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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.

26 votes

What is the oldest open math problem outside of number theory?

Stability of the Solar System ? (Question often attributed to Newton in Opticks, 1717 or 1730.) To further specify as requested by Timothy Chow, make it a few ($3\leqslant N\leqslant 8$) planets under …
LSpice's user avatar
  • 12.9k
11 votes

Pseudonyms of famous mathematicians

Thomas Young (of diffraction, elasticity, and Rosetta Stone fame) published mathematics as Emeritus Hydrophilus Apsophus Dytiscus Hemerobius A. B. C. D. E. F. G. H. S. B. L. Norbert Wiener publis …
Francois Ziegler's user avatar
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 …
Francois Ziegler's user avatar
12 votes

Autobiographies of mathematicians

19th century as requested: Charles Babbage, Passages from the life of a philosopher, 1864. George Biddell Airy, Autobiography of Sir George Biddell Airy, 1896. French scientists often wrote (and s …
Alexandre Eremenko's user avatar
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...)
Francois Ziegler's user avatar
5 votes

Mathematicians with both “very abstract” and “very applied” achievements

Mikhail L. Zeitlin, or Gel’fand-Zeitlin basis fame (1950), later switched to “game theory, the theory of automata, computer science, physiology, and mathematical methods of biology”.
Francois Ziegler's user avatar
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 …
Francois Ziegler's user avatar
5 votes

Mathematicians with both “very abstract” and “very applied” achievements

Just came across a page of 25+ of Mark Goresky’s Engineering publications.
Francois Ziegler's user avatar
7 votes

Interpretation of the action in classical mechanics

While the following may be less “physically” intuitive than the question intends, I liked it when I heard it. If you believe in the importance of Poisson brackets, it is natural to ask if they make th …
Francois Ziegler's user avatar
67 votes

Parodies of abstruse mathematical writing

Well there is C. E. Linderholm's Mathematics made difficult ("available on the internet")... Also, if I remember well, D. Nordon's Les mathématiques pures n'existent pas! has a pretty biting parody o …
Francois Ziegler's user avatar
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 …
Community's user avatar
  • 1
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 …
Francois Ziegler's user avatar
3 votes

Mathematicians with both “very abstract” and “very applied” achievements

Several answers (on Beurling, Gleason, Gröbner, Littlewood, Rankin, Robinson, Turing, Ulam, Whitney) suggest that applied work was often classified. I also heard about Vieta being his King’s cryptogra …
Francois Ziegler's user avatar
7 votes

Mathematicians with both “very abstract” and “very applied” achievements

Eduard Stiefel went from characteristic classes and Lie group representations and topology, to (early) numerical programming and computation of orbits for NASA.
Francois Ziegler's user avatar
17 votes

Mathematicians with both “very abstract” and “very applied” achievements

I have a friend to whom De Rham was famous for completely different reasons — as author of a “corner-cutting algorithm” used in Computer Aided Geometric Design (of car bodies).
Francois Ziegler's user avatar

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