Terence Tao: The Mathematics 2.0 Era Has Arrived!

Wen Ting posted from Ao Fei Temple
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Mathematics 2.0 era has arrived.

Just now, leading figure in mathematics and Fields Medalist Terence Tao officially posted:

AI is causing mathematical proofs to become abundant, and the Mathematics 1.0 era built on the scarcity of proofs is about to end.

Since OpenAI announced that it had solved the Navier–Stokes Millennium Problem, AI’s rapid advance has prompted mathematicians led by Terence Tao to both mock OpenAI and call for an urgent brake.

But the tide of history rolls forward, and the development of AI is clearly irreversible.

Tao is not simply turning into an AI brake advocate; he has posed a deeper question to the mathematical community:

How can we ensure that an increasing number of AIs provide proofs that bring greater understanding, better training, and more reliable contributions to the real world for humanity?

And in the future, what kind of mathematicians do we truly need?

From “proof scarcity” to “proof abundance,” the premise of Mathematics 2.0 has changed

Tao Zhexuan believes that in the Mathematics 1.0 era, traditional mathematics has always operated in an environment of proof scarcity.

To prove an open problem, people often need deep expertise and must invest a great deal of time and effort;

Therefore, “who solves a problem first” naturally becomes an important way for the mathematical community to measure contributions.

But now, AI is profoundly changing this environment.

Whether it’s OpenAI suddenly releasing 722 math papers overnight, tackling the Riemann hypothesis, the Hodge conjecture, the BSD conjecture, and many other heavyweight research topics;

(Details can be seen: OpenAI churns out 722 math papers overnight! Riemann, Hodge, BSD all in action, mathematicians: can’t read them all)

It even extended the three‑dimensional Hitchin‑Hodge conjecture solved by this year’s Fields Medalist Wang Hong to four dimensions.

（For details, see: Wang’s conjecture just extended to four dimensions）

All of this, without exception, is rewriting the pace of mathematical research, striking the evaluation system of the Mathematics 1.0 era, and forcing mathematicians, beyond joint boycotts, to answer an increasingly urgent question:

Beyond proofs, what truly constitutes a mathematician’s moat?

（For details, see：Terence Tao leads the charge! Human mathematicians unite to resist OpenAI）

In response, Terence Tao said plainly:

The barrier to obtaining answers has indeed lowered.

With sufficient computing power and access to cutting‑edge models, people can now obtain answers to many open problems that were previously considered very difficult, and do so in a relatively short time.

However, we still need to carefully assess whether an answer is correct, how significant the contribution is, and how it connects with existing research.

Otherwise it will lead to a concerning misalignment—solving the problem without correspondingly increasing human understanding.

Regarding why mathematics is so vulnerable to AI disruption, Terence Tao has summarized three overlapping conditions:

1. Proofs can be objectively verified;

2. Mathematical objects and reasoning processes are highly digitizable;

3. A large body of high‑quality research literature already exists in digital form.

This, combined with the massive investment from the cutting‑edge AI lab, has quickly turned mathematics into the core battlefield where model capabilities are soaring.

At the same time, Terence Tao also displayed that classic airplane bullet‑hole diagram, reminding everyone to beware of “survivorship bias”:

Most of the current frontier problems in mathematics remain unsolved.

AI’s capabilities are uneven; it excels in some areas but remains lacking in others.

AI vendors often show us only carefully selected success stories;

Meanwhile, many unsuccessful AI attempts may never get a chance to reach the public eye.

And this practice of counting only successes naturally cannot answer key questions such as success rate, resource consumption, and the degree of human involvement.

Therefore, Terence Tao calls for an urgent need to establish a more transparent and scientific evaluation mechanism that includes failure outcomes and AI compute costs in the reports.

But is it enough for AI to present correct proofs and report both failure results and compute costs?

Terence Tao clearly does not think so.

Blindly cramming problems can damage the long‑term health of mathematics

When asked what the goal of mathematical research really is, Terence Tao gave a vivid analogy:

Open problems are like lighthouses.
They guide people to explore the surrounding mathematical world, and reaching the lighthouse does not mean the exploration is complete.

Terence Tao believes that in the process of attempting to solve a problem, whether one succeeds, fails, or makes only partial progress, one may gain insights that are more valuable than the final answer.

But if an automation tool hands over the answer too early, and the evaluation system only rewards “solved,” those unexplored paths may lose the motivation to keep exploring.

After all, the Millennium Prize Problems are finite, but in actual mathematical research, the paths, understandings, connections, and new questions that grow from a single problem are virtually infinite.

He therefore warned:

If we continue to blindly optimize the “problem‑solving” metric, it will damage the long‑term health of mathematics!

Following this line of thought, we can more easily understand why Terence Tao fired at model companies so mercilessly in his latest SAIR talk: 

It’s downright insane, AI companies are accelerating endlessly, yet they have no idea what will happen afterward.

We must slow down; there’s absolutely no reason to go this fast, not a single reason!

（For details see: No, why is Terence Tao also becoming an AI slowdown advocate??）

And this concern has already appeared in his earlier public responses.

As early as early September this year, Terence Tao pointed out in a blog comment:

AI can become a tool that serves mathematical research, but chasing short‑term goals may come at the expense of the long‑term sustainability of the mathematical community.

He worries that the latter scenario is rapidly approaching:When answers are readily available, will people still be willing to take the time to slow down, understand them, and continue exploring the mathematical world around them?

However, the dramatic twist is that the impact accelerated by AI is vividly illustrated in Terence Tao’s own recent talk.

According to Terence Tao, the original theme of his speech was supposed to be“Machine-Assisted Proofs”, but with AI repeatedly “bombarding” the mathematics community recently, he had to make a clear adjustment and ultimately set the theme to“Mathematics 2.0”.

Truly… magical.

So, as AI gets better at solving problems and proving theorems, where exactly is the core moat of human mathematicians?

The answer may be hidden in Terence Tao’s proposed “Cancer Therapy Experiment”.

After proof, there’s still understanding, training, and the real world

To illustrate why human understanding remains important, Tao presented a striking thought experiment in his talk:

Suppose you let an advanced AI look for a cancer therapy that can pass Phase III trials.

After burning through compute, it produces a set of unknown chemical mixtures: the model predicts they can kill cancer cells, Lean validation passes, and they also clear Phase III trials;

But no one knows how it found them, nor can anyone determine whether the AI truly discovered a therapy or simply exploited a loophole in the testing process.

Before the needle pierces your vein, would you wish that at least one cancer specialist could understand its mechanism of action, a mathematician could grasp the mathematical reasoning behind that model, or at least a scientist could comprehend the model used to search for a therapy?

This is a thought experiment about goals, validation, and understanding.

It brings abstract mathematical discussions into a very concrete scenario:The conclusions inside the model have been verified, but someone still needs to judge whether they align with real‑world goals.

And this may be precisely why human scientists cannot be replaced—Models can generate answers, verify reasoning, and accelerate exploration, but they cannot replace human oversight.

The value of mathematical proofs must also continue along this chain.

In his earlier essay “Mathematics in the Age of AI,” Terence Tao broke problem solving into five stages:

• Generate proof;
• Verify correctness;
• Explain clearly;
• Be understood and accepted by the community;
• Eventually integrate into the field’s standard theory.

Among them, the final step is especially slow:

Researchers need to find more natural formulations, more suitable proofs, and connect the results with other knowledge before they can enter textbooks and the toolbox of the next generation of mathematicians.

This is precisely what AI finds hard to accelerate.

If AI mainly speeds up the earlier stages, the later stages may suffer from “proof indigestion.”

Therefore he argues:

Reduce the emphasis on preemptive proof generation and increase the focus on explanation, review, and knowledge organization.

And the debate over “post‑proof” has been intensifying since early October:

On October 7, OpenAI released 722 math papers in one go, completely angering the AI‑slowdown camp led by Terence Tao.

Subsequently, Tao swiftly spearheaded the creation of the Human Mathematics Association (AHM) and issued a heavyweight joint statement: 

Releasing more than 700 files at once is not research at all; it’s pure bragging about computational dominance.

We strongly urge all mathematicians to stop collaborating with OpenAI and return to a science vision centered on human understanding!

(For details, see: Terence Tao leads the charge! Human mathematicians unite to resist OpenAI)

In Terence Tao’s view, formal verification alone is insufficient; the author should also be able to explain their results clearly;

If a result lacks this explanatory ability, he considers it still incomplete.

And this series of events also hits the issue that young researchers care most about:

If AI can quickly generate papers, do we still need to pursue a master’s or PhD?

In the AI era, does mathematics still require a PhD?

Tao Zhexuan believes that in the AI era, the question of whether a PhD is necessary hinges not on the ability to produce papers, but ondeveloping a systematic capability to absorb difficult material, integrate knowledge, and pose good questions.

He uses diet and exercise as an analogy, and frankly says:

In the AI era, if you want a PhD to give you more than just a dissertation—namely, to train you to tackle hard problems, integrate knowledge, and ask good questions—then pursuing a doctorate still holds value;
But if your sole goal is to produce results, its necessity is indeed diminishing in the AI age.
It’s like when food and transportation become abundant, people need to learn to exercise on their own;
When answers are readily available, we must consciously maintain our cognitive abilities and resist the convenience of bypassing thought; these are precisely the skills cultivated in a PhD program.

So, is it possible to find a good way for AI and researchers to grow together?

Tao Zhexuan has already hinted in a talk that he is pushing forward some concrete experiments;

For example, the open mathematics model program launched by the SAIR Foundation, which he helped found, focuses in its first phase on everyday research needs such as understanding difficult arguments, checking citations, exploring examples, writing code, and formal proof verification.

It also announced that these open mathematics models will be released soon, which is something to look forward to.

△Tao Zhexuan’s presentation of a more sustainable “Mathematics 2.0” AI application paradigm

One More Thing

At the end of his talk, Terence Tao identified the main bottleneck to achieving Mathematics 2.0 as imagination.

In his view, the supply of proofs is changing, but how to harness this shift to advance understanding, training, and exploration together still requires a collective choice by the mathematical community.

And when a problem is proved by AI, the mathematician’s next question may also move toward:

What can we still learn from this answer?

And, what can we do next?

Reference links:
[1]https://teorth.github.io/tao-web/ai-views.html
[2]https://x.com/ns123abc/status/2109045309112250560
[3]https://teorth.github.io/tao-web/slides/math-2-0-caltech-2026.pdf?utm_source=chatgpt.com
[4]https://arxiv.org/html/2608.16753v1?utm_source=chatgpt.com

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