User:DavidCBryant/Hubert Stanley Wall

Yesterday I got a copy of Creative Mathematics from the Denver Public Library, though the "Prospector" inter-library loan program. So far as I'm aware, Wall only wrote two books: Creative Mathematics and Continued Fractions.

I'd like to write a biographical article about Wall for Wikipedia. Unfortunately, information is hard to come by. I think he made notable contributions to mathematics, but since cf's are undeservedly obscure in modern math, secondary sources about Wall are scarce. Anyway, I'm using this sub-page to accumulate information about him, as I come across it. DavidCBryant 13:08, 21 January 2007 (UTC)

I got an e-mail from Scott Tillinghast today – he studied under Professor Wall at the University of Texas. Here's the e-mail message he sent.

Dear sir:

Today I found your page on Hubert Stanley Wall and posted a few comments. As a student of his, I would be interested in having a Wikipedia page on him. Today I posted my own biography. I referred to Moore and Wall - made a link to the page on Moore, could not do the same for Wall. I took more courses from Wall. I have an MA in mathematics from The University of Texas. My adviser was not Wall, but department head William Guy. I have checked out the Mathematical Genealogy, and many of Wall's students are familiar names to me. Some at the University of Houston, some at North Texas State University. I withdrew in 1976 from trying to be a professional mathematican, but have persued it as a hobby. My main interests are algebraic number theory and group theory. These were not Wall's fields, and I settled on them after getting my MA. I find from the social secrity death index that was b 2 Dec 1902, d Sept 1971 in Austin. I notice your interest in continued fractions. I have wondered whether the terms of the regular continued fraction for pi are unbounded, as for e. I think this is still an unsolved problem. Also whether pi is an S number. Pi is known not to be a Liouville number. I haven't found dates for Wall. I remember that he died about 1970, but could not find himin Find a Grave. His wife Mary Kate was a lawyer who worked for the Texas Attorney General. She may headed the department on election law. Yours truly,

Scott Tillinghast

So now I have a few more facts: H.S. Wall (12/02/1902 - 09/?/1971). And his wife was named Mary Kay. DavidCBryant 13:32, 7 April 2007 (UTC)

Contrasting styles

Wall's two books are both about mathematics, but they're very different in style and tone.

Continued Fractions is a typical textbook; a little light on diagrams, perhaps. The development is rigorous throughout, and quite formal. Citations are numerous – the Bibliography has 143 entries, and these are heavily referenced throughout the book. There is only one index, but the names of mathematicians are italicized in that index. I haven't verified this yet, but I suspect that every author in the Bibliography also appears in the index.

Creative Mathematics is written in a very different style. There are no citations, at all. There's no bibliography, and no index. In this book Wall relies on primitive notions of set theory, and presents all the ideas needed to describe the real numbers as a complete Archimedean field. But he doesn't call the set of "numbers" a field. He doesn't even call them "real" numbers. The development is axiomatic throughout, but more in the style of Euclid's Elements, and quite informal in places. He doesn't mention a single mathematician by name.

I have to return Creative Mathematics to the library this week, so I'd better get as much information out of it as I can right now. DavidCBryant 13:53, 1 March 2007 (UTC)

Here's the introduction (p. 3, unnumbered) that Wall wrote:

Mathematics is a creation of the mind. To begin with, there is a collection of things, which exist only in the mind, assumed to be distinguishable from one another; and then there is a collection of statements about these things, which are taken for granted. Starting with the assumed statements concerning these invented or imagined things, the mathematician discovers other statements, called theorems, and proves them as necessary consequences. This, in brief, is the pattern of mathematics. The mathematician is an artist whose medium is the mind and whose creations are ideas.