I love how earlier Adiprasito was being mentioned in the context Huh or Adiprasito might win 2022. That was asinine. It was always Huh and only Huh.

Now people immediately start mentioning Adiprasito again because it’s a name they know that hasn’t won yet. His best work by far is combinatorial Hodge theory for matroids and someone already won for combinatorial Hodge theory for matroids and other objects, Dowling-Wilson, etc.Yeah I know JH and even he said that the work on the Lefschetz principle for spheres by KA is greater than Hodge Theory for matroids. Matroids uses a well known principle that was known before, and had been exploited for instance by Elias and Williamson (and honestly Williamson should have gotten Fields instead of Huh. Huh was just a more digestible result for public). KA and then Papadakis and Petrotou developed an entirely new idea to prove Lefschetz.

Plus he solved semistable conjecture of Abramovich and Karu, used geometric group theory to prove Dantzig conjecture in many cases, solved a problem of Legendre in his thesis.Agree on Williamson. They applied essentially the same principle, but to a more complicated problem. Probably he should have won, but this would have excluded Huh as, it was essentially the same idea.

Your comments are totally ignorant. Both Williamson and Huh could have won.

The vague idea: "extend properties that would follow from AG beyond a geometric context" is never going to just let you prove an actual theorem. And for June Huh's work on matroids, the connection to AG had not even been established. No one had any clue that the Rota conjecture could be proved using AG, until Huh did it.

For Elias-Williamson, the connection to AG had been known since Kazhdan and Lusztig in the 1980s. For McMullen and Karu's work, the connection to AG dates back to Stanley's work in the 1980s as well. So Huh's work is notable in that he found (several) new connections to AG which implied various combinatorial conjectures and then managed to extend them beyond the geometric realm.

This isn't to say that Williamson is not deserving. It's just ridiculous that you think that Huh's work is "the same" in some way.