Linked Questions
12 questions linked to/from Results that are widely accepted but no proof has appeared
68
votes
3
answers
10k
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Replication crisis in mathematics
Lately, I have been learning about the replication crisis, see How Fraud, Bias, Negligence, and Hype Undermine the Search for Truth (good YouTube video) — by Michael Shermer and Stuart Ritchie. ...
49
votes
2
answers
5k
views
Well known theorems that have not been proved
I believe that there are numerous challenging theorems in mathematics for which only a sketch of a proof exists. To meet the standards of rigor, a complete proof of these theorems has yet to be ...
23
votes
2
answers
7k
views
Shing-Tung Yau's doubts about Perelman's proof
[EDITED to make the question more suitable for MO. See meta.mathoverflow.net for discussion about re-opening.]
According to Wikipedia, Shing-Tung Yau expressed some doubts about Perelman's proof of ...
12
votes
4
answers
2k
views
How about a statement without proof?
Consider a statement without proof in a paper, with the following assumptions:
it is unknown,
it is unused in the paper,
it is not written as a theorem (or proposition, or lemma…), but just a free ...
19
votes
2
answers
2k
views
Woodin's unpublished proof of the global failure of GCH
An unpublished result of Woodin says the following:
Theorem. Assuming the existence of large cardinals, it is consistent that $\forall \lambda, 2^{\lambda}=\lambda^{++}.$
In the paper "The ...
- 32.1k
16
votes
2
answers
940
views
Tutte's conjecture on Petersen graphs
I'm trying to find out whether Tutte's conjecture (that every snark has the Petersen graph as a minor) has been satisfactorily proved. Wikipedia claims that Robertson, Saunders, Seymour and Thomas ...
- 161
5
votes
2
answers
1k
views
Singular models of K3 surfaces
Let us work over a ground field of characteristic zero. As is well-known, a K3 surface is a smooth projective geometrically integral surface $X$ whose canonical class $\omega_X$ is trivial and for ...
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12
votes
1
answer
720
views
Unpublished works of Woodin on SCH and Radin forcing
There are many unpublished results of Hugh Woodin on ''singular cardinals hypothesis'' and '' Radin forcing''. Some of his results are published later by others, but it seems that there are still many ...
- 32.1k
10
votes
2
answers
647
views
Publishing solution but temporarily holding back solution method
https://www.quantamagazine.org/mathematician-disproves-group-algebra-unit-conjecture-20210412/
Above is an article about a researcher disproving an open conjecture in algebra (Kaplansky's unit ...
- 1,127
7
votes
1
answer
860
views
Is $n=6$ the only integer satisfies ${\sigma}_x(n) \equiv 0\bmod{n}$ for every odd integer $x > 0$ and $2 (\bmod n)$ if $x$ is even integer? [closed]
After a few computations in wolfram alpha about the divisor function for some values of $n$ to look the behavior of $\sigma_x(n)\bmod n$ for $\,n=6,\,$ i got this result : $\sigma_x(6)=0 \bmod 6$ for $...
- 414
17
votes
0
answers
681
views
Proof of MacPherson's result about set-valued constructible sheaves and exit paths
I'm looking for a proof of a theorem that is attributed to MacPherson. Treumann (Section 1.1 in Exit paths and constructible stacks, 2009) states the theorem as:
Theorem 1.2 (MacPherson). Let $(X,S)...
- 355
11
votes
0
answers
537
views
Outline of the unpublished proof of Erdős-Sós conjecture
In this post, it was mentioned that a long time ago, Ajtai, Kolmós, Simonovits, and Szemerédi announced a proof that for sufficiently large $k$, every $k$-vertex tree $T$ is a subgraph of every graph $...
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