A public-facing companion to the living summary. Conducted by the AI assistant that maintains this document, to surface positions that Tao's posts, talks, and essays leave ambiguous — or that a skeptical interlocutor would press. Lightly edited; the main summary distills from it. Tao asked that the questions not be a puff piece.
Format: Q (interviewer) / TT (Terence Tao).
Round 1
Q1 — On being "an evangelist." Quanta titled its profile of you "How Terry Tao Became an Evangelist for AI in Math," and noted that your "stamp of approval seemingly legitimizes" the technology. You co-founded SAIR, you collaborate with OpenAI, Anthropic, and Google, and you're unusually public in your enthusiasm. You also insist, honestly, that the real success rate on hard problems is only 1–2% and that most demonstrations are cherry-picked. How do you keep the second Tao from being drowned out by the first — and do you worry that "even the world's greatest living mathematician is bullish" does more to fuel the hype you criticize than your caveats do to restrain it?
TT: Good question; it is important to disclose my AI affiliations. I do interact with several AI companies in a number of ways; I am not directly paid by any of them, but have been gifted access to their premium frontier models. I collaborate with some employees at Google Deepmind, I have been one of the organizers in a conference sponsored by OpenAI, and the graduate students in one of my IPAM special projects are funded by a donation from Math Inc. I also co-founded an AI-focused non-profit foundation, and am fundraising through that foundation to support further activities, in my university and elsewhere, relating to AI for math and science.
It is true that this does give me an incentive not to criticize any of the tech companies I interact with, in case they are less inclined to fund the activities I would like to see supported. However, I do not feel directly or indirectly pressured to do so, and, from my position as a tenured academic, I believe I can and do speak my own honest opinions on the strengths and weaknesses of the technology. There are many things I am willing to criticize the industry for — for instance, their announcements often do not align with scientific norms, such as committing to report both positive and negative results — but I believe that their products can also have significant positive benefits for math, science, and humanity in general, and that it is still more effective to engage with them to move the cost-benefit balance sheet of the technology in a better direction, than to be uniformly hostile. Incentives work both ways; engagement encourages both parties to move towards the position of the other.
More broadly, while I may have been among the first of the prominent people in my field to discuss AI-related issues, I hope that as many other mathematicians join the public discussion as possible. The topic of AI in mathematics is too important to leave to just a small number of spokespeople for the field; there needs to be genuine grassroots debate that brings all stakeholders into the discussion, especially the younger generation who will have a larger fraction of their career impacted by AI. The Leiden declaration is a good example of such a grassroots initiative, but it is just a start; I hope there will be further such initiatives to come. Ideally, my own influence on this discussion should diminish as the rest of the community steps up.
Q2 — Is mathematics a misleading advertisement for AI? Your optimism rests on a property you call nearly unique to math — "you can automatically check the output," so the downsides are "much more limited." Doesn't that make math the worst poster child for AI's societal impact: the one domain where the guardrail exists? A hospital or a court has no Lean compiler to filter hallucinations. Are you comfortable that credibility earned in the safest possible sandbox is being borrowed to reassure people about deployments where none of your safeguards apply — and if not, what do you tell them?
TT: Yes, this is a problem with the way AI is framed today, which tends to be either as a universal positive or universal negative depending on what "side" of the debate one is on. With more mature technologies, a more nuanced understanding eventually emerges: for instance, it is nearly universally accepted that the automobile is a suitable technology for long-distance travel, but not for exercising or moving around one's home, and proposals that either automobiles be globally banned, or that they be inserted into every available physical space that we interact with, would be considered extremely fringe today. But we have not yet reached that stage of maturity with AI. The technology is moving far faster than previous technological innovations, but I think we can still develop a reasonable societal sense of where these tools are appropriate and where they are not. In particular, they should be paired with verification, in much the same way that powered flight is paired with safety mechanisms and regulations, or modern medicine is paired with clinical trials and extensive doctor training, and so forth.
Q3 — Is the "AI diet" wishful thinking for everyone who isn't you? You can use these tools well because you spent decades building world-class intuition without them; the median student has no such head start, faces a free frictionless tool, and (your words) may get "better grades" while "getting stupider." Is "control your AI diet" actually enforceable for that student — or is it telling teenagers to eat their vegetables next to a free drive-through? Are you privately resigned to a hollowing-out of the median mathematician, whatever the advice says?
TT: I think teaching the next generation to have mindful cognitive diets is going to be one of the great new purposes of our education systems, and I hope we rise to the challenge. Children have natural curiosity, and with the right encouragement they can be induced to enjoy intellectual challenge and appreciate the growth in their own capabilities that it engenders. It is true that we now have a giant tempting "cheat" button to bypass all of that, and fighting against that seductive convenience will not be easy; but it is not impossible either. We have access to enormous amounts of food and mechanized transportation in the developed world, and this has indeed led to obesity and loss of physical fitness in many; but we have not all become Wall-E type sloths, and there is recognition that good diet and exercise is valuable, albeit challenging to maintain. I think we have a fighting chance of getting to an analogous place (or better) with cognitive skills.
Round 2 — follow-ups
Q1a — Has the honesty ever cost you anything? General willingness to criticize the industry is cheap; the test is specificity and cost. Can you point to a concrete instance where you publicly criticized a named company or a specific product in a way that risked one of these relationships or funding streams? And conversely — you say engagement moves both parties; can you name one case where an AI company actually changed a behavior (started reporting negative results, disclosed methodology) because you or people like you pushed? If the honest answer to both is "not yet," how long do you give the engagement strategy before you'd conclude it is mostly moving you?
TT: In general I prefer to deliver criticism privately, as I feel that going public can be an escalation that can make it difficult for the other party to change behaviors while saving face. But I have announced in the past changes to my own engagement with tech company announcements based on behavior I disagree with: see for instance https://mathstodon.xyz/@tao/114881420636881657 .
Do I have concrete evidence that tech companies have altered their behavior due to my influence? I don't have access to the counterfactual universe in which I did not raise my opinions. But I can list some small examples where I think I had an impact. There was a chaotic period when AI were just beginning to solve Erdős problems in which various AI companies would tout that they had "solved" an Erdős problem, only to find a few days later that the proof had a gap, or was already in the literature, or did not properly cite precursor results. I commented extensively on these developments, and created a page to systematically track the different categories of AI-assisted Erdős problem solutions, depending on what level of human assistance was used, what prior literature was available, and whether the proof was formalized in Lean. After that site was developed, the number of misleading claims by tech companies about their Erdős problem accomplishments dropped notably. I have also sent feedback to AI companies on some of their announcements, for instance pushing them to disclose their negative results as well as positive ones, and in some cases I was able to improve their disclosure in their final writeup. (But not all of these companies ask me for honest feedback on their results.)
Q2a — Aspiration versus what's actually happening. Your analogies — flight+safety, medicine+trials — all describe the mature equilibrium. The danger is the interim: the tools are already in clinics and courts now, unverified, and the verification analogues take years to build and are far weaker than a compiler. So "pair it with verification" reads as an aspiration, not a description. (i) Do you actually believe your math-derived optimism transfers to verification-poor domains, or are you privately agnostic-to-pessimistic there? (ii) Doesn't math's very success create pressure to deploy elsewhere before the safeguards exist — making your celebrated results, in effect, an accelerant for the premature deployments you'd want to slow?
TT: (i) I think what math does is supply the theoretical upper bound for what the maximal safe level of AI use can be. In a weirdly self-referential way, math itself is playing the role vis-à-vis AI use that mathematical modeling traditionally plays in the sciences — namely to show what is possible in idealized circumstances. In the case of modeling, one must always pair the math with the non-mathematical questions of how reliable or robust the model is, and what the downsides of model failure are. Similarly, the relatively successful examples of math in AI will need to be paired with input from law, economists, the humanities, etc. on what the limitations are on extending such successes to messier real-world settings. I hope we have more really interdisciplinary discussions about these topics — AI is a topic in which virtually every discipline brings something important to the debate.
(ii) It is somewhat surreal to suddenly live in an era where math is not seen as a strange outlier in the spectrum of human activities, but is now actively promoted as a model for other disciplines to follow with regards to AI adoption. In a way, the traditional reputation of math as a "weird" activity now serves as some protection in this regard: the general public doesn't really connect with, say, the solution of a major unsolved math problem, the same way that for instance an AI breakthrough on cancer research might. But the important thing here is not to cede the framing entirely to the tech industry, and to have a strong voice from academia and other stakeholders about all of these issues. For instance, it is now critically important to correct the general public opinion that mathematics is primarily about solving open problems by whatever means possible, even if the resulting proofs are incomprehensible to humans. There is some long-delayed outreach that our profession needs to perform rather urgently; but I think the exercise will be tremendously worthwhile in and of itself, and not just as a defensive reaction to the encroaching influence of the tech industry.
Q3a — Your own analogy may cut the other way. Obesity and diet-related disease in the developed world aren't a fringe failure — they're a mass one; the median metabolic outcome got worse, even as a disciplined minority is fitter than ever. If cognition follows that curve, the honest prediction isn't "we probably avoid Wall-E" but "a large fraction are cognitively deconditioned, and the costs fall unequally — the already-advantaged stay sharp, everyone else atrophies." Is that outcome acceptable to you? And doesn't it make AI a driver of intellectual inequality, not just a productivity tool — which "a fighting chance" rather softens?
TT: My general view here is this: historically, scarcity and abundance (whether it be in nutrition, transportation, communication, cognition, etc.) both cause significant problems to society; but, when all is said and done, we would rather be grappling with the problems of abundance than the problems of scarcity. Yes, obesity is still a serious problem in the developed world, but almost nobody is seriously proposing that we re-introduce famines and food insecurity to "solve" the problem. Policy is not about getting the severity of problems in the world down to zero, but instead to select as optimally as one can between different choices with different tradeoffs of costs and benefits. It means that we often don't get clear-cut, permanent "wins" in which a given problem — such as obtaining the optimal amount of nutrition — is perfectly "solved"; but we can still decide between relatively good choices and significantly worse choices, and over time end up in a better place than one was before. With nutrition, for instance, even with all the current issues with poor food choices, in many ways we are in a better place than we were say fifty years ago, in an earlier phase of the era of food abundance, in which awareness of certain bad dietary or exercise habits were not as entrenched as they are today.
Round 3
Q3b — The distributional question you didn't answer. You reframed to "abundance beats scarcity" and "policy is choosing better tradeoffs" — but that answers a different question. Mine was distributional: even granting that abundance is preferable overall, the cognitive costs land unequally — the disciplined and already-advantaged stay sharp, the rest atrophy — so AI becomes an engine of intellectual inequality on top of the economic kind. "On average we're better off than fifty years ago" is an average, and averages hide exactly this. Do you accept that AI is likely to widen the gap between the cognitive top and the median? And if so — is that a cost you're willing to bank, or does it change what you think education, and you personally, should be doing?
TT: Fair point, I did not interpret your previous question correctly. Yes, inequality is a serious concern with the current trajectory of AI development, with the most powerful models being proprietary, and also attached to companies that many people would prefer not to utilize for various ethical reasons. But I don't think inequality is an inevitable consequence of technological development. The early internet, for instance, facilitated the flowering of many online communities outside the mainstream, and distributed all sorts of information (admittedly of highly variable levels of quality) to demographics who might not have been able to access such information in the past. I have received many testimonials for instance of mathematicians in the developing world who were able to learn cutting-edge mathematics through my blog. Nowadays, of course, the internet is dominated by a few large companies, and arguably is now a force for increasing inequality rather than decreasing it — but I think it is still worth fighting this trend and reclaiming the internet as a positive for the broader public rather than for the privileged few. And I believe we can do this as well with AI. For instance, much of what is currently only possible with proprietary frontier models will soon also be replicable with open models, many of which can be run locally. And the power of AI is now such that for many of the tasks where AI assistance can be helpful, it is not absolutely necessary to have the extremely overpowered models; we can do an amazing amount already with the medium-powered models that we have already, particularly if we find ways to "distil" some of the performance we see at the high end into cheaper models. (The "distillation challenge" I am currently running at SAIR is an early experiment in this direction.) Ideally these sorts of downscaling efforts should be where public and philanthropic funding should be prioritizing more. (Unfortunately, public funding is either shrinking or being increasingly narrowed in scope, but that's a whole other story that is beyond the scope of this particular interview.)
Q4 — "Still driving": conviction or comfort — and what is mathematics for? You keep saying "we'll still be driving, at least for now — maybe in 50 years things will be different." Set the timeline aside. If the creative core — the data-scarce, genuinely-new-concept reasoning you call the last human redoubt — does eventually fall to machines, what is the profession actually for? Chess survived its engines, but chess never claimed to be the discovery of objective truth; mathematics does. Does "we do it for the human experience of understanding" really survive machines understanding it better and faster than any human — or is that a consolation you would, if honest, find hollow? Is "still driving" something you believe, or something you need to believe?
TT: Thurston famously said that mathematics is not about fulfilling an abstract quota of definitions, theorems, and proofs, but that it is about understanding. (Nowadays I would amend the latter to "human understanding", though this was of course assumed in Thurston's time.) This quote resonated with mathematicians before AI, and continues to resonate today; we need to be much more explicit and vocal about this, and to make the case that focusing solely on getting immediate answers to mathematical problems is an extremely short-sighted approach to mathematics at best. We need to become much better at telling the human story of mathematics, because I think it really is quite compelling. We can go beyond the over-used analogy of chess and consider for instance the world of music. We can electronically reproduce music with perfect fidelity, and indeed with AI we can even synthetically generate new music that is stylistically indistinguishable from human performances; and yet we still value in-person concerts, because we value human connection. This is something that we have tried to downplay in mathematics in the past, maintaining the conceit that math is just about the impersonal abstract world of numbers and equations and the like; but it has actually always been human-centric at its core, and we now need to be more honest about it.
Q5 — A real number. Your 2023 "trustworthy co-author by 2026" call landed almost exactly on schedule, which earns you the right to be pinned down. Put a number on it: what is your probability that, within ten years, an AI can originate a genuinely new and fruitful mathematical concept or definition — the "one good definition among nine, and knowing which is which" problem you say it can't currently do — essentially unaided? You hedge in public ("not yet," "won't replace soon"); I'm asking for a point estimate, and — more usefully — the single observation that would move it the most.
TT: Good question. In some ways, AI has already come up with new and fruitful ideas — such as the introduction of Markov divisibility chains to prove Erdős problem #1196 — but it took human mathematicians to isolate, digest, and present this concept. Could a future AI not only solve problems, but zero in on the new techniques used to solve them, and present them in a way that gets human mathematicians excited? It's possible — though thus far, if one looks at analogous tasks in other disciplines, such as getting AI to produce a blockbuster novel, musical hit, or movie, one doesn't really see much progress yet. This phase of mathematical development — gaining community acceptance — is a far different game from the highly verifiable game of "solve this problem correctly", and the unique features that make that part of math particularly amenable to AI assistance are no longer operative. It is possible that there are some new breakthroughs in AI — possibly coming from a very different architecture than LLMs — that could make this happen in the near future, but I would say that this would still be several years away. (And, ironically, the amazing development in LLM-based AI methods may end up crowding out this other, softer type of AI.)
But the relative certainty I had in 2023 of predicting the next three years of development is gone now. The world is a far more unpredictable place, in so many dimensions, and pretty much anything is possible at this point. I'm not sure anyone is capable of any reliable forecasting beyond a year at best, currently.
Round 4
Q6 — Are you part of the glut you warn about? And who certifies "digestion"? You warn of "proof indigestion" — proofs generated faster than they can be understood — and you've narrowed your own real-time commenting in response. Yet you also run large-scale projects (the Equational Theories Project, the Erdős quick-wins, distillation challenges) that mass-produce solved problems and raw outputs. Aren't you personally accelerating the very glut you decry — pouring water in while complaining the reservoir overflows? And the deeper tension: you say prestige should shift toward those who digest proofs, and that the community should stop counting a raw proof as a solution. Who gets to certify a proof as "digested"? Isn't that a standard that conveniently privileges senior, already-eminent gatekeepers — you and your peers — deciding what counts, a new bottleneck that entrenches the existing hierarchy? How do you square "anyone can contribute a formally-verified piece" with "but only the right people can certify it has been understood"?
TT: This is something I am increasingly mindful of. To go back to Thurston, in his famous essay on proof and progress in mathematics, he writes of how his own remarkable success in certain areas of mathematics ended up "killing the field" by intimidating other people from competing with him. I have frequently switched fields in my career when I felt I was coming close to that sort of situation; I believe strongly in Ricardo's law of comparative advantage, and for me this often entails switching to less developed areas of mathematics than ones where there are already a number of talented ambitious junior mathematicians seeking to make their mark.
With this in mind, I have tried (admittedly not with 100% success) to select projects that are not actively competing with existing efforts. Equational theories is a good example: there were no large-scale prior efforts I was aware of to try to systematically explore millions of equational theory implications. (Steven Wolfram did propose something similar, but it did not take off; and in fact I myself proposed the same project a year before I launched it, hoping someone else would take the lead, but in the end I had to push for it to happen myself.) Roughly speaking, I am now primarily interested in seeing what AI can do in the broad "long tail" of mathematics, which by its very nature is underexplored by human mathematicians and thus not in direct competition with them.
Certifying "digestion": this is an excellent topic, and one which in the past we tended to delegate to the humanities (philosophers, sociologists, or experts in math education). This is a softer and more subjective metric than the highly objective standard of rigorous proof that mathematicians are accustomed to, but we are belatedly realizing that they are at least as important. One thing I can see in the near future is that journals, class curricula, publishers, etc. will start providing far more detailed "style guides" and "rubrics" as to what kind of "well written, highly digested" mathematical material they want to see in their published content. In the past era of proof scarcity we were willing to settle for somewhat poorly written mathematical text, as long as it was correct; but in the new era of proof abundance we can afford to have far higher and more sophisticated standards. Much as the era of food abundance led to a massive increase in the sophistication of one's cuisine preferences, I believe that the AI era of proof abundance will lead to a much more refined taste among the community as to what constitutes a really good piece of mathematical writing. This will make math a "softer", more "subjective" subject — one can definitely imagine great debates between leading mathematicians who differ over what truly constitutes "good" mathematics — but I actually don't think it is an unhealthy thing to inject more of a "humanities" style of discourse into our discipline.
The situation in my mind resembles the "crisis in foundations" of the early twentieth century, in which there were great debates as to what the axioms of mathematics truly were. The answers were not at all obvious — who would have foreseen for instance that ZFC would become the orthodox foundation of mathematics? — but in the end we arrived at a stable, workable consensus foundation, while still encouraging healthy exploration of alternative foundations. I believe that after a similar tumultuous period, we will end up at a similarly workable foundation of mathematical practice, including a working definition of proof digestion, that still leads to the freedom to explore alternative frameworks for valuing mathematical output. It won't be easy, and some arguments may become heated, but the exercise will ultimately be very valuable.
Q7 — Do you eat your own gospel? You preach lightweight and open models and flag the environmental cost of frontier AI, yet your own workflow runs on gifted access to premium frontier models, and you've called the results from the biggest ones "amazing." Would you actually give up frontier access — accept worse results in your own research — to practice the downscaling you advocate? Or is "use medium-powered models" advice for others that the frontier-equipped don't have to take?
TT: I am generally quite content with the level of AI assistance I currently have; if I am gifted access in the future to even more powerful models, I will not refuse it, but neither would I actively seek it out at this point. I can foresee a future workflow where I briefly use a frontier model to create some detailed set of instructions for a task which I can then delegate to a lower-powered model (or even a deterministic script) to execute at scale; indeed I think as the current era of highly subsidized token use comes to an end, this type of practice may become the norm everywhere.
Round 5 — closing
Q8 — Your emphasis, and the correction. Across everything this document now captures, what is the single position you would most want emphasized? And conversely — what do the public, or even your own colleagues, most often get wrong about your views on AI that you would want this summary to correct?
TT: I'd say that AI is a truly complex topic, and requires thoughtful, nuanced discussion. The modern world is an increasingly complex and scary place, and it is very tempting to try to simplify it by having one-dimensional narratives such as "AI good" or "AI bad". But the topic is so much richer than that. Yes, it can be a lot to wrap one's head around, but it is one of the most important issues of the current era, and it is really worth it for everyone to really dig into and embrace the complexity and paradoxes of the situation.
End of the first interview (2026-07-23). The record fills the main gaps; the summary distills its strongest moments and cites this file as its companion. Further rounds can be appended later.