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Results tagged with big-list
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user 1532
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.
6
votes
The use of computers leading to major mathematical advances II
At ICM 2022 Kevin Buzzard gave a talk "The rise of formalism in mathematics" about computer verification of mathematical proofs (item E). It is about writing large chunks of mathematics in "lean" (or …
7
votes
The use of computers leading to major mathematical advances II
The paper Constructions in combinatorics via neural networks by Adam Zsolt Wagner uses reinforcement learning algorithm and the deep cross-entropy method, to find explicit constructions and counterexa …
16
votes
The use of computers leading to major mathematical advances II
An example of type C. DeepMind launched an endeavor for using machine learning (and deep learning in particular) for finding conjectures based on data. Two recent outcomes are toward the Dyer-Lusztig …
2
votes
Generalizations of the four-color theorem
Closely related conjectures are the following: An acyclic colouring of a graph is a colouring of its vertices so that the subgraph spanned on union of every two colour classes is acyclic (a forest). G …
2
votes
What precisely Is "Categorification"?
Here is a very nice lecture about categorification by Jacob Lurie: Categorification of Fourier Theory. (I thank Arye Deutsch for telling me.)
(Update June 5, 2021): Here are four lectures by Catharina …
- 24.7k
6
votes
Proposals for polymath projects
The $3^d$ conjecture
Here is a problem of mine from 1989 that could be the basis of a good polymath project.
The $3^d$ conjecture: Let $P$ be a centrally symmetric $d$-dimensional polytope. Then $P$ h …
8
votes
Tweetable Mathematics
Every set of integers with divergent reciprocals contains 3-term arithmetic progressions. Erdos and Turan conjectured; Bloom and Sisask proved; Bateman and Katz's method for cap set used. link.
#TWTM …
13
votes
The most outrageous (or ridiculous) conjectures in mathematics
Let me promote a comment of Terry Tao into an answer and mention two conjectures.
(See, e.g., Thom - Finitary approximations of groups and their applications and De Chiffre, Glebsky, Lubotzky, Thom - …
9
votes
Tweetable Mathematics
This is based on a real tweet of Ryan O'Donnell on the proof of MIP*=RE which disproves Connes' Embedding Conjecture from 1976.
MIP* = RE, by Zhengfeng Ji, Anand Natarajan, Thomas Vidick, John
W …
14
votes
Tweetable Mathematics
This is actually a real tweet by Ryan O'Donnell on Huang's proof of the sensitivity conjecture.
Hao Huang@Emory:
Ex.1: ∃edge-signing of n-cube with 2^{n-1} eigs each of +/-sqrt(n)
Inte …
5
votes
Experimental mathematics leading to major advances
In March 2019, Andrew Booker in the paper Cracking the problem with 33 showed that 33 is a sum of 3 cubes in $\mathbf Z$. This is a striking example of a case where checking the solution is very easy …
3
votes
Experimental mathematics leading to major advances
Another famous example is Harald Helfgott's 2013 proof that every odd integers greater than five is the sum of three primes. "The ternary Goldbach conjecture is true". arXiv:1312.774
41
votes
Tweetable Mathematics
33 = 8866128975287528³ + (-8778405442862239)³ + (-2736111468807040)³. Andrew Booker! link.
Update 2019-09-05: $(-80538738812075974)^3 + 80435758145817515^3 + 12602123297335631^3 = 42$, https://people …
4
votes
Experimental mathematics leading to major advances
Boolean Pythagorean triples Theorem (Heule, Kullmann, Oliver 2015) — The set $\{1, \dots , 7824\}$ can be partitioned into two parts, such that no part contains a Pythagorean triple, while this is im …
4
votes
Important formulas in combinatorics
Read's 1958 beautiful formula for the asymptotic number of 3-regular graphs with n vertices
$$g_3(n) \sim \frac {(3n)! e^{-2}}{(3n/2)!288^{n/2}}.$$