User talk:DavidCBryant/Hubert Stanley Wall

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Thank you for the quick introduction to H.S. Wall's work on cf. One term while introducing the real numbers to calculus students I previewed the venture with some basic cfs like square roots of integers, noting the periodicity. This built on periodicity known for decimal development of fractions. This way I got an intermediary stage into the real realm before the great leap. The notion of an infinite process, necessary for sequences and series in calculus, gets a real boost in a practical numerical experimental way. I enjoyed the students reponse to this unusual route to the calculus routines; my supervisor confided that it looked like a better route than the propositional calculus effort he'd tried some years earlier. I'll have a look at Wall if I lay hands on a copy to note his peculiar style you note.Rgdboer 02:22, 8 March 2007 (UTC)

I was also thinking about starting a page on Wall. I took several courses from him at The University of Texas. I have copies of both books. Scott Tillinghast, Houston TX 20:31, 6 April 2007 (UTC)

Yes, Creative Mathematics is a problem book, to be worked out by the reader. It is very much in character that he did not refer to mathematicians. You may have noticed he thinks that "Bolzano-Weierstrass theorem" is a high-faluting name. He often had his own names for theorems. Many of his theorems and notations were non-standard. He was an ardent promotor of a socratic method of teaching. He wanted his students to develop their own proofs.

So I find it tedious to read other people's proofs and easier to understand my own. Scott Tillinghast, Houston TX 20:47, 6 April 2007 (UTC)

The Mathematics Genealogy shows that he earned his doctorate at the University of Wisconsin in 1927. His adviser was Edward Van Vleck. Listed are 66 students who earned their doctorates under him: 5 at Northwestern University and the others at The University of Texas. I recognize many names, mainly from the faculties of North Texas State University and the University of Houston. Scott Tillinghast, Houston TX 19:01, 7 April 2007 (UTC)

More information[edit]

Today I went to the Fondren Library (Rice University) to find out more about Wall, perhaps obituaries. The librarian found me an entry in Who Was Who in America, vol. V (1969-1973).

b 2 Dec 1902, near Rockwell City IA

d 12 Sept 1971 Austin, buried near Rockwell City IA

m Mary Kate Parker, 18 Oct 1947. I could swear I heard him call her Mary Kate and this source confirms it. I do not know how many children, but was a son who did not go into mathematics. I would like to verify Mrs. Wall's position in the Texas Attorney General's office.

B. A. 1924, M. A. 1924, Cornell; Ph. D. 1927, U of Wisconsin; D. Sc. 1970 (honorary)

post grad., advanced studies 1937-38

fellow, U Wisconsin, 1924-26; assistant 1926-27

Northwestern University: 1927-44 instructor, asst. prof, assoc. prof, prof.

Ill. Inst. Tech.: 1944-46 lecturer, then professor

UT Austin: 1949-70, hired as full professor

member, American Mathematical Society

The entry lists the 2 books we already know, and these are the only books listed in the Fondren Library catalog.

I searched the American Mathematical Monthly. They had announcements of deaths, but often a year late, little further information.

I looked at the AMS Bulletin, but found just mathematics, not biography. I did find an interesting paper on the Higman–Sims group, but that's my interest, not Wall's.

I am hoping to find a biographical article and a listing of his papers.

Scott Tillinghast, Houston TX 00:29, 11 April 2007 (UTC)

Website about Wall's papers[edit]

Guide to the H. S. Wall Papers, 1902, 1929-1974, 2006

Scott Tillinghast, Houston TX 06:11, 12 April 2007 (UTC)

Wall listed quite a number of his own papers in his book on continued fractions. It would not list anything after 1948, probably no papers on other fields. I never heard of any papers he published in the 1960's, but he did not encourage his students to read his papers. I had the impression that by 1961 he devoted his time to teaching. Scott Tillinghast, Houston TX 19:07, 12 April 2007 (UTC)

I talked to Charles Tucker, a professor at the University of Houston who got his doctorate under Wall. He suggested a journal issue that was dedicated to Wall. Rocky Mountain Journal of Mathematics, v 4, no 2, Spring 1974. Scott Tillinghast, Houston TX 18:37, 21 April 2007 (UTC)

I contacted Arizona State University, which publishes the Rocky Mountain Journal of Mathematics. The reply I got was that they do not now have the issue on stock, but in a few months they will be transcribing old issues. The Fondren Library's copy is in storage, like many old books, and I will have to arrange carefully for a time when I can go see it. Scott Tillinghast, Houston TX 03:13, 28 April 2007 (UTC)

Sketch for Article[edit]

The mathematician Hubert Stanley Wall was born Dec. 2, 1902 near Rockwell City IA, died Sept. 12, 1971 in Austin TX.

On Oct. 18, 1946, he married attorney Mary Kate Parker, who was a Texas Assistant Attorney General who specialized in election law.

He earned a B A degree at Cornell University in 1924, and then in 1927 a Ph D at the University of Wisconsin under Edward Van Vleck, whose advisor had been Felix Klein.

He taught at Northwestern University from 1927 through 1944. He taught at the Illinois Institute of Technology (Chicago) 1944-1946. From 1946 to 1970 he was a professor at The University of Texas at Austin.

At Northwestern University Wall supervised 5 students who earned Ph D degrees. At The University of Texas he supervised 61.

A Socratic method[edit]

Wall and several colleagues were champions of a Socratic method of teaching mathematics, often called the "Texas method." He was allied with Robert Lee Moore, Hyman J. Ettlinger, and others. They did not use textbooks and would present theorems for their students to prove. They expected students to devise their own proofs.

Until the late 1950's the University of Texas had separate departments of Pure Mathematics and Applied Mathematics. Even after they were united there was much factionalism. The pure mathematicians had offices and classrooms on the 3rd floor of Benedict Hall. Applied mathematicans were often called "the 2nd floor"; that was where the Department office was located.

Wall liked originality and was somewhat idiosyncratic about mathematics. For some reason, he did not care for measure theory and did not include in his courses, even though it is generally considered to be something every graduate student should know. He would offer his own variants of classical theorems. He had his own nicknames for several classical theorems. The "measles theorem" was a theorem, possibly due to Weierstrass, that a uniformly convergent sequence of continuous functions converges to a continuous function. He declared in a book of his that "Bolzano-Weierstrass Theorem" was too much of a mouthful.


Wall wrote two noteworthy books. His text on Continued Fractions was an important work on this subject, especially from the standpoint of complex analysis. He had written several important papers on continued fractions.

His Creative Mathematics was an exposition of his Socratic approach to mathematics. He claimed it could introduce an intelligent high school student to mathematics, although that has been a point of controversy. The book starts with an axiomatic development of the real numbers and develops real analysis. Theorems are all given as exercises for the reader.


Who's Who in America, vol. 5 (1969-1973)

Mathematical Genealogy

Scott Tillinghast, Houston TX (talk) 00:31, 12 August 2008 (UTC)

Wikipedia's Expert Peer Review process (or lack of such) for Science related articles[edit]

Hi - I posted the section with the same name on my talk page. Could you take part in discussion ? Thanks ARP Apovolot (talk) 20:16, 25 October 2008 (UTC)