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Results tagged with big-list
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user 4613
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.
-2
votes
Examples of theorems with proofs that have dramatically improved over time
Liouville's Theorem that there exists a transcendental number had its proof greatly improved by Cantor who showed that a mere counting argument suffices.
Liouville's argument needs facts about how ra …
22
votes
Results true in a dimension and false for higher dimensions
The sausage conjecture:
Which way of arranging $M$ unit balls in $\mathbb{R}^n$ minimises the content of their convex hull? For $M$ small the answer is always to arrange them along a line, so that t …
30
votes
Decision problems for which it is unknown whether they are decidable
In Conway's Game of Life, the problem of deciding whether a given pattern with finitely many live cells is a Garden of Eden (i.e. whether it lacks a predecessor).
The main obstacle is that there could …
5
votes
Atlas-like websites on specific areas of mathematics
The Cunningham Project seeks to factor the numbers $b^n \pm 1$ for
$b = 2$, $3$, $5$, $6$, $7$, $10$, $11$, $12$, up to high powers $n$.
16
votes
Big list of comonads
Given a topology on a set $X$, let $2^X$ be the poset of subsets of $X$ ordered by inclusion. Then the interior operator for the topology is a comonad on $2^X$. In fact the topologies on $X$ correspon …