After Math Falls, What's Next? with Julia Kempe (NYU/Meta)

Julia Kempe on Why Math Will Fall Next, Superhuman Provers, and the Return of the Renaissance Researcher

In this episode, we sit down with Julia Kempe, a Professor at NYU's Center for Data Science and researcher at Meta FAIR's Foundations of Reasoning team,  for a wide-ranging conversation on the future of AI research.

We dig into why verifiable domains like mathematics may be on track to "fall" the way Go did. With formal verification through Lean and the Mathlib infrastructure, LLM agents can now generate and check proofs at scale, and Julia makes the case that a new industry of automated mathematical discovery is closer than most mathematicians believe. We explore why Erdős problems are already falling, what's still missing for harder fields like analysis and physics, and how synthetic data, curation, and verification fit together.

From there we get into the energy and scaling limits of frontier models, the case for academic research that big labs can't pursue, how to advise PhD students when Claude can already do their first-year work, the rise of AI safety and security as research priorities, and Julia's optimistic argument that AI tools are bringing back the Renaissance generalist  -  the researcher who can finally work fluently across math, biology, and beyond.

Timeline

• 00:00 — Introductions
• 01:00 — Defining reasoning and verifiable domains
• 04:00 — Lean, Mathlib, and the formalization of mathematics
• 10:00 — Constructive proofs, Erdős problems, and the new wave of "AI mathematicians"
• 14:00 — Will math be "solved"? Art, photography, and the changing nature of creative work
• 18:00 — Why physics is harder than math
• 22:00 — Moravec's paradox, evolution, and why robotics lags behind language
• 27:00 — The Renaissance is back: generalist researchers in the age of AI
• 29:00 — Advising students: math, programming, and what core education still matters
• 32:00 — Teaching and assessment when GPT can do the homework
• 35:00 — Anti-AI backlash, energy costs, and the security threat
• 40:00 — Scaling vs. efficiency
• 42:00 — Model collapse, synthetic data, and what's left to squeeze from the internet
• 44:00 — What's exciting next: AI for science, safety, robotics, memory, and planning
• 47:00 — Annotation costs as a proxy
• 50:00 — Superhuman models and what security even means against them
• 52:00 — AlphaGo as precedent for verifiable superhuman performance
• 54:00 — Hallucination, the Mirage paper, and whether these are solvable problems
• 56:00 — Why coding isn't fully solved yet
• 58:00 — Agent security, prompt injection, and the Wild West of deployed agents
• 1:01:00 — Regulation: what's needed and what's possible
• 1:04:00 — Advice for PhD students and what research academia should pursue
• 1:09:00 — Startup opportunities: robotics, security, and AI for finance
• 1:12:00 — Closing thoughts: use the tools, and build grassroots AI for good

Music:

• "Kid Kodi" - Blue Dot Sessions - via Free Music Archive - CC BY-NC 4.0.
• "Palms Down" - Blue Dot Sessions - via Free Music Archive - CC BY-NC 4.0.
• Changes: trimmed

About: The Information Bottleneck is hosted by Ravid Shwartz-Ziv and Allen Roush, featuring in-depth conversations with leading AI researchers about the ideas shaping the future of machine learning.