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Results tagged with big-list
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user 3106
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.
7
votes
Hard problems with an easy-to-understand answer
Lomonosov's theorem that a bounded operator on a complex (infinite-dimensional) Banach space that commutes with a nontrivial compact operator has a nontrivial invariant subspace had a surprisingly sim …
16
votes
Examples of theorems where numerical bounds on $\pi$ played a role
In the paper, Space vectors forming rational angles, by Kiran S. Kedlaya, Alexander Kolpakov, Bjorn Poonen, and Michael Rubinstein, the authors classify all sets of nonzero vectors in $\mathbb{R}^3$ s …
- 82.7k
1
vote
Which popular games have been studied mathematically?
Mastermind was already mentioned in the question, but the link points only to Knuth's analysis, which assumes that the code is chosen uniformly at random. It is more realistic to model Mastermind as a …
2
votes
Proofs of the Chevalley-Warning Theorem
Whether the following proof is different from the other ones already mentioned could be debated, but to me it feels different enough to be worth mentioning separately. As noted in Gjergji Zaimi's answ …
- 82.7k
22
votes
Daunting papers/books and how to finally read them
I can think of two distinct reasons why a particular paper or book might seem daunting. The first is the sheer size. The second is that I don't understand what's going on.
If the only issue is sheer s …
2
votes
What do named "tricks" share?
A trick is a mathematical life hack.
A life hack is a simple but unexpected solution to a somewhat frequently occurring problem. So it is with a trick; it provides a simple and unexpected solution to …
1
vote
What are examples of mathematical concepts named after the wrong people? (Stigler's law)
De Bruijn sequences are so named because Nicolaas Govert de Bruijn enumerated them in 1946, but he later acknowledged the priority of C. Flye Sainte-Marie, who enumerated them already in 1894.
12
votes
Which journals publish experimental results in pure maths?
The Journal of Experimental Mathematics was launched in June 2023. It is a Diamond Open Access journal, meaning there are no charges to authors nor readers. I don't know the full story, but looking at …
10
votes
Books containing new results
The question seems too broad to me; it's almost like asking for a comprehensive list of long papers. For example, Aschbacher and Smith's Classification of Quasithin Groups spans two books and over a …
9
votes
Results from abstract algebra which look wrong (but are true)
The Auslander–Buchsbaum theorem that every regular local ring is a unique factorization domain.
I should say that the first time I saw this theorem stated, I was not immediately surprised, but that wa …
2
votes
Examples of errors in computational combinatorics results
It is well known that the Appel–Haken–Koch proof of the four-color theorem was controversial because of its use of an electronic computer, but it is not as well known that the original proof had many …
6
votes
Unnecessary uses of the axiom of choice
The highly-upvoted, accepted answer (by Theo Johnson-Freyd) to another MO question, Why worry about the axiom of choice?, points out that the usual proof of the Poincaré–Birkhoff–Witt theorem assumes …
4
votes
What are some examples of theorem requiring highly subtle hypothesis?
Gödel's ontological proof requires a subtle assumption that if $\varphi$ is an essential property of $x$ then $x$ must possess $\varphi$. The first time that Gödel showed his proof to anyone was in 1 …
2
votes
What are examples of theorems which were once "valid", then became "invalid" as standard def...
This old question attracted my attention again today, and I have a proposal for how to think about it. I suggest that we think about sentences $S$ with the property that at some time $t_0$ in the past …
5
votes
Results that are widely accepted but no proof has appeared
The comments by Monroe Eskew and Andrés E. Caicedo concerning unpublished results of Hugh Woodin deserve to be made into an answer IMO. As a concrete example, Caicedo wrote:
There is the fact that Tu …