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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.
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 …
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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. …
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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 …
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6
votes
Siegel zeros and other "illusory worlds": building theories around hypotheses believed to be...
This is more of a theoretical/mathematical physics example, but it can happen in mathematical physics that a lot of stuff is built around hypotheses which are essentially known to be false from the be …
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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 …
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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.
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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 …
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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 …
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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 …
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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 …
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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 …
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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 …
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13
votes
Each mathematician has only a few tricks
Tao has recently submitted a preprint on exactly this topic in the case of the mathematician Jean Bourgain. The tricks in question are quantification of qualitative estimates, dyadic pigeonholing, ra …
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3
votes
How to explain to an engineer what algebraic geometry is?
I would just say that very roughly speaking it's a subject where you are doing geometry and thinking about geometry, but you write about it formally like it is algebra and you use algebra (which can b …
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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 …
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