Inside AI’s Brutal Race to Solve a Famous Math Problem | Terence Tao

Summary
In an interview produced by New Scientist, physics reporter Karmela Padavic-Callaghan speaks with UCLA mathematician and Fields Medalist Terence Tao about the evolving relationship between mathematics and artificial intelligence. Tao reflects on AI’s ability to brute-force solve problems versus human conceptual understanding, recounts the controversial AI-driven proof of a Navier–Stokes blow-up, discusses his book Six Maths Essentials, and addresses escalating AI safety and alignment risks.

What is shown

• [00:00] Teaser clip of Terence Tao discussing AI outstripping safety and alignment development.
• [00:30] Title sequence: “Terence Tao: The new era of mathematics”.
• [00:35] Karmela Padavic-Callaghan introducing Terence Tao and his background across analysis, number theory, compressed sensing in MRI imaging, and mathematical commentary.
• [02:00] Tao outlining how AI acts as an answer-generation engine rather than an intuition- or connection-building medium.
• [04:45] Discussion of OpenAI’s reported solution to a version of the Navier–Stokes Millennium Prize problem using multi-agent compute swarms.
• [07:15] Tao detailing the intense race where human mathematicians were beaten by OpenAI’s compute-heavy model deployment by a single day, resulting in a 100-page opaque proof accompanied by a Lean formal certificate.
• [10:19] Padavic-Callaghan displaying Tao’s book Six Maths Essentials.
• [10:57] Tao explaining his three-world framework (physical reality, observational data, and mathematical models), using the 2008 financial crisis as an example of model breakdown.
• [18:20] Tao explaining the three stages of mathematical education: pre-rigorous, rigorous, and post-rigorous.
• [25:10] Tao evaluating AI itself as an open mathematical problem, noting the lack of foundational theory behind deep learning and neural network representations.
• [30:45] Discussion on AI agent security risks, prompt injection, exploits in formal verification systems like Lean, and competitive dynamics among major tech labs.
• [35:30] Discussion of prime number research, the parity barrier, and historical progress on bounded prime gaps.

Claims & numbers

• Karmela Padavic-Callaghan notes that OpenAI claimed to solve a version of the Navier–Stokes problem by deploying large compute power and an unprecedented swarm of AI agents.
• Terence Tao states the Millennium Prize problems were established in 2000 with seven grand challenge problems and a $1 million prize each, with the Poincaré conjecture being the only one solved roughly 20 years prior.
• Tao states human mathematicians came within hours of a Navier–Stokes singularity result, finishing a day before OpenAI’s team released their result after pouring millions of dollars in compute into their model.
• Tao states OpenAI’s Navier–Stokes proof was 100 pages long and verified via a formal proof certificate in Lean, yet provided almost no human-understandable mathematical insight.
• Tao states financial models in 2008–2009 failed because they incorrectly assumed mortgage defaults were largely uncorrelated or followed Gaussian distributions.
• Tao mentions that bounded prime gaps, initially bounded at 70 million by Yitang Zhang and reduced to 246 through collaborative efforts, have recently been pushed down under 200 through human and AI efforts.
• Tao states David Hilbert presented his famous 23 open problems at the International Congress of Mathematicians in 1900, concluding with the motto “Wir müssen wissen, wir werden wissen” (“We must know, we will know”).

Notable quotes

• [04:08] “Math is the glue that connects all the other sciences together. That’s the part that hasn’t really been impacted by AI yet.” — Terence Tao
• [08:06] “We’ve learned almost nothing mathematically from what they did... It’s like strip-mining the landscape.” — Terence Tao
• [34:04] “I think nobody wants to go this fast, but everyone feels like they have no choice.” — Terence Tao

Assessment
This is an authentic long-form journalistic interview conducted by New Scientist with Terence Tao. Tao candidly addresses current developments, theoretical limitations, and safety concerns regarding AI integration in high-level mathematics without promotional staging.

Described by gemini-3.8-flash on 2026-10-29 from the video’s audio and frames.