The AI Invasion Has Come for Mathematics (opinion)

The sudden onslaught of AI-generated proofs, some resolving old and very high-profile questions, appears to mathematicians as very much like an occupation by a foreign power. We, the autochthons, are quite suddenly confronted with an alien force, marching down our very own streets, wielding terrifying new weapons and harboring very different and often opposed cultural values. This force is commandeering our resources and threatening our livelihood. Its objectives are exploitative, extracting value from our fields and returning it to the metropole. In its public pronouncements it resembles a traditional colonial power, asserting that any opposition is backward, primitive and antiprogressive—and that resistance is futile. The future is theirs. Like any occupying force, it is grabbing the low-hanging fruit and in time will move on; it has no interest in developing the local economy or in sustainability.

On Tuesday, OpenAI released hundreds of new mathematical findings, following closely on the resolution by OpenAI’s bots of the Millennium Prize problem addressing the Navier-Stokes equations. This was a true blitz: 10,000 internal agents spent 88 hours and produced a proof apparently satisfying the criteria of this challenge, issued by the Clay Mathematics Institute some 25 years ago. The company is thought to have spent millions on this stunt. The mathematical community that had been converging on this example—and it is just that, an example—has been digesting this new work with professional interest.

Normally the effort and expense required to achieve some great goal is rewarded by societal celebration of the result. But we can see what community valued the announced resolution of the Navier-Stokes challenge. It wasn’t the mathematics community—mathematicians have, rather, generally expressed concerns about the potential inadmissible and unacknowledged use of recent work by human mathematicians. No, it was the AI community. From a mathematician’s perspective, spending even a fraction of this money on the human mathematical community would have been far more worthy of celebration.

The advent of new technology invariably leads to a reassessment of values. When, for example, video lectures became easily produced— following COVID-19, even expected—we thought afresh about the value of the in-classroom experience. Our reaction to the advent of AI must be similar: What is the value of human discovery of mathematical truths? We have traditionally imagined that the principal value of carefully thinking through and recording a proof is that we are making a contribution to the edifice of mathematical knowledge. Now that many of those contributions can be offloaded to machines, we have to reassess what the actual value of human mathematical thought is.

The incorporation of LLMs as a routine component of academic research is a tidal force now acting on the mathematical community. Wealthy institutions like Massachusetts Institute of Technology can afford licenses to fancy frontier models, while less well-endowed institutions cannot. This is a matter of equity analogous to the availability of journal subscriptions at wealthy institutions but not at poorer ones. That disparity has been somewhat alleviated—but by no means eliminated—by preprint servers like arXiv. The federal government has insisted that federally funded biomedical research should be publicly available, in an effort to overcome the same sort of inequity of access. Similarly, since generative AI is here to stay, equable access to high-performance LLMs should be a right guaranteed by government. To the extent that is not the case, our use of this technology is of questionable morality. Of course, at present the tech companies have a further unfair advantage.

This occupation is likely to continue in some form indefinitely. It seems likely that the violence of the current initial phase will subside in time, as the occupying force finishes sweeping up the valuable resources lying near the surface. Will it result in a kind of settler-colonial regime, in which employees of big tech are increasingly credited for advances and welcomed into academic departments? There will be refugees, fleeing this new order; in fact, graduate students in mathematics are feeling extremely insecure about their long-term job prospects and indeed about the continuance of the mathematical enterprise itself.  

LLMs and their attacks on mathematics are creations of large corporations. The leaders of these companies have motives for their behavior. They have staged an invasion, throwing their great resources into a concerted attack on mathematics. They offer us suitably hobbled copies of their arsenal, reserving the “frontier models” for themselves. They invite us to serve as “advisers.” Is this a form of collaboration, in the political sense? Such advisory committees provide these companies with a useful cover, a proof of acceptance by the local culture. But much more is at stake. Mathematics is not the only country experiencing this invasion and occupation—all of academia is experiencing the same, and many other parts of the economy are under threat. Even more importantly, the physical infrastructure supporting the AI weaponry is inflicting great damage. We unassuming mathematicians have suddenly found ourselves thrust into the battle, pawns in a much larger game.