From Axioms to Zeta-functions: if it involves shapes, numbers, or logic, we've (probably) got a theory of it!
The Croot-Lev-Pach-Ellenberg-Gijswijt bound on cap sets
Simple Set Game Proof Stuns Mathematicians | Quanta Magazine
quantamagazine.org
Lots of stuff happened a month ago (I still need to make a post about how we now know E_8 is an optimal sphere packing). The additive combinatorics blogs kind of exploded:
- An old but good post by Ellenberg on what this problem was
- The Croot-Lev-Pach Paper that drove this result
- Ellenburg's speculation, announcement, and retrospective of the proof
- The Ellenberg-Gijswijt Paper
- Terence Tao gives a reformulation of the proof
- Another good post on the evolution of the capset bound
- Another post about the proof
- The "emergency" polymath post made in response to these precipitous advances
- Reflections by Timothy Gowers on the results
Addenda:



