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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.
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 …
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 …
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 …
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 $n$.
-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 …