25
votes

### Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]

Quoting the first two paragraphs of V. I. Arnol'd, On teaching mathematics, Uspekhi Mat. Nauk 53 (1998) 229-234, translated to English in Russian Math. Surveys 53 (1998) 229-236 (a transcription may ...

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21
votes

### Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]

Michael Atiyah, On the Work of Edward Witten:
In his hands physics is once again providing a rich source of
inspiration and insight in mathematics. Of course physical insight
does not always lead to ...

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17
votes

### Who says understanding physics helps mathematicians? (A reference request) [Take the word "who" literally.]

Saunders Mac Lane:
The recent fruitful interchange of ideas (connections, fiber bundles, etc.) with physics (quantum gravity and all that) has been a decided stimulus and a source of new ideas and ...

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14
votes

Perhaps it is correct that this opinion is "widely acknowledged" but it is not unanimous.
Here I collected some statements of some prominent mathematicians related to this question.
Some of ...

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7
votes

### Theorems with many distinct proofs

Stan Wagon, Fourteen proofs of a result about tiling a rectangle, The American Mathematical Monthly, vol. 94, 1987, pp. 601-617. Summary at https://maa.org/programs/maa-awards/writing-awards/fourteen-...

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7
votes

### Online, evolving, collaborative foundational text projects

I've released today the Clowder Project, which aims to essentially become a Stacks Project for category theory.
I plan to eventually make it into a comprehensive resource for category theory, in the ...

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6
votes

### Noteworthy, but not so famous conjectures resolved recent years

Øystein Ore proved in 1951 that for $n\gt4$ we have that all elements of $A_n$ are commutators. He subsequently conjectured that this is true for all finite non-abelian simple groups.
In this ...

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5
votes

Mark Levi's book The Mathematical Mechanic: Using Physical Reasoning to Solve Problems is full of concrete examples of applying physical intuition in geometry, including even a proof of Gauss Bonnet ...

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4
votes

### Math conference-organizing checklist?

A detailed checklist is here.
We organize many smaller conferences/workshops, where the participation of the participants is the key thing. No idea if that applies to this situation, but you might ...

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4
votes

### Theorems with many distinct proofs

In 1940 Gödel proved the consistency of the continuum hypothesis with the Zermelo-Fraenkel axioms of set theory, by introducing the constructible universe $L$ and subsequently founding the subfield of ...

4
votes

### Odd differential forms

For a connect smooth manifold $M$, there is an orientation covering $\pi:\tilde M\to M$, where $M$ is a two-copy of $M$ if $M$ is orientable and is a connected orientable manifold if $M$ is ...

3
votes

### Theorems with many distinct proofs

Quadratic reciprocity had $6$ proofs by Gauß. Plus two were found posthumously. He proved it first in his Disquisitiones Arithmeticae. He called it "the gem of arithmetic". Euler and ...

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2
votes

### Analysing/studying simple groups with Sylow-$2$ subgroups

To answer in a different direction from Derek, while it is true that there are (once $n$ gets moderately large) a forbidding number of isomorphism types of $2$-groups of order $2^{n},$ fusion and ...

2
votes

### Rough paths theory - why is it natural?

The phrase "postulating" might be a bit misleading. Often, the iterated integrals (the second order process) are defined in some canonical way. Besides, all rough path lifts differ by the ...

1
vote

### Research-only permanent positions worldwide

In Japan there is the RIKEN (Institute for Physical and Chemical Research). As the name suggests, their focus is on the experimental sciences, but they employ some pure and applied mathematicians too.
...

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1
vote

### Video lectures of mathematics courses available online for free

I am surprised that no one mentioned the channel "The Bright Side of Mathematics". This guy has videos on many undergraduate and postgraduate level courses.
I hope this helps :)

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