The most influential mathematician of his generation stands in a German lecture hall and explains a foundation he is rebuilding from scratch. Almost nobody watches it.
This is Peter Scholze at Bielefeld University, November 2025, opening lecture of a new public series called Ars Mathematica.
Scholze became a full professor at 24 and won the Fields Medal at 30. His work on perfectoid spaces reorganized entire areas of arithmetic geometry inside a decade.
Condensed mathematics is his attempt to fix something deeper: the way analysis and algebra refuse to sit together properly. He is proposing new foundations for how mathematical objects carry topology.
Watch how he pitches it to a general audience. No prerequisites assumed, no dilution, a working mathematician showing why abstraction opens rooms you could not otherwise enter.
A researcher I know rewatched the middle section twice and said it was the first time condensed mathematics felt like an idea rather than a rumour.
Free on YouTube from a university channel, subtitles on.
Some people prove theorems. He is replacing the floor.
On the ground at Jantar Mantar I ask @SauravDassss of @Cockroachisback when there might be another round of talks with government , his response to PM Modi tweet on NEET Exam, the violence last night at Tolstoy Marg and what the path ahead is as protests take place in multiple other cities. More ground reports here https://t.co/y349lZ2fTT
Fields Medal Winner 2026 Jacob Tsimerman:
"I do not do mathematics only to find truth. I do it largely because I enjoy it and I am good at it."
A part of his tweet on the joy of problem solving:
"I’ve seen some people say that they only do mathematics to find truth and others valourize that as the only virtuous way to be. I do not do mathematics only to find truth. I do it largely because I enjoy it and I am good at it. I also find it beautiful and am grateful I get to spend my days understanding beautiful things. But I enjoy the challenge, the process, resolving confusions, finding strategies, grappling with problems. I would like to push for this being de-stigmatized. Mathematicians are people who need money, housing, food, love, exercise, and a great deal of other stuff including various forms of meaning. There are many people whose primary enjoyment of math comes through problem solving in one of its incarnations. If that disappears, that is not a trivial issue and many of them might not want to do it anymore (even if there were some way to proceed)."
Opinion: I think this is how most of us feel in some form but havent yet internalized well given how fast things are changing. Please read his full tweet below for a bigger picture.
Knot theory is an area of math that seems simple but gets weirder the deeper you go. John Pardon’s proof on the “distortion” of knots “is a paper you can sit down and read,” said mathematician Kai Cieliebak.
Today, Pardon was awarded the Fields Medal:
https://t.co/HQxvV5fOr1
The 2026 Fields Medals have been awarded at the International Congress of Mathematicians in Philadelphia.
The recipients are:
• Yu Deng (University of Chicago)
• John Pardon (Stony Brook University)
• Hong Wang (New York University & IHES)
• Jacob Tsimerman (University of Toronto)
The Fields Medal recognizes outstanding mathematical achievement by researchers under 40. Each post below summarizes the official citation and key contributions.
We are establishing a new subfield: Quantum Number Theory.
See: https://t.co/6VT2nQ5RUe
Of course, nothing is completely new. Related ideas include Prof. David Tong’s work, etc.
https://t.co/yoFWWuLWkl
But we will now derive new theorems and formulate new conjectures.
ウィトゲンシュタインの博士論文審査の再現。審査の常識に完全に反している型破りなやり取りで審査員(ラッセルとムーア)は"Don't worry, I know you'll never understand it"とまで散々いわれてしまうが、結果はもちろん合格。世紀の『論考』の前には審査員も形無しだ。https://t.co/h9xKW2FdKy
A mathematical group called 𝘋₆ comprises the six transformations that leave an equilateral triangle unchanged. These transformations — rotations and reflections — are not commutative. The order in which each is performed determines the final outcome. https://t.co/lPUVTvhUvD
The two assumptions in Penrose's 1965 singularity theorem are: 1. A trapped surface, where gravity is so strong that light cannot escape, like in a collapsing star. 2. The weak energy condition, ensuring matter has non-negative energy density, so gravity pulls things together. These suggest singularities are inevitable in general relativity, crucial for black holes and the Big Bang. However, quantum gravity might resolve singularities, and the assumptions may not always hold, like with exotic matter. The theorem's significance is clear, but its classical nature and limitations spark ongoing debate.
In 1965, the mathematical physicist Roger Penrose proved that, given two simple assumptions, space-time must end at points called singularities. The paper has been called “the most important paper in general relativity” since Einstein’s. https://t.co/1dtLupkA7k
Oh my fucking god. Geometric deep learning is SO awesome, holy shit what a wonderful field to be invested in. Holy smokes SHEAFS TOO, I’m so happy you don’t even know man this is why we do math right here, RIGHT HERE. I am so happy finally after so many weeks wow.