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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
Analogues of P vs. NP in the history of mathematics
A couple of other answers have mentioned Shelah and cardinal invariants, but not the following famous result that IMO is a pretty good answer to Scott's question.
Theorem (Malliaris–Shelah). $\mathfr …
- 2,031
121
votes
Not especially famous, long-open problems which anyone can understand
Gourevitch's conjecture1:
$$\sum_{n=0}^\infty \frac{1+14n+76n^2+168n^3}{2^{20n}}\binom{2n}{n}^7 = \frac{32}{\pi^3}.$$
1Jesús Guillera: About a New Kind of Ramanujan-Type Series; Experimental Mathemati …
- 82.7k
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 …
- 82.7k
25
votes
Accepted
Two (probably) equal real numbers which are not proved to be equal?
As mentioned in another MO question,
Gourevitch's conjecture is a nice example:
$$\sum_{n=0}^\infty \frac{1+14n+76n^2+168n^3}{2^{20n}}\binom{2n}{n}^7 = \frac{32}{\pi^3}.$$
EDIT: As mentioned by Jorge …
- 82.7k
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 …
- 82.7k
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
8
votes
Proofs of parity results via the Handshaking lemma
There is a nice paper by Kathie Cameron and Jack Edmonds, Some graphic uses of an even number of odd nodes, with several examples of the use of the handshaking lemma to prove various graph-theoretic f …
- 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 …
- 82.7k
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 …
- 82.7k
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.
- 82.7k
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 …
- 82.7k
13
votes
A search for theorems which appear to have very few, if any hypotheses
The graph minor theorem. In every infinite sequence of finite graphs, one is a minor of another.
I think this one is a very good match to the original request for "a search for unexpected regularity …
- 82.7k
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 …
- 82.7k
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 …
- 82.7k