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.
I have to say this daily, but if Muslims did this to ONE Jewish temple, the world would be OUTRAGED.
Israel has now destroyed over 1,000 mosques in Gaza and the West Bank.
It’s the single biggest destruction of holy sites in the modern HISTORY OF THE WORLD.
Everyone needs to see this. Hundreds of Israeli settlers are coming down from hilltops and setting entire Palestinian villages on fire. Full on pogroms.
🚨 Top mathematicians just issued a clear warning about AI: Don't believe the hype.
Over 2,300 mathematicians, including Fields Medal winners Terence Tao and Peter Scholze, have signed the Leiden Declaration on Artificial Intelligence and Mathematics. Endorsed by the International Mathematical Union, it is the most significant collective response from a major academic discipline evaluating frontier AI impact.
The core message is straightforward: current AI tools have real constraints when applied to complex work, and commercial incentives are pushing claims beyond what the technology can reliably deliver.
Read the full declaration here: https://t.co/hKSXoSt4Tr
Why this matters beyond mathematics
The declaration identifies five threats that apply to any field deploying AI:
1) Plausible but unreliable outputs.
AI produces arguments that "look" correct but contain subtle errors. In high-stakes work, human verification is critical and costly.
2) Attribution collapse.
Models trained on published work don't properly cite sources. Training data was often obtained by exploiting licenses or violating copyright protections.
3) Distorted incentives.
AI use becomes incentivized for its own sake, warping hiring, funding and recognition.
4) Press release science.
Results announced "on market timelines" before community evaluation can take place. Commercial incentives drive firms to "overstate the capabilities of their products."
5) Loss of autonomy.
Research priorities shift toward what is automatable rather than what is significant.
The leap: chatbots → agentic AI → software → research
We have moved from chatbots to agentic systems. Now AI is solving 80-year-old mathematical conjectures. The declaration is not about toy problems. It is about frontier systems being deployed in contexts where correctness matters.
What this means for your industry
The same risks apply wherever AI is used in high-stakes work: law, medicine, finance, engineering. The declaration's core insight is simple:
AI generates narrative, not truth. Verification cannot be automated away. Human accountability is non-negotiable.
💼 I’ve written a more detailed breakdown of how these risks show up in practice and what organisations are doing about them. It’s available for subscribers.
☕️ What have you observed in your industry? Have verification or hidden costs issues already appeared in your AI deployments?