then can establish the context under which the name is used, so that there's no confusion. You can quickly sample various highschool textbooks via a Google Books search, in case you want to check it out yourself (a few samples: [6], [7], [8], [9], [10], [11]). This usage of the term is actually not a particular English thing either at least in German highschool literature it is more or less a standard term for the polynomial of degree one and and occasionally used in that fashion in university level calculus books and in some engineering books as well. It even used in such classics as Bronstein (the European analogon to Abramowitz and Stegun).--Kmhkmh (talk) 13:34, 6 February 2013 (UTC)

Several remarks:

• It is clear that "linear" has two related but different meaning in mathematics, namely "of degree one" and "commuting with addition". The meaning of this adjective depends on the object that is qualified and on the context. As far as I know, the ambiguity occurs only with "linear function" and sometimes "linear polynomial". In the latter case, "linear" has usually the first meaning and affine is rarely (but sometimes) used. For the second meaning (homogeneous polynomial of degree one), the standard is to use "linear form".
• Strangely linear form, which is a standard terminology is a redirect to linear functional, an unusual terminology for the same notion; this leads to a strange hatnote explaining that a linear functional may be a functional, but not necessarily.
• Even more strange: linear polynomial is a dab page that asserts that a linear polynomial may be several things, but not a polynomial!
• The use of "linear function" for "polynomial function of degree one" appears in wp in piecewise linear function (piecewise affine function does not exists).
• Several editors have considered the usage in other languages. In French, although "function" (fonction) and "map" (application) are formally almost synonymous (a map is defined everywhere, a function not necessarily), "function" is used, in practice, only for real and complex valued functions, and is never user for linear maps between vector spaces. Thus "linear function" means "polynomial function of degree one" and "linear map" means "additive map" even for a map which is a real valued function. My feeling is that these informal conventions are also used in English by most professional mathematicians.

Thus, I suggest

1. To rewrite linear polynomial, may be as a redirect to the future "linear function" (done as a redirect to Polynomial#linear polynomial)
2. To move linear functional to linear form (done)
3. To merge the present state of linear function into linear map, and to explain there that "linear function" is sometimes a synonymous, but has frequently another meaning, may be with a hatnote {{distinguish}}.
4. To write the article "linear function" devoted to polynomial functions of degree one, with explanation and hatnote to distinguish with "linear map"
5. Do not make a dab page "linear function that will be more confusing"
6. Update linear and linear (disambiguation) (the latter being rather confusing)

D.Lazard (talk) 16:00, 6 February 2013 (UTC)

I agree with you that the better solution is to make linear function be the one that allows an additive constant term, and to have a hatnote pointing to the other one (which could reasonably be called linear map). Doing it with a disambiguation page is both more confusing and unnecessary (we don't generally need dabs with only two links). As I already commented earlier (in a remark that was quickly sidetracked into the sort of pedantry that has led us into this mess) we should also consider how linear predictor function fits into this picture. It's a bit of a confusing example because it starts out as a function with a constant term but then later on in the article (by introducing an auxiliary variable) turns it into a linear map. —David Eppstein (talk) 18:43, 6 February 2013 (UTC)

Linear functional is a fairly common synonym for linear form, by the way, but I think one that tends to be used more in analysis rather than algebra. Sławomir Biały (talk) 21:48, 6 February 2013 (UTC)

At some point a long time ago, someone replaced "linear" with "affine" in the article Logical connective. I let it go, because I don't know what the kids are calling it these days. However, if there is a distinction, please help make sure the appropriate term is being used. My understanding of the concept as it relates to logical connectives is that when the truth-value of both statements always makes a difference or never makes a difference to the resulting truth value (as for instance they do when connected by "and" or "if and only if") then the connective is linear. When both statements do not always but also do not never make a difference (as they do not for "or" or "if...then") then the connective is not linear. This usage of the terminology is consistent with what Post used in his writing on functional completeness. Greg Bard (talk) 16:06, 6 February 2013 (UTC)

Just remove that affinity section. The only things that satisfy that are the logical equivalence relations or their negatives and a quick google search gives nothing so it can't be exactly a common term there. The link is definitely wrong. Dmcq (talk) 18:38, 6 February 2013 (UTC)

No, don't remove it. We have Post using the term "linear" so if no one knows any better, we will use "linear" if necessary. Greg Bard (talk) 00:54, 7 February 2013 (UTC)

There is a bit of a problem with that too in that there is linear logic, and really how often do people use the term? In fact where did Post use it? Dmcq (talk) 12:30, 7 February 2013 (UTC)

There are lots of papers and books on the theory of clones and coclones (not only on) the two-element set. I fail to see the relevance of linear logic to this issue, but unlike Girard’s naming conventions, the terminology here makes perfect sense: an n-variate Boolean function is affine/linear in the sense mentioned by Greg Bard if and only if it is an affine mapping from the n-dimensional affine space over $\mathbb {F} _{2}$ to the 1-dimensional space. Which also shows that the naming issue of linear vs. affine for this concept is exactly the same one as being discussed in this thread, and if any consensus comes out of this discussion, it applies to it as well. The only actual problem with the Logical connective article is that despite the name and the lead paragraph, it only deals with classical logic and its two-valued semantics.—Emil J. 13:51, 7 February 2013 (UTC)

I had considered that but being pedantic an output of always false is also a linear output whereas in that article they have every input affecting the output - which if one expressed it using the equivalence relation with ⊕ one would have to say was affine as one might have all false going to true. Having a term for something with just the two possibilities seems overkill as I can't find references for the words in the context of logical connectives. Dmcq (talk) 16:20, 7 February 2013 (UTC)

I think you are misreading it. The condition is that every variable either always affects the output (i.e., for every assignment, switching the truth value of this particular variable changes the value of the function) or never affects the output. The constant false function is the case where no variable affects the output. Also, you seem to be under the false impression that connectives or truth functions have to be binary, there are in fact infinitely many possible affine connectives. One reason why affine/linear connectives are important is that they form a maximal clone, and as such appear in Post’s characterization of functional completeness. Let me stress again that this classical result is about connectives of arbitrary arity.—Emil J. 16:54, 7 February 2013 (UTC)

Sorry yes I misread. That does make more sense and I've found some references to affine even if I couldn't find any for linear or affinity in this context. The link to affine transformation still seems rather strained to me, and I think having some non boolean logic relation satisfying that in a useful way seems unlikely. Dmcq (talk) 18:16, 7 February 2013 (UTC)

Well I think I'll just leave the bit about 'affinity' in Logical_connective#Properties and its link to affine transformation alone. It may sound strange to me but I'm no expert. Dmcq (talk) 18:36, 7 February 2013 (UTC)

Comment added to my preceding post: I have not found in WP any definition of "linear function of several variables". All the implicit definitions that I have found are equivalent to that of linear form. None of the given definitions for univariate functions extend immediately to the multivariate case. For the definition as linear form, if $f(x,y,z)$ is a linear function of three variables, then $f(x,y,1)$ is not linear. This is a further witness that one has to consider different definitions of "linear" in algebra and in calculus. The future article "linear function" should also consider the multivariate case. D.Lazard (talk) 17:32, 6 February 2013 (UTC)

Policy on cross-reference pages

It has been proposed at this page to make the concept of cross-reference pages (formerly "multiple-cross-reference pages") into a Wikipedia guidelines. Opinions should be posted there.

The first several such pages were math pages and the concept first appeared on this present WikiProject talk page. See Category:Cross-reference pages. Michael Hardy (talk) 04:29, 8 February 2013 (UTC)

See Category:Cross-reference pages for the few current examples. Michael Hardy (talk) 04:31, 8 February 2013 (UTC)

Ordered set under the scope of WikiProject Mathematics?

Just came across Ordered set, it needs a lot of work and seems to me to be under the scope of WP Mathematics. I added a reference, but that is as far as I can go with this page with my limited mathematics understanding. Currently the page is not listed as being under any WP. Cheers, Keetanii (talk) 03:04, 7 February 2013 (UTC)

I think it needs, not so much work, as deletion. Wikipedia is not a dictionary and we don't have to document every possible phrase that might come up in mathematics. There is nothing to say that is not already covered at either partial order or total order. A disambig page that points to those two might be OK, but what's the point? Alternatively, just redirect to partial order, the more general of the two. --Trovatore (talk) 04:44, 7 February 2013 (UTC)

Could rederict to order theory alternatively. AHusain (talk) 05:06, 7 February 2013 (UTC)

Well to some degree an encyclopedia is a dictionary on steroids, meaning technical terms should be covered. Whether they havetheir own entry or potentially just a redirect and coverage in a larger article is separate matter. But one should be able to look up the term in WP.--Kmhkmh (talk) 19:12, 7 February 2013 (UTC)

I've changed it to a cross-reference page, so far having only two items. Any time you see it proposed that a title could redirect to any of two or more articles, and all of them seem just about equally reasonable redirect targets, one should consider making it a cross-reference page listing all of them. Michael Hardy (talk) 04:05, 8 February 2013 (UTC)

Interesting idea. I'll have to let it percolate for a while before I can be sure whether I like it, but it does seem to be a niche not currently filled. --Trovatore (talk) 10:25, 9 February 2013 (UTC)

A ten-year old error in an article?

In 2003 I created the article titled Kolmogorov's zero–one law. It says

Suppose

$X_{1},X_{2},X_{3},\dots \,$

is an infinite sequence of independent random variables (not necessarily identically distributed). Then, a tail event is an event whose occurrence or failure is determined by the values of these random variables but which is probabilistically independent of each finite subset of these random variables.

I think that's stood there since 2003.

I wonder if I should have said something else instead, as follows. One would not assume independence of the random variables in the sequence, and one would say that a tail event is an event whose occurrence or non-occurrence is determined by the values of the random variables in the sequence but whose occurrence or non-occurrence is unchanged by changing the values of finitely many of the random variables in the sequence. I think that says the same thing if they're independent, but not if they're not. For example, suppose p is a random variable taking values in (0,1) and each random variable in our infinite sequence of Xs is 1 with probability p and 0 with probability 1 − p, and are conditionally independent given p. Then the Xs themselves are not independent because if one of them is 1, that makes it more probable that p is large and thus more probable that the next X is 1. Then the event that

$\lim _{n\to \infty }{\frac {X_{1}+\cdots +X_{n}}{n}}>1/2$

would be a tail event by the second definition but not by the first. (The probability that that limit is more than 1/2 is actually just the probability that p is more than 1/2. This tail event would not violate the zero–one law because the hypothesis of independence does not hold.)

The definition given in that article is good enough for that article because independence is assumed. But should I have given the latter defintion?

Tail event currently redirects to Kolmogorov's zero–one law. Michael Hardy (talk) 00:38, 9 February 2013 (UTC)

"... a tail event is an event whose occurrence or non-occurrence is determined by the values of the random variables in the sequence but whose occurrence or non-occurrence is unchanged by changing the values of a finite subset of the random variables in the sequence."

You left out the underlined phrase. JRSpriggs (talk) 10:34, 9 February 2013 (UTC)

Fixed. Thanks. Michael Hardy (talk) 18:10, 9 February 2013 (UTC)

Gaussian elimination vs. Gauss–Jordan elimination

I've proposed to merge Gauss–Jordan elimination into Gaussian elimination. While it is true that most textbooks treat these as distinct concepts, I think having two articles is unnecessary. Gauss–Jordan elimination could be a subsection of Gaussian elimination. Does this seem like a good idea?

For me, the ideal article arrangement would be to join both articles into one titled Row reduction. I think it would be much easier to explain the concepts under this less ambiguous title. Because "Gaussian elimination" may or may not stop after it's in row echelon form (before the matrix is reduced), depending on the textbook. Thoughts? Mark M (talk) 09:13, 9 February 2013 (UTC)

Yes, a good plan which makes sense. Stating any differences in what authors refer to as "Gaussian elimination" or "Gaussian–Jordan elimination" shouldn't be a problem in a sentence or two. Row reduction is the main operation, and yet it's just a redirect. M∧Ŝc²ħεИ_τlk 09:47, 9 February 2013 (UTC)

I would suggest to merge also these two articles with Row echelon form. In fact, row echelon forms are defined independently of any algorithm and Gaussian and Gauss-Jordan eliminations are the most natural algorithms to compute them. Without such a merge, I do not see how to explain that "the result of Gauss-Jordan elimination is independent of the way of doing Gauss-Jordan elimination". By the way, properly speaking, Gauss-Jordan elimination is not Gaussian elimination followed by a further reduction; this "further reduction" is mixed with Gaussian reduction. It is only the unicity of the result that allows to call Gauss-Jordan elimination these two different algorithms. D.Lazard (talk) 10:19, 9 February 2013 (UTC)

List of well-known mathematical operations

I tried to compile a list of mathematical notations which a reader of an article about physics is presumed to know: see WP:MOSPHYS #Mathematics (it’s a draft yet). IMHO the extent of the “well-known notation and semantics” should be first standardized outside articles on fundamental mathematical – certainly, the article ring (mathematics) may not deal with the “multiplication” operation as with a known concept, even if any reader is familiar with the notation.

Does anybody see flaws, omissions, or have other insights? BTW parts of this material may be later reused by (or moved into) WP:MOSMATH. Incnis Mrsi (talk) 10:47, 4 February 2013 (UTC)

It seems like the cross product and wedge product would also be there, if the dot product and bra-ket notation are... I'm not entirely sure of the purpose of that section, though. Is it to show the preferred format of each operation? Or, as the final note suggests, notations which can be assumed to be known? I can understand the former purpose, but the latter purpose would be problematic to figure out. I would be really amazed if tensor contraction is really better known than the cross product... Rschwieb (talk) 21:58, 4 February 2013 (UTC)

Surely this depends on context? E.g. (to pick two fairly recently created mathematics articles) I'd expect a different level of background knowledge for a reader of Good filtration than for a reader of 888 (number). Otherwise it wouldn't be possible to write articles about highly technical subjects without immediately getting bogged down in definitions. —David Eppstein (talk) 22:33, 4 February 2013 (UTC)

Not necessarily definitions. I said that anything outside the standard list shall be declared, with links. Incnis Mrsi (talk) 07:37, 5 February 2013 (UTC)

Yes. For example, $|D|$ would mean the complete linear system of a divisor in algebraic geometry (not absolute value). This sort of program strikes me as feasible as trying to stabilize conventions across math articles. -- Taku (talk) 01:57, 5 February 2013 (UTC)

I do not see anything wrong with 21st-century physicists who know contraction better than the notation from the age of James Clerk Maxwell. To "show the preferred format" is a secondary aim. First of all, the list should, by exclusion, prescribe to declare certain notations in articles. Incnis Mrsi (talk) 07:37, 5 February 2013 (UTC)

I'm not sure what "prescribe to declare" means, but if it means that you are prescribing what notation should be used in articles, then I think i agree with Taku that this is infeasible. It is also overstepping the bounds of being encyclopedic. On the other hand, if the purpose is to list the different things the same notation can be used for, then that would be useful for a reader trying to track down a bit of notation. Rschwieb (talk) 14:34, 5 February 2013 (UTC)

Do you actually read what I said? The primary aim is to form a list of notation which are presumed to be known for a reader which has interest in math formulae. Other notation, of course, may be used, but it must be declared(explained). For example, in Majorana equation:

“

$-i{\partial \!\!\!{\big /}}\psi +m\psi _{c}=0\qquad \qquad (1)$

written in Feynman slash notation. Here ψ_c is the charge conjugate of ψ, which can be defined in the Majorana basis as

$\psi _{c}:=i\psi ^{*}.\$

”

It declares the use of $\partial \!\!\!{\big /}$ and _c symbols, but i, *, and := are assumed to be known notations. Incnis Mrsi (talk) 09:54, 6 February 2013 (UTC)

To maintain our civil environment here I will interpret "Did you actually read what I said" as "Given my history of problems communicating in English I would appreciate elaboration on your last comment." In words you say the purpose is to make a table of notation which is "safe to assume is understood". In action a table was made which includes comparatively obscure notations (You cannot claim that bra-ket and tensor contraction are on a par with "+" and "sin(x)". The tensor contraction does not even render in my browser.) and has so far it has omitted something as simple as the cross product. Given the apparent clash of words and action, I had to get clarification on what the task was.

At any rate, I think I can stop asking for clarification and go frame my comments for the original post. Flaws: highly subjective, needs a good way to explain multiple meanings of single notations. Omission: cross product, (probably) wedge product. Rschwieb (talk) 15:30, 7 February 2013 (UTC)

Regarding the the list entries themselves, the tensor contraction code has problems, as it does not parse (Failed to parse (lexing error):...). In the braket entry, the phi and angle brackets seem to be in boldface, whereas the other symbols are not. Perhaps this is browser dependent. In your notation example above, I have never seen ":=" used in a physics textbook; this sort of notation is more popular with computer scientists.

Regarding presumption of knowledge of mathematical notations, I don't think we can establish a single threshold, for two reasons. First, what notation needs to be explained is dependent on the expected audience for the article. The article on quantum mechanics may be viewed by people wanting to learn about it--they probably won't know the braket notation. A high school student wanting to learn about Newton's laws of motion may not know calculus. This is not to say that all notation must be explained in all articles, but which notation gets explained is dependent both on the subject material and the expected audience. Second, mathematical notation is, to use a CS concept, highly overloaded. |A| may mean set cardinality, determinant, complex magnitude, vector norm (yes, I've seen this done), the complete linear system of a divisor, ..., and occasionally absolute value. Thus even familiar notations may need to be explained depending on context. --Mark viking (talk) 18:00, 14 February 2013 (UTC)

calculate

Can somebody calculate the midway point between 500 and 2,200,000,000 please? Please show the calculation as well. Thanks Pass a Method talk 19:50, 9 February 2013 (UTC)

You're more likely to get help with your homework at Wikipedia:Reference desk/Mathematics. Deltahedron (talk) 20:17, 9 February 2013 (UTC) Tr

Ask yourself: What does it mean to say that m is the midpoint between a and b? How can I express that as a mathematical equation? If I solve the equation for m, what do I get? JRSpriggs (talk) 06:54, 11 February 2013 (UTC)

Disambiguation help needed with Matrix algebra

Matrix algebra has a large number of incoming links for which expert assistance is required. Please help if you can. Cheers! bd2412 T 03:00, 13 February 2013 (UTC)

It's a little annoying to members of the project when disambiguators make changes like this, which point to the wrong article. I'm not accusing anyone of everything, except to say that people probably shouldn't be involved in mathematics disambiguation if they don't know the difference between a tempered distribution and a tempered representation—or, by extension, between a matrix algebra (as a count noun) and matrix algebra. Sławomir Biały (talk) 03:47, 13 February 2013 (UTC)

It's a little annoying to members of the disambiguation project when these pages are allowed to build up such large numbers of incoming links that they crowd the list of the most linked-to disambiguation pages. Now, I note that Adjoint representation has recently been made a disambiguation page (and a WP:TWODABS page at that), and nothing has been done about it. Disambiguators disambiguate, and presented with a list of incoming links like this, will likely try to fix them all by making the best guess from the context of the terms. I have made posts here several times requesting the sort of expert assistance that you suggest we need. Frankly, I think it would be fantastic for everyone involved if this project could just take over the maintenance of all of its disambiguation pages. Cheers! bd2412 T 05:22, 13 February 2013 (UTC)

What means “a WP:TWODABS page”? This wording is apparently chosen to suggest that certain guideline discourages disambiguations pages with only two entries, which is a lie (if I do not see here something which BD2412 did not say at all). Incnis Mrsi (talk) 07:33, 13 February 2013 (UTC)

That is incorrect. The guidelines do indeed discourage the making of disambiguation pages with only two entries if one of the topics is primary (i.e. substantially more likely to be the target sought), because such a page is not needed as a navigational device. It is important to remember that the purpose of disambiguation pages in the first place is merely to assist readers in finding the topic they are trying to find. If the reader is just as likely to be assisted by a redirect to one of two possible articles, which has a hatnote pointing to the other, then there is no basis for making a disambiguation page in the first place. The existence of such a page will only complicate the efforts of the reader to find what they are looking for. Consider: if a term has only two meanings, at least fifty percent of the time the reader must be looking for one of those meanings. If that title is a disambiguation page, then the reader must figure out which meaning to go on to. In other words, they would type or click the name and get taken to a page from which they need to make another click to get where they really want to go. Where there are only two possible meanings, having the more likely of those meanings at the undisambiguated title means that at least half the time, the reader landing on that page does not need to click any further, because they have found exactly what they are looking for. For the reader who is looking for the sole other meaning, it is right there in the hatnote, so they are not inconvenienced any more than they would be if they had gone to a disambiguation page. The basic question, of course, is which of the two pages is the primary topic that should be at that title, but that is often much easier to determine then people imagine, particularly if only one page contains an exact match to the title. In short, avoiding a disambiguation page in a WP:TWODABS situation inconveniences no one, while saving at least half the people who come to the page from having to read, decide, and click again. bd2412 T 12:57, 13 February 2013 (UTC)

The guideline states:

As discussed above, if an ambiguous term has no primary topic, then that term needs to lead to a disambiguation page. In other words, where no topic is primary, the disambiguation page is placed at the base name.

What is not clear? The term has no primary topic ⇒ it must lead to a dab page. Hence, by modus tollens, “something other than disambiguation is possible” ⇒ “the term must have a primary topic”. I do not see here even a hint from BD2412 that some title of (matrix algebra, adjoint representation) has some definite primary topic. BD2412’s eloquences above (starting from “It is important to remember that the purpose…”) represent a well-known tendency, deeply entrenched in minds of many Wikipedians which deal with popular culture topics, but having less support among Wikipedian scientists. It does not represent an official guideline by no means. Users which create and maintain a quality content do not forget that dab pages make Wikipedia better, in the long-term perspective. An attempt to save readers’ clicks by eliminating the dab page at a really ambiguous title will inevitably be paid by erroneous internal links. Incnis Mrsi (talk) 16:41, 13 February 2013 (UTC)

Dab pages only make the encyclopedia better when they are used appropriately. Please consider the (official) guideline WP:CONCEPTDAB, which applies to adjoint representation. Mark M (talk) 17:06, 13 February 2013 (UTC)

I known what is CONCEPTDAB and even largely participated in creation of one. If you will opt for a CONCEPTDAB for adjoint representation, then look to Adjoint, please. Apparently, there is already a botched attempt to create such CONCEPTDAB. Incnis Mrsi (talk) 18:40, 13 February 2013 (UTC)

It's really not much work to make the article a concept dab.. in fact adjoint representation of a Lie group basically already is. Anyway, please discuss this further on the RM I've linked to below. Regarding adjoint.. I hadn't noticed it before, but I think that one should be a dab. While there is technically a very broad concept, my feeling is that it should primarily be for disambiguating (which it currently does anyway). The broad concept is more likely to confuse than clarify. Mark M (talk) 19:41, 13 February 2013 (UTC)

Is this edit of R'n'B a single mistake, or a pattern of incomwpetence? For example, I would not say anything bad about a user which makes one erroneous link change for five hundreds accurate dab link eliminations. Incnis Mrsi (talk) 07:33, 13 February 2013 (UTC)

I don't know if it's part of a pattern of incompetence, but the tempered representation wasn't the only worrying thing about that edit. The editor was unsure that Cauchy's theorem should point to Cauchy's integral theorem, which strongly suggests that he lacks a basic literacy in mathematics. We've also heard from Wikiproject disambiguation before, about incoming links to disambiguation pages where (in my opinion) none of the disambiguations would have been correct. I just don't see that disambiguation should trump all other considerations. Obviously, it's something that we should do, but not at the expense of having a link point to the wrong article. Sławomir Biały (talk) 13:52, 13 February 2013 (UTC)

First, R'n'B is one of our best disambiguators, an editor for whom a charge of "incompetence" treads close to being a personal attack. Second, this is a general purpose encyclopedia, for which "basic literacy in mathematics" means no more than knowing what a square root is and knowing the difference between a numerator and a denominator. Part of the problem with efforts to disambiguate math concepts is that the articles themselves border on the unreadable, sinking immediately into inaccessible technical jargon. Ideally, it should be possible for the average reader to figure out which disambig term is the right solution by reading a line or two of the articles linked on that page. If it isn't, then the problem lies in the writing. As an intellectual property attorney, I know that I need take great care to avoid dropping into legalese, and to remember that I am writing for a general audience, even if other attorneys may read what I have written and find it simplistic. As for instances wherein none of the disambiguations are correct, what good does it do the reader who wants to find out what Cauchy's theorem means in an article if even the disambiguation page says nothing about the particular theorem being referenced? In that case, the best solution is to turn the link into a red link for the name of the article that should exist, but is missing. bd2412 T 17:29, 13 February 2013 (UTC)

Do you believe that Cauchy's integral formula "sink[s] immediately into inaccessible technical jargon", whereas the article tempered representation is immediately evident to someone who "know[s] what a square root is"? If so, that is a fascinating point of view. In Wikipedia, there are articles aimed at many levels of technical understanding. Obviously, someone with a grade-school knowledge of mathematics should not be editing an article about advanced mathematics. Period. I'm utterly baffled by your suggestion that the opposite should be the case. Do we live in backwards world? Sławomir Biały (talk) 02:09, 14 February 2013 (UTC)

Whether or not people with "grade-school knowledge of mathematics" should be editing these article, this is a wiki, which means that there is no controlling the level of education of those who edit. There is no button by which editing can be limited to those with an understanding of mathematics that even most Wikipedia administrators do not possess. What I am proposing, therefore, is that for ambiguous topics like the various theorems listed on Cauchy's theorem, the topics should be written clearly enough that an average person coming upon a link to the disambiguation page will be able to figure out how to fix the link. Such a level of clarity happens to coincide with the fact that the articles themselves may be read by that average person, and should be written with sufficient clarity for that reader to understand the topic. bd2412 T 02:18, 14 February 2013 (UTC)

[edit conflict] In other words, you think we shouldn't have articles on topics that are sufficiently advanced that grade-school mathematics students can't be expected to understand what the topic is, at least in the cases where the topic might one day be referred to by an ambiguous title? That seems very limiting to me. For instance, I doubt anyone without at least the equivalent of an undergraduate mathematics education could ever be expected to properly distinguish the topics in Zeta function, but should that mean we can't have an article on the Riemann zeta function and the Riemann hypothesis? —David Eppstein (talk) 02:35, 14 February 2013 (UTC)

I have seen some very complex topics described with sufficient clarity that the average reader can indeed at least understand the topic well enough to fix an errant link. It takes some talent, and hard work, but it is doable. As for Zeta function, that does not seem to be an ambiguous topic at all, since all of the links are partial title matches which, if the lede is to be trusted, are merely types of the thing described by the lede. In other words, this is a list of zeta functions, not a list of terms unrelated but for the fact that they share the exact same name (as with Mercury, the planet, and Mercury, the automobile, or Phoenix, the city, and Phoenix, the mythological bird. bd2412 T 03:07, 14 February 2013 (UTC)

On the contrary, there have been cases where zeta function is used, intending some specific zeta function, and needing disambiguation to a more specific article (for instance, in a context where something else in the article says "nonzero characteristic" and to disambiguate it properly you need to infer from that that probably Local zeta-function is the right one). The more you assert that these examples don't exist, the more it seems that your own ignorance is what's on display. They do exist, and telling us that we need to make a royal road for ignorant disambiguators won't make them go away. —David Eppstein (talk) 03:22, 14 February 2013 (UTC)

In that case, here is a list of all disambiguation pages with incoming links. Please go through it, find those pages that are mathdabs, and fix those incoming links so that they point to the appropriate article. You might notice that this thread began with me coming here to ask for exactly this sort of expert assistance. Do this, and you'll never need to deal with us ignorant disambiguators. bd2412 T 03:52, 14 February 2013 (UTC)

You seem to think that everything on Wikipedia should be basically understandable by anyone able to read basic English, and that such persons should therefore be editing every article. Fourth graders should edit articles on the Langlands program, why not? Fortunately, that is not the perspective of most editors, who must maintain constant vigil against the barbarians always ready to destroy what we have made. Wikipedia is an encyclopedia, not a primary school. Sławomir Biały (talk) 02:33, 14 February 2013 (UTC)

I do think that everything on Wikipedia should at least have an introduction or summation that is basically understandable by anyone able to read basic English. Whether I think people with that level of skill should be editing articles is irrelevant. They are able to, and they do so. Of course, you wouldn't need to defend articles against the ministrations of disambiguators if your project would fix those disambiguation links so that they point to the right page. bd2412 T 03:14, 14 February 2013 (UTC)

I'm sorry, but in mathematics there are some topics that just cannot be explained to someone with only a basic knowledge. At least, there are topics that no one in the history of the subject has managed to be able to do so. That's just a fact. Now I'm sure you've seen topics that you felt were quite abstract, yet presented in a very clear way. But mathematics is the science of abstraction: everything we do is abstract. You might find this notion personally objectionable, but that isn't really up for debate. It's actually quite rare that mathematicians can find a good way to explain what it is that they do. When they are successful, they write a book about it, win awards, and make a lot of money. The basic standard of mathematics exposition for advanced topics are the "What is..." column of the AMS Notices and the "Princeton Companion to Mathematics". However, these generally assume mathematical literacy at a postgraduate level. If you know of any other sources of mathematical exposition, we would love to hear them. But, yeah, we all know how biology articles are easy to read because every word means something, but mathematics articles are impossible to read because every linked word is just another abstraction. Sławomir Biały (talk) 03:58, 14 February 2013 (UTC)

None of this will be of any concern if this project will undertake to fix links currently pointing to disambiguation pages so that they instead point to the article meant by the context of the link. bd2412 T 04:09, 14 February 2013 (UTC)

This conversation is getting a bit sidetracked, but I'd like to thank the disambiguators for their hard work. It seems to me they are doing their best to make sense of articles that are in pretty sad states to begin with; so thank you. If there is this much resistance from every wikiproject, it's a wonder they get anything done at all! Mark M (talk) 07:25, 14 February 2013 (UTC)

I think we can all agree that it would be better if mathematicians resolved more disambiguations. The problem is: Most people have better things to do than clicking on all links in an article they are working on to see if there are disambiguation pages among the links. And working on the disambiguation project's list is certainly not everybody's idea of fun, especially when there is no guarantee that it contains mathematical articles.

Two things immediately come to mind that we could do:

• The disambiguation project could inform the maths project when a maths dab page moves to a prominent position. Then editors who have a clear idea what they are doing can work on the problem.
• Members of the mathematics project should consider installing User:Anomie/linkclassifier. I have had it for a while, and I wouldn't want to do without it any more. Links to pages that are at AfD or have a CSD tag or prod appear in reddish colours. Redirects appear in green. And, importantly in this context, links to disambiguation pages have a yellow background. Editors using this script will recognise each link that requires disambiguation immediately when reading or working on an article. Hans Adler 05:38, 13 February 2013 (UTC)

IMO, matrix algebra should restored to a redirect to Matrix ring (its state of the beginning of 2005), and a hatnote {{Redirect}} should be added in the target.  Done D.Lazard (talk) 05:58, 13 February 2013 (UTC)

Substantiation? A confusion between the matrix algebra M_n(F ) and a matrix algebra (certain its subalgebra or, in other words, a faithful representation of some associative algebra in Fⁿ) does exist, isn’t it? Incnis Mrsi (talk) 10:57, 13 February 2013 (UTC)

Surely, such a confusion may exist. It must be resolved in matrix ring or in an article about matrix algebras, whichever name it should have. The dab page was not related with that confusion, but with the confusion between the subarea of mathematics and the algebraic structure(s). By the way, I have linked the hatnote in matrix ring to matrix (mathematics); another good choice would be linear algebra. I will add it to the hatnote. D.Lazard (talk) 11:23, 13 February 2013 (UTC)

Thanks very much for that pointer to linkclassifier. That's very useful for someone who just wants to check for problems in pages they have some interest in, I think it should be in the standard toolbox for anyone who is interested in properly cleaning up articles. Dmcq (talk) 09:05, 13 February 2013 (UTC)

Agreed; thanks for the link! -- Avi (talk) 17:11, 14 February 2013 (UTC)

I agree with the above comments, that neither Matrix algebra nor Adjoint representation should be disambiguation pages, per WP:TWODABS. I think Adjoint representation of a Lie group should be moved to Adjoint representation, and Matrix ring moved to Matrix algebra. I suppose we will need to start Requested Moves to accomplish such moves? Mark M (talk) 09:31, 13 February 2013 (UTC)

If you like to move “Adjoint representation of a Lie group” back to the short ambiguous title, but are unable to substantiate, then your RM will unlikely have high chances to succeed. Incnis Mrsi (talk) 10:57, 13 February 2013 (UTC)

Incnis, I cited the guideline WP:TWODABS, which clearly supports the case for a move. In fact, the concepts are so closely related, WP:CONCEPTDAB probably applies as well. Just because it's a technically ambiguous term doesn't mean we need to force the reader through a disambiguation page. Mark M (talk) 12:19, 13 February 2013 (UTC)

See above. Any possibility of de-disambiguating Adjoint representation implies that the term has a WP:Primary topic, not only “the topic that they are most likely searching for”. Arguments for the former? Incnis Mrsi (talk) 16:41, 13 February 2013 (UTC)

Incnis, I think you are getting hung up on small differences. The adjoint representation of a Lie group and of a Lie algebra are so closely related that textbooks sometimes cover them both in the same chapter. Consider Representation (mathematics). It's not a disambiguation page, even though there are several meanings. Similarly Adjoint representation should not be a disambiguation page. Mark M (talk) 16:55, 13 February 2013 (UTC)

I agree with Mark. It is not the case that a term with more than one meaning must automatically point to a disambiguation page. If it was, then Apple and Blackberry and Avatar would be all be disambiguation pages, which they are not. Those pages relate to the primary meaning of the term, and each has a hatnote providing several other possibilities. The question in terms of deciding whether to have a disambiguation page at all, and whether to have it at the base page name or at a "Foo (disambiguation)" name, must always, always be: what will most efficiently bring readers to the topic that they are most likely searching for. For a title with only two topics, the most efficient path will virtually always be to have the more prominent title at that page (or redirecting to that page), and to have a hatnote indicating the second-best option. bd2412 T 13:15, 13 February 2013 (UTC)

I would have thought that Matrix algebra should point to something like matrix multiplication -- ie how to do algebra with matrices, as the most entry-level and probably most commonly searched-for meaning of the term for the general reader. Of course a matrix algebra is a different thing, as is the notion of matrix algebras in general, but I suspect they may not be the most commonly sought (or even the most commonly linked) meanings of the term. Jheald (talk) 13:23, 13 February 2013 (UTC)

Hmm.. while I see your point, I'm not really convinced. The term "Matrix algebra" is definitely used in the sense of the article Matrix ring. Perhaps some people readers might use the term "Matrix algebra" to mean "algebra with matrices".. but matrix multiplication is linked from the first sentence of Matrix ring anyway, plus there is a hatnote further explaining the situation. So while you might be right, without convincing evidence that this is causing a problem, I don't see a reason to move. Also, the two concepts you are contrasting are in fact very closely related, of course. Mark M (talk) 14:14, 13 February 2013 (UTC)

I agree with Mark. I had a quick look on the links to matrix algebra. Most of them are well redirected to matrix ring. The other fall in two categories: in some mathematician biographies, "matrix algebra" could better be rewritten as "matrix algebra". In any case, for such non technical articles, such links seem rarely followed. The other category of links is related to software libraries; as, from a computing point of view, "matrix algebra" is not really different of "linear algebra", these links would be advantageously replaced by linear algebra. Thus, this a clear application of what BD2412 wrote above: "particularly if only one page contains an exact match to the title"; the only page containing an explicit definition of matrix algebra (in boldface) is matrix ring. D.Lazard (talk) 14:42, 13 February 2013 (UTC)

Looking at the discussion, I'm wondering about the "disambiguation" in the matrix ring article itself:

"Matrix algebra" redirects here. For the subarea of mathematics, see Matrix (mathematics) and Linear algebra.

If find that line rather odd and irritating. What exactly is the "subarea of mathematics"? And are we to believe that matrix ring itself is not mathematics (as the formulation may suggest to a (naive) reader)? As far as the general problem is concerned I agree with Sławomir Biały, the style guide should not trump content. If for some reason no really appropriate article as a link target exists (yet), the the link target should remain the disambiguation page (for now). Enforcing a different not really appropriate link target just to comply the style guide is a no-go from my perspective.--Kmhkmh (talk) 15:17, 13 February 2013 (UTC)

I have rephrased the hatnote as follows:

This page is about a type of algebraic object. For algebraic operations on matrices see also Matrix (mathematics) and Linear algebra.

I had to do it by hand because we have the unusual situation that the alternative use is covered by the present article as well, just not at a level of abstraction appropriate for a typical reader looking for "matrix algebra" as a subfield of algebra. So I used "see also". Hans Adler 23:16, 14 February 2013 (UTC)

I do not agree: the new hatnote does not mean anything for readers that do not come to this article through the redirect "matrix algebra". Thus "redirect here" must be restored. I suggest: "Matrix algebra redirects here. For the algebraic theory of matrices see ..." I have not the time now, but unless somebody finds a better wording, I'll do this change later and transfer this discussion on the right talk page. D.Lazard (talk) 07:19, 15 February 2013 (UTC)

I have changed the hatnote of Matrix ring as announced. I have also copied into talk:matrix ring those of the above posts that concern this article. It you continue this part of the discussion, please do it there. D.Lazard (talk) 14:29, 15 February 2013 (UTC)

I had simply forgotten the first sentence and I think it would have been enough to add it. Still, your version is shorter and it works for me. Thanks. Hans Adler 18:15, 15 February 2013 (UTC)

Requested move

Since this discussion is getting a little disorganized, I started a requested move here, to move Adjoint representation of a Lie group -> Adjoint representation. So please comment there. Thanks, Mark M (talk) 17:19, 13 February 2013 (UTC)

Finitely generated

FWIW I just disambiguated a bunch of links in Finitely generated (disambiguation). Doing so involved creating a new stub, finitely generated object — please improve it. And I'd like to thank Hans Adler for suggesting User:Anomie/linkclassifier — I installed it because of this discussion, and find it very helpful not just for spotting ambiguous links but also unnecessary redirects. —David Eppstein (talk) 19:06, 14 February 2013 (UTC)

Requested move part 2

There is also a requested move for Adjoint endomorphism → Adjoint representation see Talk:Adjoint endomorphism#Requested move. Its been open a while now but there is not really enough discussion to establish a consensus and close it.--Salix (talk): 20:44, 16 February 2013 (UTC)

Why is it physics?

New article Reflection Principle (Wiener Process) "is within the scope of WikiProject Physics" and "needs attention from an expert in Physics"; why? Boris Tsirelson (talk) 17:03, 14 February 2013 (UTC)

For the first, any WikiProject may lay "claim" to any article it wants to, so I don't see that it matters. (Though perhaps this is just someone's confusion about "Brownian motion".) For the second, probably you should ask User:Freebirds who is the one who tagged it. --JBL (talk) 18:45, 14 February 2013 (UTC)

I tagged it as requiring an expert in math, and gave it a math category. It needs some words, not just the symbols, though. — Arthur Rubin (talk) 19:39, 14 February 2013 (UTC)

Yes. Also it could be added to the mini-disambig (or how to call it?) in the beginning of "Reflection principle". Boris Tsirelson (talk) 20:07, 14 February 2013 (UTC)

It's usually called a hatnote, but that one looks crowded enough that it should probably be turned into a proper disambig. —David Eppstein (talk) 20:47, 14 February 2013 (UTC)

In response to the original question: Physicists might know something about Wiener processes too. (But of course they can't be trusted...) I do think that a better solution for the encyclopedia would be to fix the article, rather than quibbling about which project was notified and adding templates and then arguing about whether those templates were applied in the correct bureaucratic fashion. But of course, it's always easier to talk about work than it is to do work, and it generally pays better too. Sławomir Biały (talk) 23:04, 14 February 2013 (UTC)

You are right: I am lazy :-) Boris Tsirelson (talk) 07:37, 15 February 2013 (UTC)

I speak for myself as well... Sławomir Biały (talk) 23:52, 15 February 2013 (UTC)

Arthur, don't forget to add a reason for your expert tag. RockMagnetist (talk) 22:25, 14 February 2013 (UTC)

I dove in and edited the article a bit. I tried to make the lead a bit more intuitive, added an illustration, added words to explain a little the notation and equations, added wiki links and a couple of references verifying new assertions. I am not an expert, and worryingly for Sławomir, I am a physicist, so feel free correct anything I mucked up. --Mark viking (talk) 23:07, 15 February 2013 (UTC)

Negation (algebra)

I accidentally discovered this "article" which strays into the topic of additive inverse, if not to say that it is a WP:POV fork. There are few inbound links and I could undertake my own corrective actions. But I am not familiar with the terminology enough to decide either “negation (algebra)” may (and should) redirect to “additive inverse”, or some more elaborate solution is preferred. For example, negation in a boolean algebra (structure) is namely a negation, not the additive inverse. Incnis Mrsi (talk) 08:40, 9 February 2013 (UTC)

Negation is the operation that takes an element to its additive inverse.. so I agree, I think there should be only one article (with "negation" defined in the "additive inverse" article). I'm usually in favour of merging articles, given the chance. :-) Mark M (talk) 09:18, 9 February 2013 (UTC)

That's a very elementary article, but that seems appropriate for the topic. Merging the two while preserving most of the content seems the best solution, though integrating the elementary treatment with a modern mathematical one could be tricky. Hans Adler 09:30, 9 February 2013 (UTC)

There is also negative number. Merging Negation (algebra) into it may be more appropriate with the levels of the articles. In any case, this would explain the etymology (making negative) and the reason to have these two meanings in mathematics. Independently of any merging, I suggest to rename Negation (algebra) as Negation (number), because, I do not believe that "negation" is used for other additive inverses than numbers, boolean rings and boolean algebras. D.Lazard (talk) 09:57, 9 February 2013 (UTC)

IMHO there is no need to create yet another clumsy title. I could solve all content problems myself without deliberations, moving each chuck of text to an appropriate destination. I am interested, mainly, in opinions of native speakers what we should do with the title “negation (algebra)”: redirect it to “additive inverse”, redirect to negation (disambiguation), or make a stand-alone dab page? What is the primary topic of “negation (algebra)”? Incnis Mrsi (talk) 10:54, 9 February 2013 (UTC)

Just saw this. I notice you didn't list "delete it" as an option. I think that should at least be considered. Not every search term has to have a target. --Trovatore (talk) 08:06, 18 February 2013 (UTC)

See also this discussion from a few years ago. And the word "negation" is used with respect to things that aren't necessarily "numbers".. for example the more abstract setting of rings and algebras (you could negate the complex number i, but you wouldn't call -i a negative number). This would be an argument against redirecting to negative number. The term "Negation (algebra)" isn't going to be a popular search term anyway, so I think there would be no harm in merging it into the article about the abstract concept of additive inverse. Mark M (talk) 11:34, 9 February 2013 (UTC)

It was informative to reveal some obscure discussion in 2010 as the origin of the problem, but you apparently do not read what I write. I say in the third time: there is no problem to decide to where the content should be transferred (you may describe it with “to merge” verb of else). There is a problem about the title. Is the alternative meaning from boolean algebras and similar structures notable enough? If it is, then a disambiguation page, a disambiguation redirect, or a {{redirect}} hatnote (as the last resort) are appropriate. If it is not, then it has just to be redirected to “additive inverse”, it is obvious and shall not be repeated several times. Incnis Mrsi (talk) 12:48, 9 February 2013 (UTC)

You appear to be concerned about the title "additive inverse", and that most people don't care about this more abstract and encompassing concept.. and I agree. My point is that there is already a disambiguation page at Negation (disambiguation). In the event of a merge, this disambiguation page should obviously be modified. Most people are probably looking for content found in either the article Negative numbers, or even Plus and minus signs, so those should be linked from Negation (disambiguation). But I don't think there should be an article called Negation (algebra).. so the incoming links to that article should be sent elsewhere, and the content merged into additive inverse. There is nothing currently in the Negation (algebra) article that isn't easily available in other better written articles. So I don't follow your question about notability.. nobody's going to search for "Negation (algebra)", they will search for "Negation". So we just have to make sure they are directed to the right place from Negation. Right? In other words, it doesn't matter what the primary topic of "Negation (algebra)" is, because people aren't likely to search for it. Mark M (talk) 13:19, 9 February 2013 (UTC)

Proof of logical inferences

Would there be any objection to removing all those so-called "proofs" except possibly those by detailed truth table. One of the "proofs" is here, as noted in the section above. Reasons for deletion include WP:OR (not helped by WP:CALC), and the fact that a "proof" of a rule of inference has to be in some formal system, and that system is not named, and is arbitrary. I suspect most of the above-referenced user's edits are mathematically wrong. — Arthur Rubin (talk) 08:01, 18 February 2013 (UTC)

The varying formal systems are more curious to me. There was a "proof" of modus ponens via the disjunctive syllogism, and then a "proof" of disjunctive syllogism via modus ponens. I am not worried about these being original, but without some text in the articles to give their motivation it is not clear why they are there at all. The main place where one has to "prove" inference rules is in verifying that some class of structures preserves them, e.g. to show that all the classical inference rules are valid in an arbitrary Boolean algebra. But then, as you say, there is a clear set of background axioms - the axioms of the algebra - that are used in the proof. Unless there is a clear reason we can articulate for including the "proofs" in the articles, I am fine with removing them. — Carl (CBM · talk) 13:17, 18 February 2013 (UTC)

"summation theory" redirected

I found a reference to summation theory in an article and linked to it. It was a red link. I redirected it to divergent series. Are there opinions of the appropriateness of that? Michael Hardy (talk) 17:16, 18 February 2013 (UTC)

It seems very reasonable to me, in the sense that the divergent series article is basically a definition followed by a detailed exposition of summability methods. In fact Summability and Summability methods already redirect there. There is a Category:Summability methods category which has no main article. If such a main article ever gets created, that would be the best target; until then, your redirect seems like the best solution. --Mark viking (talk) 19:12, 18 February 2013 (UTC)

It seems that that "main article" already exists and it's called divergent series. It the main article ought to be called summability methods or the like, then that should be done with the "move" button, not by creating a new article. But I wondered if there might also be some _other_ topic also called "summation theory", to which the article that used that term was referring. Michael Hardy (talk) 15:38, 19 February 2013 (UTC)

Looking at what links to the summation theory redirect page, only this page and Gunnar Kangro link there. In the Gunnar Kangro article summation theory is used in the lead, but summation methods is used in the research section; my understanding is that these two terms were meant to be synonyms. Summation (disambiguation) could refer to math sums, neuroscience, or law; there could conceivably be theories of the other two. --Mark viking (talk) 17:51, 19 February 2013 (UTC)

Linearly ordering the mathematics articles

A desirable property of mathematics articles would be that the the links in the head of articles describing a topic point to simpler topics. That won't of course always be the case, for instance one would also say where something is used. However I was wondering if there was a tool to automatically give a 'depth' order to the articles so most of the references at the tops of articles pointed to 'earlier' articles whether that might help with finding and fixing usability and circularity problems.

The sort of thing I was thinking of which mightn't take too large an effort would go something like this: first collect the links in each article and the order they first appear in them so the ones at the start can be given more importance. Then one would try to optimise a total order of the articles to minimise the cost of links pointing the wrong way. This would then enable one to do things like list articles with the links in the top quarter of their text which point to deeper articles. I guess there might also be room for other useful analysis if the ratings of the articles were also associated with them.

Perhaps something like this could make the business of determining the level the lead and start of articles should be aiming at a bit more objective and make it easier to fix some of the recurring problems people have with following the links and just getting to more difficult topics. Dmcq (talk) 10:49, 19 February 2013 (UTC)

I don't think they should necessarily point to simpler topics. They should (usually) point to more general topics (but only about one step more general; for example, you wouldn't like directly to mathematics from the lead of Stone–Čech compactification, but rather "one step more general" to general topology). The more general ones also tend to have simpler leads, but that's just a correlation. --Trovatore (talk) 11:05, 19 February 2013 (UTC)

That's interesting - so links that point a long distance downwards could also be problematic. Dmcq (talk) 12:05, 19 February 2013 (UTC)

I suppose they could, but I haven't noticed it being as much of a problem. I mean, sure, it would be really weird to link Stone–Čech compactification from the lead section of mathematics, but who would be tempted to do that? Whereas links to over-general articles is something I see regularly (not just in mathematics articles). --Trovatore (talk) 03:00, 20 February 2013 (UTC)

Oh, maybe more to the point: There are two issues that need to be distinguished — what gets linked, and what gets mentioned. You probably wouldn't link the SCC from the lead of mathematics because you probably wouldn't mention it there. But if for some reason you did mention it, you should absolutely link it.

On the other hand, it's quite possible the SCC article will mention the word "mathematics" — but that mention should not be linked, because someone reading about something as detailed as the SCC is not particularly likely to suddenly want to see the top-level article on mathematics. Is my distinction clear? My reasoning? --Trovatore (talk) 03:11, 20 February 2013 (UTC)

I guess you meant a partial ordering, though. Linearly ordering mathematics is a mistake that only school curricula are allowed to make :) Rschwieb (talk) 14:55, 19 February 2013 (UTC)

I was only linearly ordering for the purpose of making the business easier to deal with, though that does prompt the idea of if one assigned real numbers rather than integers one could group a wide branching part all close together, that sounds like an interesting problem of what rationale one would use for that. Dmcq (talk) 17:03, 19 February 2013 (UTC)

A directed graph of topics already exists in the form of the categories for an article. Looking at the categories of an article often leads to more general topics and their associated main articles, which can have simpler expositions. I use categories any time I want to get my bearings and "back up a step". It also seems a convention to place a little context in the lead sentence of an article, e.g., "In the mathematical discipline of general topology, Stone–Čech compactification...". But I don't think we should necessarily reproduce all the categories of an article in the lead. --Mark viking (talk) 18:05, 19 February 2013 (UTC)

I want something quite a bit finer than that, something that would for instance out of the articles about logarithms, exponentiation, the exponential function and various related topics indicate those terms in the lead of them which might need to be checked because they led to something more specialised or which wasn't normally introduced till later, or even things which are too simple at that level and one shouldn't be bothering with the article if one doesn't know them. Also to do this automatically on a large body of articles so problem articles can be spotted and prioritized. Unfortunately in the interest of rigor many articles, especially the less visited ones, use terms in the lead which one wouldn't normally come across until one were already quite familiar with the topic. Dmcq (talk) 18:19, 19 February 2013 (UTC)

Anyway if someone has a student who wants a data mining project this sounds like a simple one with possibilities for extension. Personally I've already got enough on my plate with two rather more complex ones of my own (not Wikipedia I'm afraid). Dmcq (talk) 19:35, 20 February 2013 (UTC)

Linking the orphaned Stanley symmetric function

The article Stanley symmetric function has been an orphan for pretty much all of its year and a half of life. I've finally linked it from symmetric polynomial, but if anyone else has ideas about what articles could link it (or for any improvements to the article itself), that would be helpful. Thanks. --JBL (talk) 03:50, 20 February 2013 (UTC)

Quasisymmetric_function also has the Stanley paper as a reference. It could be useful to link to Stanley symmetric function in the Applications section of that article. --Mark viking (talk) 03:59, 20 February 2013 (UTC)

Great, thanks! --JBL (talk) 18:40, 20 February 2013 (UTC)

Calculus and mathematical analysis

The first line of mathematical analysis is (with the link removed)

Mathematical analysis is a branch of pure mathematics that includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions

The first line of calculus is

Calculus (...) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series.

In other words we have two branches of mathematics that have essentially the same object of study. The relationship between these "branches" is not clearly explained an any of the articles. A merge of these two articles seems not a good solution and will certainly not get a consensus. Thus the articles have to be edited to clarify the situation. For the first lines, I suggest to replace "pure mathematics" by "mathematics" per WP:NPOV and to begin Calculus by

Calculus is the part of mathematical analysis that is usually taught in elementary courses of mathematics.

But my knowledge of the subtleties of English language and American educational system is not enough to be WP:BOLD and do this edit myself. Moreover, this change of the first line would imply to edit calculus in depth and this is outside my competences. D.Lazard (talk) 13:17, 20 February 2013 (UTC)

Good point. Analysis is part of applied math also! As far as the calculus page is concerned, the second paragraph of the lede states that "This subject is a major part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis." This seems clear enough. Tkuvho (talk) 13:22, 20 February 2013 (UTC)

I had a look on Mathematics Subject Classification. "Calculus" and "analysis" each appear in the titles of several two digits entries, but always with qualifiers. In section 97-Mathematics education, there is a section "analysis" (97Ixx) but no section calculus". Therefore, it is dubious to call them "branches of mathematics". Using "parts of mathematics" would be more accurate and more neutral point of view. D.Lazard (talk) 18:12, 20 February 2013 (UTC)

I see, I understand your concern now. Calculus is certainly not a branch of mathematics if by "mathematics" one means "modern research mathematics", which is basically the viewpoint of MSC. It is less clear to me that wiki pages should follow the MSC perspective. "Mathematics" in the lay sense of the term certainly includes calculus. Tkuvho (talk) 18:25, 20 February 2013 (UTC)

There is no question that calculus is mathematics. The question is, is it a "branch" of mathematics? It seems to me that it's part of the same branch as analysis, but it's not a subbranch of analysis, because that would imply that at some point it had branched away and started investigating its own concerns. The "living" part of the branch is what we now call analysis; calculus is the unchanging wood further towards the trunk. --Trovatore (talk) 20:36, 20 February 2013 (UTC)

I don't think this is a good idea. I would not say that calculus is a branch of mathematical analysis. For one, calculus was historically prior to mathematical analysis. It might be better to say that mathematical analysis started as an attempt to extend the methods of calculus, and to put those methods on a solid logical foundation. Anyway, regardless of which is a branch of which, I don't see that it helps readers to point that out in the first sentence. Someone who doesn't already know what "calculus" means is not going to know what "mathematical analysis" means. Sławomir Biały (talk) 13:38, 20 February 2013 (UTC)

In Category:Mathematical analysis, it is stated that

Analysis is a branch of mathematics that deals with real numbers and complex numbers and their functions. It has its beginnings in the rigorous formulation of calculus and it studies concepts such as continuity, integration and differentiability in general settings.

which seems to nicely summarize the relation between the two fields an d might serve as an alternative first sentence for the analysis article. For calculus, the first sentence is correct, but needlessly abstract. Anyone who wants to know what calculus is will not know what limits, derivative and integrals are. I'd rewrite the first paragraph as

Calculus is a branch of mathematics focused on the study of rates of change and accumulation of quantities, as represented by functions of variables such as time or space. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (rates of change), and integral calculus (accumulation), that are related by the fundamental theorem of calculus. Both branches make use of the fundamental notions of the limit and infinite series. Calculus has widespread uses in science, economics, and engineering and can solve many problems that algebra alone cannot. The word "calculus" comes from Latin (calculus) and means a small stone used for counting.

--Mark viking (talk) 17:27, 20 February 2013 (UTC)

Mark, I was thinking the same thing; your wording for the calculus intro is better than the one I had thought of, so I added it to the article (hope you don't mind). Mark M (talk) 17:55, 20 February 2013 (UTC)

The study of "area" should be mentioned at least with the same level of priority as "rate of change". I agree that the mention of limits is less essential in the lede, as they are a technical tool rather than a quintessential subject of calculus. Tkuvho (talk) 18:03, 20 February 2013 (UTC)

Thanks for reviewing my rewrite and including it in the Calculus article. I agree with Tkuvho that area (and slope, too) are good, concrete concepts that should be in the first paragraph. I have added the second sentence

Informally, the rate of change of a function f(x) at a point corresponds to the slope of the curve at that point and the accumulation of a function in an interval from a to b corresponds to the area between the curve and the x-axis in that interval.

The paragraph doesn't flow quite as well as before, but is perhaps more accessible. As always, please feel free to improve the prose. Thanks, --Mark viking (talk) 20:26, 20 February 2013 (UTC)

I've taken this bit out; I think "accumulation" is a better term than "area", just as "rates of change" is better than "slope". Perhaps further down in the introduction, but I think the second sentence is too early to have so many jargon words (point, slope, curve, interval, area, x-axis..). Mark M (talk) 20:53, 20 February 2013 (UTC)

I think this is a very nice intro. One thing it leaves out is convergence of sequences and series; this is both historically important to the development of calculus and a standard part of a complete high school or college calculus curriculum; is there a way to fit it in? --JBL (talk) 18:44, 20 February 2013 (UTC)

Agreed, convergence and sequences should be in there, too. I changed one of the sentences to read,

Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit.

--Mark viking (talk)

I still have some issues with the word "branch" as applied to calculus. I don't think it's a branch. Maybe "collection of techniques"? --Trovatore (talk) 20:37, 20 February 2013 (UTC)

I'm not wedded to "branch". Perhaps we could say "Calculus is traditionally divided into differential calculus (rates of change), and integral calculus (accumulation),..." and in the next sentence, " Both approaches make use of..." ? --Mark viking (talk) 20:48, 20 February 2013 (UTC)

I've removed the word "branch" from the opening sentence:

Calculus is a collection of mathematical techniques in the study of rates of change and accumulation of quantities.

I like the structure of the current opening paragraph; though maybe the clarity of the first sentence could be improved / simplified.. "study of rates of change" seems clumsy. Mark M (talk) 09:25, 21 February 2013 (UTC)

I'm quite happy with the current version of the lead, as edited most recently by David Eppstein. (I was also quite happy with Mark viking's original proposed version, but the current one is less wordy.) This is a substantial improvement over what was originally there. Sławomir Biały (talk) 22:11, 21 February 2013 (UTC)

Seismic inverse Q filtering

Would an expert please take a look at this new article. It is sourced to one book, which makes me think that the subject may not meet the notability requirements. Thanks.--ukexpat (talk) 20:26, 21 February 2013 (UTC)

Note: I am not an expert. The article looks somewhat promotional, but seems to have some good information, too. Inverse Q filtering has been around for some time; here is a 1987 article that might be the first to call it that, and there were isolated results earlier than that, as mentioned here. So I think "inverse Q filtering" is notable. But all articles I found (admittedly a quick search on GScholar) on "Seismic inverse Q filtering" involved Y. Wang, the author of the book, which raises the question of the existence of independent sources for this specialization. If the article was renamed to inverse Q filtering and some independent refs added, I think it could pass notability standards. --Mark viking (talk) 20:51, 21 February 2013 (UTC)

RFC on Tau

Someone has opened a new formal discussion on whether Tau, the alternative circle constant, is notable enough for its own article. The link is

User_talk:Tazerdadog/Tau_(Proposed_mathematical_constant)#RFC:Article_Notability

--JohnBlackburne^words_deeds 15:39, 22 February 2013 (UTC)

Algebra

I have edited algebra to clarify the function of this article (WP:DABCONCEPT article and article about a mathematics area). I have also transformed algebra (disambiguation) into a redirect, moved History of elementary algebra to history of algebra, and adapted the first lines of Elementary algebra and abstract algebra. The main parts of my edits are:

• A complete rewriting of the lead to make it clearly a WP:DABCONCEPT
• Inserting a new section "Algebra as branch of mathematics" to explain what is algebra and how the answer to this question has evolved.
• Splitting the history section into "prehistory" and "history".

As these edits are very far to be minor and this article is a vital one, some reviews of my edits would be helpful.

Moreover this article needs some more work implying some decisions that may be controversial.

• The section history is a stub that should be expanded. My competence in history of mathematics is not enough to do it myself.
• There are sections dedicated on two among the sub-areas (elementary algebra and abstract algebra), and almost nothing a bout the remainder of algebra, outside links without explanation in the new lead and in the section Topics containing the word "algebra".

My opinion is that

• The lists in section Topics containing the word "algebra" should be moved at the end and transformed in a kind of section "See also". In particular, the list of the sub-areas should be completed by the sub-areas whose names do not contain the word "algebra".
• The sections "Elementary algebra" and "Abstract algebra" contain material that duplicate unnecessarily part of the content of the corresponding article and that have to be replaced by a description of what are these areas and how they interact with other sub-areas of algebra. For example, describing what is a polynomial is not useful here, but it is important to mention that polynomials are considered in elementary algebra, and that the theory of polynomials is much wider and has numerous aspects that are far to be elementary (Gröbner basis and Resultant, for example)
• The other main sub-areas of algebra (see the lists in the lead and in section "topic") need to appear at the same level as "Elementary algebra" and "Abstract algebra" (WP:NPOV) in sections describing their subject and their interrelations.

This is a wide program that I am unable to do alone. But I think that the vital importance of the article deserve it.

I'll copy this post in talk:algebra.

D.Lazard (talk) 16:23, 24 February 2013 (UTC)

I agree with the need for algebra to be more than a mere disambiguation page. One broader issue is the level of detail that the page should go into. For instance, we have overlapping lists of abstract algebraic systems in algebra, Outline of algebra, abstract algebra, algebraic structure, and the tree in Category:Algebra. It's a bit of a mess. People searching for the term 'algebra' could have experience levels ranging from the typical 10 year old to Nicholas Bourbaki.

My opinion is that the most elementary aspects of algebra should be first in the article, to direct the most inexperienced users to the appropriate articles without the distraction and intimidation of up-front indecipherable jargon. That would suggest putting the "Elementary algebra" section right after the lead or perhaps after the "Algebra as a branch of mathematics" section, if we can make that section less imposing.

For the more advanced subjects, we could make things less confusing by cutting down on the number of redundant articles noted above. My opinion is that it would be best to have a single list of abstract algebraic systems in either the algebra article of the some other article pointed to by the algebra article. I don't think it is a problem for duplication of concepts like polynomials in the elementary and advanced, sections, however. Such objects are treated differently in the two different domains.

For history, it would probably be best to keep this as a minimum in the algebra article, just enought to provide a context for the more specialized articles like History of algebra and Timeline of algebra. Should there be a list of prominent algebraists in the article?--Mark viking (talk) 21:51, 24 February 2013 (UTC)

Michael Sean Mahoney

Michael Sean Mahoney wrote a biography of Fermat that's quite popular by Scholar standards: 170 cites. On the other hand, his other work does not seem to be that influential. Should we have a biopage for him? Tkuvho (talk) 14:35, 13 February 2013 (UTC)

Not unless there are secondary reliable sources writing about him, including any peculiarities of his biography of Fermat. JRSpriggs (talk) 15:20, 13 February 2013 (UTC)

Note that in this case not only his notability as mathematician needs to be considered but that as a (popular science) writer as well. --Kmhkmh (talk) 16:04, 13 February 2013 (UTC)

He was actually a historian, not a mathematician (nor a popular science writer). Actually there were many responses to his book, including one by Andre Weil. Weil didn't like the first edition. Mahoney seems to have taken into account some of Weils' criticisms in the second edition. Tkuvho (talk) 15:52, 18 February 2013 (UTC)

To say that Weil didn't like the 1973 book is a vast understatement. I came across Weil's review in the 1980s and was stunned by Weil's thorough thrashing of Mahoney's competence as a scholar. Perhaps Mahoney's disastrous book motivated Weil to tell the early history of number theory properly, as he did in his masterful Number Theory: An Approach Through History from Hammurapi to Legendre. — Myasuda (talk) 02:13, 21 February 2013 (UTC)

The review may have made a number of good points, but Weil's claim that as every mathematician knows, there has never been a "deutscher Mathematiker-Verein" seems overdone (apparently it should have been Vereinigung rather than Verein). Even in 1973, German was hardly a language that every mathematician needed (though certainly it was a useful one). --Trovatore (talk) 03:24, 21 February 2013 (UTC)

That particular comment of Weil's was one of the least consequential ones that I can recall from that review. Why did you bring up that particular one? — Myasuda (talk) 03:32, 21 February 2013 (UTC)

Because it was the one that most annoyed me. --Trovatore (talk) 03:35, 21 February 2013 (UTC)

Weil held Mahoney to a very high standard, perhaps appropriately so. Note that there were other reviews that were much calmer. Regardless of Weil's reaction, Mahoney's book has been influential in terms of scholar cites: 170 last time I checked (this went up to 173 in the last few days). There is little doubt that it is an influential book, even though it may have been flawed. Mahoney did a number of other notable things; was a Sloan fellow; etc. If somebody wishes to chip in at Michael S. Mahoney that would be fine. Tkuvho (talk) 21:37, 21 February 2013 (UTC)

I disagree with your comment that Weil was holding Mahoney to a very high standard. Based on Weil's very detailed and erudite review, one can easily see that Mahoney's book failed to meet a rather low standard of scholarship. Did you actually read more than the first page of Weil's review? — Myasuda (talk) 04:18, 22 February 2013 (UTC)

Hi User:Myasuda and thanks for your interest in this new page. I would like to comment that I also think Mahoney's book has its shortcomings, and obviously I have the highest esteem for Weil. Do you think this disqualifies Mahoney from having a bio page in wiki? The problem of historians of mathematics not being sufficiently familiar with the actual mathematics of their historical period is not an uncommon one. I did read Weil's review from beginning to end (and perhaps more than once). As I mentioned, there were other reviews that were far less critical. Tkuvho (talk) 09:33, 22 February 2013 (UTC)

Well, based solely off of Weil's analysis of Mahoney's Fermat book from 1973, I would not endorse Mahoney's bio page. I am not, however, familiar with Mahoney's other body of work. Koblitz's comments on page 92 of his autobiography Random Curves don't say much in Mahoney's favor (e.g., he speaks of Mahoney's "rather thin list of accomplishments"), other than he was popular with students. But Koblitz was also speaking about Mahoney regarding the time period leading up to his full tenure and not after that. Did any of Mahoney's other works on the history of mathematics receive a review in the Bulletin of the AMS (or the Notices)? I would find this informative. — Myasuda (talk) 14:22, 22 February 2013 (UTC)

I am not aware of reviews in Bulletin and Notices. This does not necessarily mean there were none. On the other hand, there were numerous other reviews. Some of them can be found on M. S. Mahoney. I don't think either Weil, Bulletin, or Notices should have the final word on whether a notable historian should have a bio page. Tkuvho (talk) 16:45, 25 February 2013 (UTC)

Form/structure/application of Template:Tensors

Not a burning issue, but input/feedback may be helpful at Template talk:Tensors if time/inclination allows. Thanks, M∧Ŝc²ħεИ_τlk 09:34, 25 February 2013 (UTC)

Update: I created a navbox version there, since some editors think that's the better form. M∧Ŝc²ħεИ_τlk 09:18, 26 February 2013 (UTC)

I'm going to change {{tensor}} to the navbox version - due to consensus and no objections for that. M∧Ŝc²ħεИ_τlk 21:14, 26 February 2013 (UTC)

mathematics: natural science?

This discussion is copied from Talk:History of science. I thought it might be of interest to WPM participants. Tkuvho (talk) 12:46, 26 February 2013 (UTC)

Sorry to barge in from the cold but there does not seem to be an entry for "mathematics" under the various sciences listed in the "natural science" section of History of science. Was this discussed in the past? Tkuvho (talk) 17:39, 25 February 2013 (UTC)

The explanation is simple: Mathematics is not listed as a science because it does not qualify as a science. The scientific method requires that hypothesis and predictions be tested to confirm correctness. This is not possible with mathematics as it is a form of logic (e.g. there is no means to independently test and verify that 1+1=2). Mathematics is instead one of the primary "languages" used by science. --Allen3 ^talk 19:01, 25 February 2013 (UTC)

Mathematics has always been considered marginal in definitions of the history of science. Here are two recent ones:

• Science comprises, first, the orderly and systematic comprehension, description and/or explanation of natural phenomena and, secondly, the [mathematical and logical] tools necessary for the undertaking. Marshal Clagett, Greek Science in Antiquity, (1955)

• Science is a systematic explanation of perceived or imaginary phenomena, or else is based on such an explanation. Mathematics finds a place in science only as one of the symbolical languages in which scientific explanations may be expressed. David Pingree, "Hellenophilia versus the History of Science," (1992)

--SteveMcCluskey (talk) 19:37, 25 February 2013 (UTC)

I believe Allen3 and SteveMcCluskey are using "science" as a shorthand for natural science. Agreed that mathematics is not a natural science, but let's not forget that there are other branches of science besides the natural sciences. Mathematics is in fact a formal science. Gandalf61 (talk) 13:21, 26 February 2013 (UTC)

It will be possible to find literature that says math is a science, and also possible to find literature that says it is not a science - both in very reliable sources. This is because there are so many different notions of what 'science' is, and also different notions of what 'mathematics' is. One nice explanation that I have seen is at [12]. — Carl (CBM · talk) 15:49, 26 February 2013 (UTC)

Thank you for this link, I enjoy it. Boris Tsirelson (talk) 13:47, 27 February 2013 (UTC)

There is some plausibility to the view that mathematics is a formal science, but ultimately it is too restrictive. Furthermore, such a view originates around the end of the 19th century. Up until that point everybody viewed mathematics as integral part of what was known as "natural philosophy". Whatever one's particular views may be on this, it seems an omission not to include mathematics in a summary of the natural sciences in the context of the history of science. If a few editors subscribe to this view, we could develop a paragraph for inclusion at history of science in the list of natural sciences. This does not contradict a possible interpretation of math as a formal science, but merely seeks to reflect the full spectrum of possibilities. Tkuvho (talk) 15:57, 26 February 2013 (UTC)

I'm not at all sure that is correct. For instance Newton's Principia was the mathematical principles of natural philosophy, it didn't treat maths as part of the subject matter of natural philosophy but something outside it. I think even in Aristotle's time it had divided into what we would consider pure and applied maths where he had maths mixed with the sciences but others would have classed it more in line with something like music. Dmcq (talk) 00:52, 27 February 2013 (UTC)

It is an interesting philosophical question. But for the WP articles on natural science or history of natural science, the perhaps more relevant question is: Are there reliable sources, historical or otherwise, that assert that mathematics is a part of natural science? If so, then these could be used to add mathematics as another natural science to these articles. --Mark viking (talk) 01:11, 27 February 2013 (UTC)

Of course there are; see Naturalism in the Philosophy of Mathematics for example. — Carl (CBM · talk) 14:04, 27 February 2013 (UTC)

I hardly see that as supporting including mathematics in the history of science. To me having the whole question of whether there is any link proposed in such an abstract way indicates the exact opposite if anything is the practical fact . Dmcq (talk) 14:54, 27 February 2013 (UTC)

It is not a simple matter. It is very common for universities to classify the mathematics department under their "natural sciences" college. However, in truth mathematics and logic are not "under" natural or other sciences, they are "above" them. This is to say that math and logic are metatheory to the theories whose subject matter is physics, chemistry, biology, geology, etcetera. Philosophy and logic are also metatheory to the various theories of the arts. Every art and science, within the context of scholarly academia obey the laws of logic, and this includes mathematics. Greg Bard (talk) 01:21, 27 February 2013 (UTC)

It seems to me that the real question that we should focus on is not whether mathematics is a natural science, but what role the history of mathematics has in the history of science. This seems to be a glaring omission from the history of science article, which fails to mention prominently the history of mathematics. It scarcely needs to be emphasized that, until relatively recently, the history of mathematics and science were one and the same. I don't personally think that mathematics is a science, but failing to mention the role of mathematics in the history of science seems, well, a bit whiggish. Sławomir Biały (talk)

Mathematics is a science in the fullest sense. Indeed, elementary mathematics (such as arithmetic or geometry) is the most easily and thoroughly tested and confirmed of all sciences. Count out two marbles in one hand and three marbles in the other hand; then combine them (addition) on the table top; the result is five marbles as one can determine by counting. Thus 2+3=5 is empirically confirmed. JRSpriggs (talk) 07:26, 27 February 2013 (UTC)

That's not science, that just shows that maths has been used to model the real world. As said before it is a metatheory as far as science is concerned, just like the scientific method. Until recently only a few people contributed to both maths and science, Archimedes would I'd have thought of as being the earliest and 'The Method' which used the crossover idea of levers to do integration got lost. You don't really get anyone like that again till Newton but after that mathematical physics has contributed to both science and mathematics and maths and statistics have increasingly being used in all the sciences. How many people though have contributed both at the suck it up in a pipette tube level to chemistry or dissecting a frog level to biology and also to advancing maths? Dmcq (talk) 08:24, 27 February 2013 (UTC)

I think as has been said before one needs sources on the history of science that link maths in. And for weight it should appear in a reasonable proportion of histories. I don't think one can put more than a very basic amount in really from what I've seen. I think it is interesting how the belief that the world follows rules and the rules can be codified in mathematics arose so early with things like the belief the planets must move in circles, but that is not what the histories go on about. Dmcq (talk) 08:46, 27 February 2013 (UTC)

Note that we are discussing the article history of science, not "history of natural science". This article contains sections for "natural science" and other sciences such as social sciences. The subdivision is somewhat artificial and math seems to have been lost in the shuffle. I agree with the sentiment expressed by User:JRSpriggs and User:Sławomir Biały that we are dealing with a glaring omission as far as the article history of science is concerned. Tkuvho (talk) 13:58, 27 February 2013 (UTC)

The real question is what do histories of science say with any weight on the subject? Dmcq (talk) 14:57, 27 February 2013 (UTC)

History of science currently lists psychology as a science but not mathematics. This is hardly defensible. Tkuvho (talk) 16:27, 27 February 2013 (UTC)

Perhaps at this point substantive discussion should move back to Talk:History of science? --JBL (talk) 16:51, 27 February 2013 (UTC)

Requiring a ring to have unity by definition

Hi all,

I have started a poll on whether or not "Wikipedia" requires a ring to be unital at Talk:ring (mathematics). The feelings among algebra editors are that this is the way, but we can also use perspectives from other-type of editors. (I'm assuming this doesn't concern a generic Wikipedia editor.) -- Taku (talk) 19:08, 27 February 2013 (UTC)