We study mathematics for pretty much the same reasons that we study astronomy. The stars and planets are already out there, and, despite millennia of human observation, there is more we don’t know about them than we do. Same with mathematical truths: they are out there, and have always been; but, as of late, we also have a powerful new telescope, which dramatically changes the scope and volume of exploration. It also affects our perception of geometry: Some stars which used to appear distant are proving much more tractable; others will remain as obscure as before, in need of new ideas for approaching them.
So the story will go, if anyone is left to tell it. Yet, there’s a competing story, according to which “we”, humans, won’t need to understand anything, as this exploration will be completely undertaken by machines. They will get better at everything we do, including finding new conjectures and explaining their discoveries to curious humans, but by the time a person has understood something new, they will be far ahead.
Knowledge is power, and, while I do not know whether such a development is possible, no freedom-loving human should be celebrating the subjugation of human intelligence to artificial intelligence, a Middle Ages in reverse. In more realistic terms, though, it is not about subjugation of humans to machines, but to the owners of those: that’s why so many trillions of investment are flowing into AI. To return the investment, the companies will have to capture staggering percentages of society’s economic output. This requires not just “empowering scientists and mathematicians with tools that accelerate discovery”, but collecting scientific production in-house, being not just a tool but also the owner of intellectual property that will translate itself into patents and pharmaceuticals.
Talking of intellectual property, LLMs which have been trained on my and everyone’s intellectual work, funded by universities and public agencies and published on the arXiv under licenses for non-commercial use, and in journals under various copyright agreements, are now collecting money from my university, which is entering into business agreements in order to remain on the frontier of research. As we enter our prompts into the LLMs, we improve the way in which they will respond to others, without, of course, quoting us. This likely happens whether we have disabled the “training” option or not – or, at least, there is no way to reliably tell, as there is no independent way to audit the inner workings of an AI company.
You would think that a machine powerful enough to outsmart humans would not require such levels of opacity. That it would be able to rush ahead without training data from the last few years of research. That the prompts and any available information on its path to discovery would be made available for the benefit of its future users. That its outputs would be readable and compatible with formalized proofs, and that by solving 400 problems it would generate 1000 conjectures, as humans would have done. Clearly, the machine is not there yet.
But, for the purposes of capturing scientific production, maybe it doesn’t need to get there at all.
Maybe all it takes is vibes taking precedence over expert assessment, and a mathematical community in a state of paralysis. Professional organizations unable to utter a word about the startling misconduct and the theft of intellectual property. Institutions collecting petty donations and staying silent on these same issues. Self-appointed advisory bodies unable to make a determination of whether their advice was followed. A few Fields medalists formulating amateur predictions and repudiating the goals of the medal. And a political environment which was already hostile to science letting the private sector enjoy the gold rush, without any oversight on safety and intellectual property, or any robust plans to create public AI infrastructure for science.
That’s all it will take to convince a generation of aspiring scientists to switch course, and for our society to stop nurturing mathematical skills and understanding. The stultification of humanity will bring the goal of a superhuman machine one step closer.
Received 26 September 2026, revised 20 October 2026.
Add to the discussion