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user 19276
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
1
vote
Encyclopedia of Mathematics?(non-Alphabetical)
The Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen (20+ volumes) was organized from basic to advanced, as was its French translation. It's a bit dated though.
Nowaday …
- 31.5k
11
votes
Guidelines for writing proofs in math papers
As basic hygiene, please state theorems before, not after their proofs. I find nothing more annoying than the style where some seemingly random agitation is followed by
... and therefore we have p …
4
votes
mixing theorem with definition (definition with proof)
Dixmier always solves this as follows, e.g. in C*-algebras — surely one possible example of good exposition (E. C. Lance’s translator‘s preface: “With is clear and straightforward style, this remains …
- 31.5k
8
votes
The meaning and purpose of "canonical''
This seems broader than the other question which was interpreted mainly in the “category theory” sense (1.).
An early, maybe earliest,a case of sense (4.) “normal form” is Jacobi (1837) calling canoni …
- 31.5k
32
votes
Accepted
Famous cases of multiple papers by the same author published in same issue of same journal
Roger Howe famously filled an entire issue of Pacific Journal of Mathematics (volume 73, no.2, 1977) with 8 different papers. (Also, Euler...)
5
votes
Accepted
Papers whose title defines a new terminology
Jean-Pierre Serre: Gèbres, Enseign. Math. (2) 39 (1993), 33–85.
2
votes
Papers whose title defines a new terminology
Diener, Francine; Diener, Marc
Chasse au canard. I. Les canards. (French) [Duck hunt. I. The ducks]
Collect. Math. 32 (1981), no. 1, 37–74.
Benoît, Éric
Chasse au canard. II. Tunnels—entonnoirs—peig …
20
votes
Accepted
Historically, which came first: the Lie algebras or their classification?
The classification came first. As Killing says in his introduction (translation by Coleman (1989)):
For each $l$ there are four structures supplemented for $l = 2, 4, 6, 7, 8$ by exceptional simpl …
- 31.5k
4
votes
Problem based representation theory book
Kirillov’s Elements of the theory of representations is written in quite this spirit. From the original MR:
The book includes a large number of “exercises” (with hints for proving them), most of …
4
votes
Naming convention: Adjective for linear operators that are endomorphisms
L. Kadison (2012, preprint p. 8) uses endo-operator. (That’s “attributive”, but I guess “predicative” use could still work, in the same way MacLane says an arrow is epi.)
- 31.5k
4
votes
Mathematical words outside of mathematics
French intellectuals of a certain period made à la limite into a widespread idiom (or verbal tic) meaning, not just “borderline” or “in a pinch” as dictionaries say, but the taking of an argument to s …
2
votes
How are Poisson brackets and the variational principle related?
The direct connection between Poisson bracket and non-commutativity is pretty clear, at least if you agree that the (later introduced) Lie bracket $[X,Y]$ of vector fields measures the non-commutativi …
- 31.5k
27
votes
Nontrivially fillable gaps in published proofs of major theorems
If a 25-year interlude will do, there is
R. F. Coleman has sent me his preprint ["Manin's proof of the Mordell conjecture'', Preprint, 1988; per bibl.] concerning my proof of Mordell's conjecture …
4
votes
Which math paper maximizes the ratio (importance)/(length)?
Boyer’s vote, in A History of Mathematics (1968, p. 395):
in 1640, the young Pascal, then sixteen years old, published an Essay pour les coniques. This consisted of only a single printed page—but …
4
votes
How to buy Spivak's A Comprehensive Introduction to Differential Geometry
(Comment $\to$ answer at Willie Wong’s suggestion.)
The now-overhauled Publish or Perish web site, https://mathpop.com, lists nine of their books with links to Amazon pages. That includes Comprehensiv …
- 31.5k