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Results tagged with big-list
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user 119114
Questions designed to generate a "big list" of certain results, examples, conjectures, etc. via many individual answers, each contributing one or a few instances. Such a question should typically be in Community Wiki mode (CW); after asking, please, flag for moderators attention requesting the question to be made CW.
0
votes
Fields of mathematics that were dormant for a long time until someone revitalized them
I believe that at the time that Stokes began studying fluid mechanics it was something of a dead subject and his contributions which we all know played a large part in reviving interest in it.
22
votes
Prominent non-mathematical work of mathematicians
I'm surprise no-one has mentioned Isaac Newton. He spent almost half his career outside academia fighting against forgery at the Royal Mint. He was also an MP and wrote a huge amount on biblical chr …
0
votes
Least collaborative mathematician
I've checked the complete list of works of Isaac Newton and it does not look as if he ever had a co-author for a single one of his works (I didn't check the entire thing though as it includes over 150 …
0
votes
Examples of simultaneous independent breakthroughs
Last month (September 2020) Chodosh and Li uploaded a preprint showing that a closed aspherical manifold of dimension $4$ or $5$ does not admit a Riemannian metric with positive scalar curvature.
On e …
0
votes
Modeling in pure math
Basically every branch of pure mathematics uses modelling of some kind, and the idea that pure mathematicians deal with 'exactness' and do not need to model or approximate the phenomena they are study …
1
vote
Quick proofs of hard theorems
See Perelman's proof of the soul theorem in differential geometry for an example.
3
votes
A book you would like to write
I would like to write 'the best book on differential geometry', a genuinely pedagogical, useful and visual introduction to differential geometry for students who are coming to the subject for the firs …
2
votes
Which math paper maximizes the ratio (importance)/(length)?
The paper 'You cannot hear the shape of the drum' by Gordon, Wolpert and Webb is very short
considering the importance of the result and the sophistication of the methods used. It answers a questio …
1
vote
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
The Gauss-Bonnet theorem can be proved using the Gauss
map, but the theorem itself appears to be due to Blaschke and the
original proof procedure is due to Rodrigues.
It seems that neither the theorem …
4
votes
Books that teach other subjects, written for a mathematician
There are many sources on general relativity for mathematicians (see, for example, the lecture notes of Schoen and the textbook Geometric Relativity by Dan Lee).
It's been a while since I read any che …
3
votes
Mathematicians with both “very abstract” and “very applied” achievements
A similar story to that of Leray is David Gilbarg. He originally did his PhD on algebraic number theory with Emil Artin, but then switched to more applied topics because of the Second World War, beco …
12
votes
PhD dissertations that solve an established open problem
Does Scholze's PhD thesis count, as if I remember rightly he applied perfectoid spaces to prove some important special case of Deligne's weight-monodromy conjecture? (Not an expert, correct me if I'm …
4
votes
Time-saving (technology) tricks for writing papers
In terms of backing up documents, I used to send literally everything I write to a friend of mine who would read it and make comments, and in fact I still send almost everything to them even now.
This …
6
votes
Lunch seminars for PhD students
At Warwick Mathematics Institute in the UK they do indeed have such a seminar, called the Postgraduate Seminar. It's organised by PhD students for PhD students only and the talks are given by PhD stu …
5
votes
Books containing new results
This is a physics example and I think the first edition was in 1995, but if I remember rightly there are some important results derived in Weinberg's textbook The Quantum Theory of Fields: Volume I. …