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These terms have become common in Lie theory and related algebraic geometry and combinatorics, as seen in many questions posted on MO, but it's unclear to me where they first came into use. Probably …

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 …

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 …

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 …

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 …

This question is prompted by a recent MO question on explicit computations of Weyl group invariants for certain exceptional simple Lie algebras: 37602. Like some others who started graduate study in …

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 …

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 …

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 …

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 …

The question involved here is natural and very classical, but I'm unsure what has been formally stated and proved in the literature. The only approach I know involves assembling facts that apparently …

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 …

The IMU acts as sponsor of the ICMs and maintains a fair amount of information at http://www.mathunion.org/ including a list of all past venues with online links from 1998 on (as you've already encoun …

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 …

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 …