What's new

[This is a guest post by Noah Giansiracusa.

[This is a guest post by Ben Green.

[This is a guest post by Ben Antieau, crossposted from his blog.

[This is a guest post by Henry Cohn.

[This is a guest post by Emily Riehl.

[This is a guest post by Bryna Kra.

[This is a guest post by Nestor Guillen, crossposted from his blog.

[This is a guest post by Steven Strogatz.

[This is a guest post by Silvia De Toffoli and Eamon Duede.

Parallel to the other crowdsourced resource drive on this blog, I would like to collect books, writings and other resources that discuss or explain the purpose(s), value(s), and nature of mathematics.

[This is a guest post by Claire Voisin.

[This is a guest post by Burt Totaro.

I am proud to be among the list of 25 initial signatories — all Fields Medallists — to the declaration below, which grew out of discussions between ourselves over the last week.

[This is a guest post by Andreas Thom.

[This is a guest post by Lucas Fagan.

[This is a guest post by Anima Anandkumar.

Given current events, I think it is worthwhile to start collecting useful online resources with regards to AI and mathematics in general.

There’s some exciting very recent work by Alpöge and Buckmaster, building upon prior work by Córdoba and Martínez-Zoroa, in the general topic around the infamous global regularity problem for the incompressible three-dimensional Navier-Stokes equations.

A recent tradition of the ICM is to have a non-technical popular article written for each of its medallists.

Mathematical Discourse is a new online, peer-reviewed mathematics journal, publishing videos of mathematics research talks of the highest quality.

Ben Krause, Hamed Mousavi, Joni Teräiväinen, and I have just uploaded to the arXiv our paper Quantitative bounds for sets lacking polynomial progressions with shifted prime difference.

In recent months there has been a proliferation of AI-generated proofs of various old and new results, some of which have been formalized in the proof assistant language Lean.

This post concerns the following conjecture of Sendov, as well as its strengthening by Phelps–Rodriguez: Conjecture 1 (Sendov’s conjecture) Let , and let be a degree polynomial with all zeroes in the unit disk.

A function of one variable can be translated in space by a spatial shift to obtain a new function and also modulated in frequency by a frequency shift to obtain a new function One can compose these two operations to obtain a time-frequency shift: As per t…

The notorious Jacobian conjecture can be formulated concretely over the complex numbers as follows.