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Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.

18 votes
3 answers
2k views

Heat map of current mathematics

The recent article on Quanta (by Natalie Wolchover) concerning $\aleph_1$ vs. $\aleph_2$ suggests that there is excitement within that community: Juliette Kennedy: "It’s one of the most intellectuall …
Joseph O'Rourke's user avatar
7 votes
1 answer
862 views

Windows into new mathematical worlds [closed]

Yitang Zhang's Annals of Mathematics primes-gap result opened a new window, which Polymath's reduction from $70\times 10^6$ to $246$ attests. Perhaps Harald Helfgott's celebrated proof of the odd Gol …
15 votes
3 answers
998 views

Thom's Principle: rich structures are more numerous in low dimension

Marcel Berger states Thom's Principle as: "rich structures are more numerous in low dimension, and poor structures are more numerous in high dimension." This is in Geometry II (Springer-Verlag …
Joseph O'Rourke's user avatar
0 votes
1 answer
703 views

"Mathematics is the science of the infinite" [closed]

The title is the first sentence of Hermann Weyl's 1930 essay, "Levels of Infinity." He focuses on "the distinction between actuality and potentiality, between Being and Possibility." He opine …
Joseph O'Rourke's user avatar
103 votes
15 answers
17k views

Have you solved problems in your sleep?

I have hit upon major (for me—relative to my trivial accomplishments) insights in my research in various sleep-deprived altered states of consciousness, e.g., long solo car-drives extending through th …