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

1 vote
Accepted

Archive of the Work of J Sutherland Frame

The short answer is "no". Frame did interesting work, though usually outside the conceptual mainstream of representation theory. Some of his calculations of character tables (such as that of the …
Jim Humphreys's user avatar
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
18 votes

When and why did the postdoctoral position originate?

This is really a blog question, with no single answer. There are 150+ Ph.D. programs in mathematics in the U.S., plus various institutes. As noted already, there is no central planner. Before the …
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 …
22 votes
4 answers
4k views

How did "Ore's Conjecture" become a conjecture?

The narrow question here concerns the history of one development in group theory, but the broader context involves the sometimes loose use of the term "conjecture". This goes back to older work of …
Jim Humphreys's user avatar
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 …
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 …
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
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
3 votes
0 answers
172 views

Origin of the standard result on convex hull of weights of an irreducible finite dimensional...

What is the earliest published statement and proof of the well-known result: for a simple Lie algebra over $\mathbb{C}$ or other algebraically closed field of characteristic 0, the convex hull (in the …
Jim Humphreys's user avatar
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
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 …
6 votes
2 answers
1k views

Convention about "long" roots for simple Lie algebras of types ADE?

The classification of simple Lie algebras (over $\mathbb{C}$ or other sufficiently large field of characteristic 0) correlates these Lie algebras with the irreducible reduced root systems (in Bourbaki …
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
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 …

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