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 intellectually exciting, absolutely dramatic things that has ever happened in the history of mathematics."
Another instance is the Fargues/Scholze advances
on "Geometrization of the local Langlands correspondence,"
which has the Langlands world excited:
Eva Viehmann: "It’s really changed everything. These last five or eight years, they have really changed the whole field."
This makes me wonder if there is something like a heat map for all of mathematics,
which would show the areas with a lot of excitement.
It seems difficult to capture this via arXiv postings,
but that is an obvious starting point.
Has anyone pursued this?
Best Answer
https://paperscape.org/ is a 'heat map' of the arxiv if you color the graph by age. Unfortunately, its ability to detect links between mathematics papers is a bit lacking compared to physics papers for some reason, but it still gives a very interesting view of the subject.