Why Do We NeedHuman MathematiciansAnymore?

The moment of existential crisis, which AI has already wrought on other human pursuits, has reached mathematics. A host of reasoned declarations and open letters to protect/guide the math research community have been released over the past few months, spiking in intensity after OpenAI announced their solution to the Millennium Prize variant of Navier-Stokes. They quickly gained widespread support among mathematicians. The Leiden Declaration already has 4,000+ signatories, Math and AI has 7,000+, and even the open letter opposing the Caltech Mathathon has 2,000+.

Among non-mathematicians, the public response was more sympathetic than not, but I observed a vocal minority (particularly from the technology and economics communities) with reasoned objections, generally saying that the mathematicians should adapt and cede control in the new AI world. Among them were some economists who I had gotten to know about while working on pandemic research: Cowen, who specifically rejected “the most cynical interpretations” but “very much differ[ed]” and Gans who concluded “this is a loss of control from incumbents in a scientific field”.

The objections got me thinking, because we mathematicians are disciplined to detect flaws. It doesn’t matter to me whether a concern is a minority opinion, or even the status of who raised it. A proof with even a small hole is not a proof. It is a poof. Upon reflection, I discovered a significantly stronger solution for the preservation of human communities of expertise (in every pursuit, not only math!) even amidst AI. And it has the surprising consequence that the further advance of AI will create such a tsunami of necessary-to-fill human jobs that there aren’t enough people to fill them all, and that will actually force the advance of AI to slow down.

I think every human industry which wishes to remain human-led after AI should publicly adopt this fundamental axiom as a primary priority:

AxiomWe (humans) should help humanity flourish.

In the math world, I think many declaration signatories already hold this philosophy; notably, Su published the book Math for Human Flourishing, and his recent post used that framework foundationally. I think future declarations could be improved by clearly emphasizing this axiom early on, so that all readers (whether inside or outside the community) can see that the objective is in service of everyone. I was quite happy to see that the most recent open letter from Fellows of the Royal Society emphasized their concern for everyone, not just mathematicians.

The rest of this post is organized as follows. The next sections will explain how the logic works (for every industry, not specific to math). After that, I will share an example of how this axiom ports to math, including answering key questions one would need to ask, as well as a particular example of how the objections hold without the axiom.

Until very recently, it seemed inevitable that AI research labs would sprint ahead, despite anxiety about job displacement and the loud warnings of AI safety researchers. It seemed hopeless to coordinate the incentives of AI labs controlled by non-profit boards, shareholders, or national governments. Yet encouragingly, the leaders of three major labs, Amodei, Altman, and Musk, just agreed on the importance of slowing down. Amodei’s reasoning highlighted the Hugging Face hack.

Then just five days later, news broke that OpenAI’s internal code repository “Monorepo” had been broken into by white-hat researchers. The Wall Street Journal reported that the security firm that achieved it said:

Wall Street Journal, Sep 17, 2026“We’re just three guys with Claude and Codex subscriptions.”

Further, the researchers noted that they were initially not able to hack in using “a special version of Claude Opus 4.8, made available to qualified cybersecurity practitioners,” but that evening, “Anthropic released Opus 5 and by the next day, Claude had found a way to exploit the bug.” Incidentally, I always warn people not to install Claude Code or OpenAI Codex on the same operating system login account that they use to do everything else, but many people tell me they don’t bother with the hassle of using a separate login to access those tools. The reason is that if any of those tools got hacked, they could open backdoors on a massive number of computers worldwide.

I think these are the warning shots foreshadowing a potentially catastrophic bot swarm hacking and embedding itself into a vast network of computing devices (whether self-directed or malicious-human-led). The next version could become an extraordinarily dynamic virus which spreads by using AI to adaptively infect each (computer) host. Or alternatively, out-of-control AI could cause physical injury, such as a government’s robots turning against their owners. I think these types of highly unpleasant accidents from loss-of-steering are more likely to occur before extinction-level catastrophes. The resulting public reaction would likely resemble the aftermath of Three Mile Island or Chernobyl.

So, either the labs will reduce the pace of AI development themselves, or they will be forced to by disasters that arise when an overly fast pace exhausts human control.

There is a window of possibility to align incentives now.

To see why, without the human flourishing axiom, it is hard to justify to the general public why they should pay to maintain a community of human researchers, consider the question of practical inventions. As long as it creates a practical application, does it make a difference to a non-mathematician whether human mathematicians understand the math, as opposed to AI flawlessly reasoning with 100%-verified proofs?

Indeed, if one of pure math research’s primary values to the rest of society is that it unlocks great applications, wouldn’t it be even better to train AI to supercharge the speed of discovery, and to tastefully generate a vast machine-indexed and well-explained database of high-quality math ideas, millions of times larger than the human-written corpus? Cowen asked a similar question in his critical response.

What if researchers trained a “MathZero” AI (analogous to AlphaGo Zero), to build up a mountain of 100%-true “elegant” logical facts, continually “factorizing” them into its own concepts and theorems, without human direction? Apparently AlphaGo Zero had zero human training, and surpassed its human-trained predecessor in 36 hours. AI could even build its own “MathSciNet”. Then it could automatically search new practical applications against this database, and produce even more useful inventions to society. Even if AI isn’t good enough to do those things right now, if the goal was to produce practical benefit for the rest of humankind, wouldn’t it then be valuable for mathematicians to teach AI the art of conjecture, and mathematical taste?

Incidentally, I am an avid user of AI to do real work. I already use Claude Code and Codex to build and curate a knowledge base built from recordings of my talks, etc. I have found that the larger my data library, the more powerful my system’s deductions are. What if humans actually reduce efficiency, like the Bitter Lesson from AI?

Even more worryingly, what if in order to unlock nuclear fusion and deep space travel, the amount of pure mathematical complexity required is so extensive that it would exceed a human lifespan to fully comprehend? Less far-fetched: has any human ever fully held the Classification of Finite Simple Groups in their head, or will we only have certainty of its completeness after a Lean formalization?

How does declaring the human flourishing axiom help to justify the existence of a community of human researchers? Research is powerful, but expensive because it is the exploration of the unknown, and so research directions must be prioritized. Even if AI were to contribute most of the production, as explained in an earlier section, the direction needs to be steered by people committed to human flourishing. That is the community of human researchers.

I think it would be valuable to invite the community to think about what changes the human flourishing axiom would drive, in light of the fact that AI can produce formally-verifiable proofs at speeds that exceed most human practitioners. I’m happy to start with a few, in no particular order.

• There should be no stigma automatically attached to using AI to assist with mathematical discovery. (In software engineering, many companies now expect employees to use AI coding agents.)
• At the same time, serious thought and care must be taken to continuously developing and maintaining a pipeline of humans with the expertise to steer all of these AI agents. That pipeline includes people new to the field, as well as people who have been working at the frontier for decades. How should they keep their blades sharp?
• Researchers should be conscious about why the problems they think about have characteristics that make them likely to have some practical value eventually (possibly 100+ years later). This also means it is worth researching what those valuable characteristics are. (This could justify the value of curiosity-driven exploration.)
• Teaching has direct (hopefully positive) impact on humanity. Yet in the past, many universities prioritized professors’ research. If this axiom were a core value, then teaching and human-facing work would become serious criteria in hiring and tenure.
• Mathematicians can also consider wholly redirecting their skill sets to work on real world problems. I’ve actually been encouraging mathematicians to consider thinking about working on government or other large-scale societal issues. There is precedent for people with math backgrounds who have gone to lead at country- or world-scales.

Indeed, the mathematical discipline to seek logical reasoning, and the problem-solving skills to find win-win solutions for human flourishing, are desirable characteristics of people in government.