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History and philosophy of mathematics, biographies of mathematicians, mathematics education, recreational mathematics, communication of mathematics.

3 votes

Linear Algebra classic books

A more "modern" book than those already mentioned is the one by Paul Halmos here. This was first published in 1942 in the Annals of Math. Studies series, with a later edition in 1958; that edition …
Jim Humphreys's user avatar
12 votes
Accepted

Who originated the standard symbols for Lie groups GL, SL, SU, etc.?

It's hard to provide definitive confirmation of Weyl's role, but his 1939 book was highly influential in all further developments. It's important to realize that notation (and terminology) in mathe …
Jim Humphreys's user avatar
18 votes
Accepted

Why are they called Specht Modules?

The question is interesting though perhaps not strictly "research-level". Terminology in mathematics develops a bit haphazardly, and sometimes things get misleading names. In this case the work of …
Jim Humphreys's user avatar
7 votes
Accepted

Origin of the term "weight" in representation theory

Robert Bryant's comment motivates me to mention the "weighty" historical monograph Emergence of the Theory of Lie Groups (Springer, 2000) written by Thomas Hawkins. As usual with terminology such as …
Jim Humphreys's user avatar
3 votes

History of Jordan Canonical Form?

As I pointed out in my comment, there are too many questions listed here. Maybe I can clarify the term "Jordan-Chevalley decomposition" in the last one. Besides the arXiv post by Danielle Couty an …
Jim Humphreys's user avatar
5 votes

Origin of the theorem on the existence of the smallest field of definition of an affine variety

As far as I can see, Weil was indeed the main source for this viewpoint on fields of definition in algebraic geometry. However, it may be hard to pin down the specific result quoted here in his 1935 …
Jim Humphreys's user avatar
48 votes

Fraktur symbols for Lie algebras

Some of what's been said so far about the history makes good sense, but by no means all. Let me add my own perspective, for what it's worth. The font called Fraktur by LaTeX (also known as "gothic …
Jim Humphreys's user avatar
6 votes

What to do with antique math books?

Though I haven't dealt directly with them, I'm aware of another established company (in Ohio) which buys and sells advanced or rare books in mathematics: http://www.zubalbooks.com/in …
31 votes

How might M.C. Escher have designed his patterns?

The June/July 2010 issue of the AMS Notices here has a further article by Doris Schattschneider (a graduate school classmate of mine) on Coxeter and Escher. Doris has written extensively about Esche …
Jim Humphreys's user avatar
39 votes

Pseudonyms of famous mathematicians

Since some of those mentioned in other answers are among the living, let me also mention Victor Kac and his teacher Ernest Vinberg. They published a joint paper Spinors of 13-dimensional space in Ad …
5 votes

What are examples of mathematical concepts named after the wrong people? (Stigler's law)

Many of the examples mentioned go back to earlier centuries, when insulated national traditions and slow communications promoted mistaken labelling of results and concepts. A much more recent exampl …
11 votes

Is there an index for solutions to American Mathematical Monthly problems?

The American Mathematical Monthly goes back a long way, to a radically different era in mathematical life, and has never quite caught up with the present in terms of making information readily availab …
Jim Humphreys's user avatar
4 votes

A place to find original papers

Besides JSTOR, NUMDAM, and the like there is a German digital math archive GDZ at gdz.sub.uni-goettingen.de/. Some sources require access through a subscribing institution, by the way. There is n …
45 votes

Fields of mathematics that were dormant for a long time until someone revitalized them

The older theory of Hopf algebras, which grew out of algebraic topology as well as some purely algebraic theories, developed to the level of Sweedler's 1969 book and then became something of a backwat …
6 votes

Books about history of recent mathematics

History, biography, and memoir are quite different genres for mathematics. But as long as some of the latter are being recommended, I'd have to add G.H. Hardy's short memoir A Mathematician's Apolog …

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