Talk:History of the function concept

Leader needed

Wvbailey wrote the following on the Talk:Function (mathematics) after moving the history over from there, I've copied it verbatim so 'the article' at the end is the function article:- Dmcq (talk) 15:49, 31 July 2012 (UTC)

Per discussion above and apparent agreement I moved the history section to History of the function concept. Almost all the references and footnotes when with it. I suggest someone else write the summary, the effort needs new eyes, more a mathematician's eyes than a historian's. Here's a place to start: Historically there are a few deep trends. The first trend began with the intuitive notion of "mathematical formula" aka algebra (i.e. symbols as "unknowns") from this deriving analysis and the need to graph the behavior of a mathematical formula with respect to the "unknowns" when they're assigned values, then the idea of ordered pairs as derived from set theory, then the idea from computation of a "function box" and tabular lookup (e.g. Turing machines; I have not seen any earlier formal expression of a "state table" anywhere). With the Logicists we see the ernest attempt to axiomatize, formalize and locate the philosophical "essence" of mathematics, starting in ernest with Dedekind's The Nature and Meaning of Numbers, then Peano and Frege, culminating in Russell; here we see the formalization of the idea of a relation, and then its restricted form --the functional relation -- that dodges consistency violations [cf Hartley Rogers 1967]. These ideas were taken further by the set theorists (not clear where the bifurcation began and why) in an attempt to resolve problems with PM, in particular the axiom of reducibility. Since Bourbaki 1939 we've see almost every mathematician on the face of the earth creating their own symbolisms and formalisms and definitions.

The article's looking pretty thin now. Especially the references. BillWvbailey (talk) 15:09, 31 July 2012 (UTC)

Bourbaki reference

Why was the Bourbaki reference changed? At first sight it occurs to me that the reference was correct (at least almost): [1], [2] Isheden (talk) 15:35, 19 August 2012 (UTC)

Dedekind

It looks like this article could use some attention. I reorganized some material and added a paragraph on Dedekind. (The article strikes me as a bit unbalanced toward logic over mathematics.) Reader634 (talk) 09:51, 3 January 2014 (UTC)

Lede

I've added a short draft of a lede and additional material and references for functions in analysis.Reader634 (talk) 04:14, 5 January 2014 (UTC)

Thanks for all the work and the lead is the cherry on the top. It looks very good. Dmcq (talk) 09:32, 6 January 2014 (UTC)

Leibniz

Please check the edits here [3]. I find the earlier attribution to Leibniz troubling. The source doesn't mention a 1673 letter and it isn't clear whether Leibniz's use of the term "function" has anything to do with what we call a function. Better sources would be appreciated. - SindHind (talk) 10:32, 3 September 2015 (UTC)

Extremely difficult to extract any useful information from this article

The article is written so that each "development" is described in terms of the words that were used at that time.

If you came to this article — as I did — to find out who first invented the modern definition of function, and when this happened: good luck. This will not be easy. I found it impossible.

Yes, the Bourbaki definition of function is certainly logically equivalent to (or just is) the modern one.

But did anyone else come up with a logically equivalent definition before that? The article makes no effort to clarify that. Because of this, the article is for me a complete failure.Daqu (talk) 11:49, 7 June 2016 (UTC)

Sharaf al-Dīn al-Ṭūsī

hello there ive tried to add a very important piece of information about the early stages of the function concept but it was reverted. at the section of Functions before the 17th century, there are various, extended and well-documented sources about the work of Sharaf al-Dīn al-Ṭūsī of being the first to form the first concept of a function on his analysis of the equation x3+d=bx2.he was first to use an if term and the relation of the function result according to a given variable.if there are any mathematicians here that are familiar with his work i would be glad to get some feedback on this subject. — Preceding unsigned comment added by Roneln (talk • contribs) 15:22, 28 May 2018 (UTC)

@Roneln:. Thanks for coming to the talk page with this. Since I twice reverted your contribution, I want to make it very clear why I did so. This has little to do with the content you have tried to add and a lot to do with what is important in the way things are added to Wikipedia. Wikipedia is not a place where anyone can simply add their favorite piece of information ... if that were allowed we would be no better than an electronic bulletin board. In order to make Wikipedia a reliable source of information, everything that is added should come from a reliable secondary source (see WP:SOURCES). Part of the job of editors is to evaluate the sources that are provided to make sure that they are of high enough quality, and another role that editors play is making sure that a source actually says what is claimed. When these issues are questioned, the editors who are interested in the topic need to agree (by consensus) on the validity of the sources. Finding good sources takes some work and you shouldn't get discouraged if you missed the mark at first. If, as you say, there are good sources for the information you wish to add, then I, and I am sure other editors as well, will be only too glad to help in getting this statement into the article. --Bill Cherowitzo (talk) 21:33, 29 May 2018 (UTC)

@Wcherowi:.hi bill, thanks for your reply.in one of my edits I've added at least 3 related, reliable sources.i will add here a list of the best article sources I've used to add my statement.

1 1.2 2 3 4 and the last and a very important source from an online encyclopedia website called wikipedia :-) (Wikipedia) 5 --Roneln (talk) 22:05, 30 May 2018 (UTC)

As I said, finding good references is difficult. Your first two are high school course notes and the comment has been copied from somewhere without attribution. These are not scholarly works. The third[2] and sixth[5] are wikis, and no wiki, including Wikipedia, is considered a reliable source. The fourth[3] is a scholarly paper that, as far as I can tell, has never been published. The publishing process is important since that says that the material has been examined by other scholars and found to be valid. Unpublished work is lacking this validation and so, remains unreliable. This reference, as well as the book reference[4], do not support the claim you are trying to make. They are both arguing that he developed the derivative concept, not the function concept. This theory is disputed by several math historians (some of these are even referenced in the book quoted). Having said all of that, there is a possibility. The Wikipedia article cites a book by Katz and Barton. Katz is a well-known math historian. That book may contain the reference you are looking for. I do not have a copy and I can't tell from the Wikipedia article if they actually make this claim, but this would be a good place to try to find what you are looking for. --Bill Cherowitzo (talk) 23:30, 30 May 2018 (UTC)

@Wcherowi:.hi bill, so if a statement was approved once by Wikipedia community, it should be approved again? I mean if a piece of information is valid in one article it's not valid in another? shouldn't information validity be Global at the Wikipedia realm? --Roneln (talk) 19:39, 31 May 2018 (UTC)

This is not an issue of a citation being good in one place and not good in another. The problem is that I can not determine from what is written what the scope of the citation is. Does it apply to the entire paragraph, a portion of the paragraph or just to the claim that it is attached to? There are several claims made in this paragraph, so what the scope of the citation is is a crucial issue. Notice that in other paragraphs of that history section, each claim made has a citation attached, even if it is the same citation for several claims. Without actually looking at the source, I can't tell what is supported and what isn't. --Bill Cherowitzo (talk) 23:26, 31 May 2018 (UTC)

@Wcherowi: ok I've found the article here.this is the work that was used to cite the statement of sharaf al tusi to be the first to develop the function concept in the history of algebra article.it is very clear according to katz that tusi laid the first elements of a function but no one has ever continued his work.--Roneln (talk) 05:30, 1 June 2018 (UTC)

Thank you for that. I do not think that this article supports the claim that Tusi developed the function concept. There are three reasons that have led me to this conclusion. Firstly, when Katz refers to functions in relation to Tusi's work, he always puts the term in quotes. In this context the quotes would indicate that the term is not quite right, probably anachronistic. Later in the paper Katz says that the function concept is much more abstract than the simple solving of equations, which is what Tusi is doing. Finally, Katz's co-author, in yet another section of the paper, describes the history of the term "function" and how its meaning had changed over the years. Tusi is not mentioned here. I would say that the best statement that this source supports is that some rudimentary understanding of the function concept can be inferred from Tusi's work, but this was not expanded or built upon. --Bill Cherowitzo (talk) 18:07, 1 June 2018 (UTC)

@Wcherowi: of course,and i agree.since the work of sharaf al Tusi and another mathematician work named al Bruni the concept of the function has been developed immensely, by content and applications.katz does state that al sharaf used the 'function' because the term didnt exist back then and sharaf himself made a really brand new approach to this subjuct that he yet to even name it.but that doesnt mean one can passover his very important discovery and contribution, it is there, explained by process and proved by numbers.there is a clear use of a function form, in a very clear way. and to disregard it, in the history of function concept is really to disregard facts.i really think that if experienced mathematician made a clear recognition and analysis of this statement, comparing it to modern functions and function interface, he would agree you have to credit sharaf al din for his contribution.every concept starts with one point and than geeting developed.you asked me to bring you the data cited at the history of algebra article regarding Sharaf al din.if its not backed up,dont you think you should remove it from that article as well?Roneln (talk) 01:48, 2 June 2018 (UTC)

Function before 17th century

An ip user has recently edited the section "Function before 17th century". The user has completely removed info related Sharaf al-Din Tusi. This is distortion of the content https://en.m.wikipedia.org/wiki/Special:MobileDiff/1158207410 Hu741f4 (talk) 02:24, 18 June 2023 (UTC)