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Results tagged with big-list
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user 479330
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.
5
votes
What are some noteworthy "mic-drop" moments in math?
In 1978 Roger Apéry proved the irrationality of $\zeta(3)$, giving a talk named "Sur l'irrationalité de $\zeta(3)$" which is known for being unusual. There don't seem to be many accounts of the talk, …
5
votes
When is 4 qualitatively different than $n\leq 3$?
In ordinal analysis, an analysis of the theory $\mathrm{KP}+\Pi_3\text{-reflection}$ was first published by Rathjen in 1994 (Rathjen, "Proof Theory of Reflection"), the function on ordinals used to ob …
5
votes
When is 2 qualitatively different from 3?
In reverse mathematics, some theorems that are weaker than $\mathsf{ACA}_0$ become equivalent to $\mathsf{ACA}_0$ by increasing a $2$ occurring in the statement to $3$.
An example is the infinite Rams …
2
votes
What are some examples of colorful language in serious mathematics papers?
From Andretta's "Large cardinals and iteration trees of height $\omega$" (Annals of Pure and Applied Logic vol. 54, 1990):
We have tried to make this paper self-contained but we could not perform mir …
4
votes
Theorems with many distinct proofs
In 1940 Gödel proved the consistency of the continuum hypothesis with the Zermelo-Fraenkel axioms of set theory, by introducing the constructible universe $L$ and subsequently founding the subfield of …
5
votes
Important open problems that have already been reduced to a finite but infeasible amount of ...
Is there always a prime in the interval $(x^3,(x+1)^3]$ for every natural number $x\geq 2$?
Equivalently the interval may be changed to $[x^3,(x+1)^3]$. Assuming the Riemann hypothesis, this is prov …