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Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
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 …
-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 …
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 $n$.