# Talk:Harold Scott MacDonald Coxeter

## Untitled

I don't think it's reasonable to say that he was the 20th century's greatest geometer. He may have been the greatest in his particular flavor of geometry, but certainly people like Grothendieck and Thurston can be called geometers - it's like saying that Conway was the 20th century's greatest algebraist.130.238.5.5 22:23, 10 May 2005 (UTC)

## Pronunciation of name?

Hi. How did Coxeter prohop his name? I'm a native speaker of English and it's not clear even for me. Thanks for your help. 64.48.158.34 16:11, 20 May 2006 (UTC)

• I believe it is "cox-se-ter". Roger Hui 16:37, 20 May 2006 (UTC)
The biography King of Infinite Space (which I found rather dull) says that, as a firm vegetarian, he was a bit distressed to bear a name derived from cock-setter, an operator of cockfights. That's a hint to pronunciation. —Tamfang (talk) 19:23, 26 May 2009 (UTC)

## wittgenstein

The sentence that Coxeter studied philosophy of math under Wittgenstein is overstated. He went to Wittgenstein's seminar for a while, but got bored with it and stopped going. It should be replaced by saying what he really studied, with at most a passing reference to the Wittgenstein seminar. Siobhan Robers' book is a good source but I don't have it here. 76.197.56.242 (talk) 10:11, 10 August 2008 (UTC)

Roberts says:
Coxeter had enrolled in Wittgenstein's "Philosophy for Mathematicians" lecture for the 1933-34 year ... [Wittgenstein] deigned to lecture for only a chosen few ... The select group included Wittgenstein's five favourite students: Francis Skinner ... Louise Goodstein ... Margaret Masterman ... Alice Ambrose ... and Coxeter.
She also says that some of the lectures were held in Coxeter's sitting room. Wittgenstein's approach didn't appeal to Coxeter, but it doesn't sound like he "got bored". I think the sentence is accurate enough - what is missing is any mention of Coxeter's previous undergraduate and graduate studies at Trinity and his years at Princeon - I will expand the article when I have more time. Gandalf61 (talk) 12:03, 10 August 2008 (UTC)
Expansion will help. The trouble with the current version is it makes it sound as if philosophy was Coxeter's main field of study when it was just one seminar he attended. That's different from someone like Norbert Wiener, who (iirc) took a degree in philosophy but is mainly known for his work in mathematics. 76.197.56.242 (talk) 18:09, 10 August 2008 (UTC)
I've added a few sentences to put the Wittgenstein seminar in context. Gandalf61 (talk) 14:14, 11 August 2008 (UTC)

## Year of B.A. and Ph.D.

As it stands, the article doesn't agree with its sources. According to MacTutor History of Mathematics, he received his B.A. in 1929, but the article says 1928 right now. King of Infinite Space doesn't say outright when he got the degree, but says that he completed the Mathematical Tripos in 1928, went to Vienna during the summer and started on his Ph.D. work immediately thereafter. Roberts' sources for this are Trinity College records and the article "Geometry at Cambridge, 1863-1940" by June Barrow-Green and Jeremy J. Gray in Historia Mathematica, June 2006, 42. The article by Barrow-Green and Gray doesn't say anything about Coxeter's B.A., but dates his Ph.D. to 1932, at odds with the Wikipedia article and MacTutor, and also with Roberts, who says that he submitted his dissertation in 1931 (reference: the dissertation itself). There is of course the possibility that Coxeter completed the necessary work for the degrees in 1928 and 1931 but wasn't awarded the degrees until 1929 and 1932, but these sources don't say that outright. //Essin (talk) 23:50, 7 December 2008 (UTC)

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## Fallible

Mathematicians are human and subject to making mistakes, including Coxeter. One instance is cited at Bilinski dodecahedron. Apparently 48 years transpired before Branko Grünbaum noted the error.

Coxeter also claimed that the Lorentz group is isomorphic to the Möbius group in 1965:

• "The Lorentz group and the group of homographies", in L. G. Kovacs & B. H. Neumann (editors) Proceedings of the International Conference on The Theory of Groups held at Australian National University, Canberra, 10—20 August 1965, Gordon and Breach Science Publishers

While other sources also assert this isomorphism (as seen in the Möbius group article), the assertion would imply that there are parabolic transformations in the Lorentz group (Galilean transformations are parabolic but are not in the Lorentz group). The assertion is absurd. Various issues arise: the groups are in fact group actions, one on the plane the other on 4-space, and projective structure underlies the Möbius group but not the Lorentz group. Perpetuation of this error continues not only in this article but also in History of Lorentz transformations and other Encyclopedia articles. — Rgdboer (talk) 23:24, 16 August 2019 (UTC)

Can you fix this in whole or in part? Zaslav (talk) 03:23, 6 December 2021 (UTC)

One needs a WP:RS to counter the claim. Rgdboer (talk)

## Coxeter's integral

Is he the namesake of the integral

${\displaystyle \int \limits _{0}^{\pi /2}\arccos {\Biggl [}{\frac {\cos x}{1+2\cos x}}{\Biggl ]}dx={\frac {5\pi ^{2}}{24}},}$

known as Coxeter's integral? Nerd271 (talk) 13:55, 16 April 2020 (UTC)

## Title

Coxeter was always known professionally as "H.S.M. Coxeter", never "Harold Scott MacDonald Coxeter". According to WP naming principles, the article should have the name "H.S.M. Coxeter". Is there an objection to moving it? Zaslav (talk) 03:22, 6 December 2021 (UTC)