Terence Tao: Optimizing Only for Problem-Solving Harms Math

Fields medallist Terence Tao told a public lecture at Caltech on 9 October 2026 that mathematics has moved from an era of proof scarcity to one of proof abundance, and that “Further blind optimization of problem-solving alone is now actively harmful to the long-term health of mathematics.” He posted the slides of the talk, titled “Math 2.0”, on his blog on 10 October.

An 11 October article by 36Kr presented his blog under the headline “250,000 Math PhDs Face Desperate Crisis, Urgent Calls to Slow Down AI Development”. That framing goes further than the texts by Tao that we read.

What Tao Said at Caltech

In the slides, Tao calls traditional mathematics “Math 1.0” and says it operated under the assumption of proof scarcity: finding and proving a solution to an open problem “was difficult and rare, and often required significant human expertise to obtain.”

He argues that proofs are objectively verifiable, highly digitizable and backed by large, high-quality data, and that frontier AI labs have therefore prioritized mathematical problem-solving. “As a consequence of this massive investment, we are now entering an era of proof abundance in mathematics.”

He describes AI performance as “extremely jagged”: astounding in some directions and inadequate in others. He adds that, despite the impression given by press releases and social media, “most of the problems at the current frontier of mathematics remain unsolved, even with massive computational expenditure.”

The core of his argument is that problem solving is “only a proxy for more valuable long-term goals.” That proxy “was largely accurate in the era of proof scarcity, but has become misaligned in the era of proof abundance.”

On reporting, he calls for more transparent and scientific assessments of AI capability that fully report key statistics such as resource consumption and negative results, and names the First Proof project as one effort in that direction.

What He Proposes Instead

Tao’s “Math 2.0” uses AI to strengthen the ways human understanding interacts with mathematics, not only to produce proofs. His examples include “open exposition problems”, which seek motivated explanations of results whose known proofs are opaque, living networks of research results, large libraries of formal mathematics such as Mathlib, and “Ablation studies” that test whether a theorem can still be proved after removing key inputs.

He cites two large data projects as early examples of a new experimental mathematics: the Equational Theories Project, which crowdsourced human and automated arguments “to settle over 22 million true/false statements in universal algebra”, and the IGP24 challenge, which located degree 24 polynomials “with each of the 25,000 possible Galois groups at this degree.”

He also writes that some open math models are “to be released very soon”. His closing slide says the primary bottleneck to achieving Math 2.0 is not technology or institutional culture: “It is imagination.”

The Week on His Blog

The talk followed a week of posts on his blog after OpenAI released a repository of mathematical manuscripts on 6 October. On 7 October he published a guest statement by the Association for Human Mathematics, which said “Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power” and urged mathematicians “to discontinue their work with OpenAI”.

On 8 October he published a guest post by mathematician Álvaro Lozano-Robledo, written for students weighing a PhD. Its summary line reads: “Keep calm and carry on studying math.” Lozano-Robledo wrote that the issue that worries him most is “the very real possibility that we are about to lose an entire generation of mathematicians”, and that the answer to whether to pursue a PhD “should not have changed from a year ago to today.”

Tao’s own summary page of his AI views lists his ties to the field: it says he has been gifted access to premium frontier models, collaborates with Google DeepMind employees, helped organize an IPAM workshop sponsored by OpenAI in March 2026, and co-founded an AI-focused non-profit, SAIR.

What the 36Kr Article Said

The 36Kr article describes a video in which, it says, Tao called for “slowing down AI development”, and it attributes to him the words “We have to slow down AI.” It does not identify the video. We did not find those words in his Math 2.0 post and slides, in the guest posts above or in his AI-views summary page, as read on 11 October 2026.

The article’s “250,000” appears as its own question: “Are 250,000 mathematics doctoral students facing a desperate situation?” We did not find that figure in the Tao texts we read.

The article also presents a guest post by Grant Sanderson as the blog post that hit the hot search list “today”. On Tao’s blog that post, titled “If math is more than proof, we need to better celebrate the rest of it”, is dated 18 September 2026.

The Structural Read

Tao’s slides say frontier AI labs prioritized mathematical problem-solving because proofs are objectively verifiable, highly digitizable and backed by large, high-quality data, and that this investment produced the era of proof abundance.

He adds that AI performance is “extremely jagged”, and that most problems at the current frontier of mathematics remain unsolved even with massive computational expenditure, despite the impression given by press releases and social media.

The 36Kr article of 11 October framed the same week as a crisis for 250,000 doctoral students and a call to slow AI down. As we read Tao’s slides and post, his recommendation is to change what AI is used for in mathematics, not the pace of AI development.

Three Implications

FOR MATHEMATICIANS Tao’s Math 2.0 examples include open exposition problems, living networks of results, formal libraries such as Mathlib and ablation studies, alongside new problem-solving.

FOR AI LABS Tao calls for capability assessments that fully report key statistics such as resource consumption and negative results, and names First Proof as one effort in that direction.

FOR READERS OF AI-MATH NEWS Tao’s slides say most problems at the current research frontier remain unsolved even with massive computational expenditure, despite the impression given by press releases and social media.

The Business Engineer Lens

This story maps onto the Business Engineer framework AI & The Harness Theory.

The analysis puts it this way: “The next professional jump is not a better prompt. It is an operating system that wraps your AI — a harness that compresses your thinking, your team’s feedback, and the model’s raw capability into something replicable.”

As we read it, Tao’s Math 2.0 makes a similar point for mathematics: the raw capability to solve problems is not the goal on its own, and the gain comes from the structure humans build around it, in exposition, formal libraries and shared data.

What Is Not Established

As read on 11 October 2026: the source of the video quote in the 36Kr article is not identified, and we did not locate it. Tao’s AI-views page says a video and transcript of the Caltech talk are expected later, so his spoken remarks at Caltech are not reflected here beyond the slides.

We did not read his 9 October post on the Lean theorem prover in full, so it is not used here.

The Bottom Line

Terence Tao argued at Caltech on 9 October 2026 that AI has moved mathematics into an era of proof abundance, that problem-solving has become a misaligned proxy, and that the field should use AI to strengthen human understanding. The 36Kr claim that he issued an urgent call to slow AI development, against a backdrop of 250,000 PhDs in crisis, is not supported by the texts by Tao that we read.