Linked Questions
11 questions linked to/from Zagier's one-sentence proof of a theorem of Fermat
200
votes
89
answers
54k
views
Examples of great mathematical writing
This question is basically from Ravi Vakil's web page, but modified for Math Overflow.
How do I write mathematics well? Learning by example is more helpful than being told what to do, so let's try to ...
192
votes
79
answers
43k
views
Which math paper maximizes the ratio (importance)/(length)?
My vote would be Milnor's 7-page paper "On manifolds homeomorphic to the 7-sphere", in Vol. 64 of Annals of Math. For those who have not read it, he explicitly constructs smooth 7-manifolds which are ...
49
votes
28
answers
8k
views
Problems where we can't make a canonical choice, solved by looking at all choices at once
It's a common theme in mathematics that, if there's no canonical choice (of basis, for example), then we shouldn't make a choice at all. This helps us focus on the heart of the matter without giving ...
53
votes
15
answers
5k
views
Request for examples: verifying vs understanding proofs
My colleague and I are researchers in philosophy of mathematical practice and are working on developing an account of mathematical understanding. We have often seen it remarked that there is an ...
31
votes
14
answers
4k
views
An example of a proof that is explanatory but not beautiful? (or vice versa)
This question has a philosophical bent, but hopefully it will evoke straightforward, mathematical answers that would be appropriate for this list (like my earlier question about beautiful proofs ...
36
votes
5
answers
4k
views
When has the scaffolding been more important than the completed building?
Niels Abel once said(1) of Gauss, "He is like the fox, who effaces his tracks in the sand with his tail." to which Gauss replied, "No self-respecting architect leaves the scaffolding in ...
5
votes
3
answers
1k
views
Don Zagier's "Zetafunktionen und quadratische Körper"
Do you know of a text--preferably in English--whose treatment of the class number formula is based on (or follows closely) the one expounded by Zagier in sections II.8 (binary quadratic forms) and II....
- 8,842
3
votes
2
answers
224
views
What one group action can tell about another [closed]
There are two groups, $G_1$ and $G_2$. They are both acting on a set $S$.
$S$ may have some structure. The groups may too. The actions respect them.
$G_1$ is mysterious. Perhaps all we know about it ...
- 41
19
votes
0
answers
492
views
Fermat Descent and the "Grand Unified Theory" of Obstructions
In Bjorn Poonen's book Rational Points on Varieties he says that Fermat Descent is an example of cohomology. There is also a book by Soulé. Even Wikipedia mentions this with no further explanation. [...
- 22.8k
0
votes
1
answer
612
views
Number of fixed points in Zagier's involution (Fermat's Theorem) [closed]
Zagier's has found a famous one sentence proof for Fermat's theorem on sums of two squares. It centers on the following involution of the set $S= \lbrace (x,y,z) \in N^3: x^2+4yz=p \rbrace $ having ...
- 111
6
votes
0
answers
379
views
A possible variant of Zagier's one-sentence proof for Fermat's sum of two squares theorem?
Is it possible to modify Zagier's one-sentence proof of Fermat's sum of two squares theorem (see here) to prove certain non-trivial cases of Jacobi's four-square theorem (see here)?
Let $p$ be a prime ...
- 81