This post is a ChatGPT-generated translation of the original French essay Libres pensées sur l'intelligence artificielle, published on this blog on the same day.
We knew that 26 was the only number sandwiched between a square and a cube, but no one suspected that 2026 was special too. For mathematics, 2026 will be remembered as the year in which the mechanistic dream of Hilbert, Turing, von Neumann, de Bruijn, and many others became a reality. Artificial intelligence has finally managed to surpass human intelligence in certain respects, a turning point of historic significance.
But the realisation of this fantasy of automating mathematics terrifies many mathematicians, who had built their professional lives in the niche afforded by the impossibility of its realisation. Here we have all the cruelty of a La Fontaine fable. Even so, those who put the pursuit of knowledge and science first rejoice at this state of affairs, without losing sight of the many questions it raises.
Artificial intelligence has indeed managed to solve major mathematical problems, sometimes even with elegance and concision. So yes, the solutions found are combinations of existing knowledge, and could probably have been obtained by determined human teams. One might therefore be tempted to think that this is a matter of the sheer quantity of resources deployed. The fact remains that humans have been surpassed, and that this is probably only the beginning.
The great conjectures that mathematicians are so fond of play a social role. Yet they are held in a childish reverence that sometimes runs counter to the spirit of science. Indeed, what is most striking in the current uproar is the intensification of human passions. The amplification of natural stupidity by artificial intelligence is another important aspect of this La Fontaine fable.
The situation forces mathematicians to philosophise, and not everyone finds that easy. Not everyone has the cast of mind to understand and accept futility and absurdity without giving up. The need to believe, one's relationship to the absolute, and the cosy comfort of habit all play their part.
Even so, artificial intelligence does not have an answer to everything for now, and it can probably be proved that it never will. Anyone who uses it enough eventually comes up against its limits. The situation is therefore not so different from what we are used to. Devising statements and strategies remains possible, and artificial intelligence even opens up particular scope for exploring them.
A paradise for curious and imaginative minds, a hell for the more technically minded, who thrived on working through the mechanics, although we are all both at once. In the work of a mathematician, creativity plays an important but limited part, while a large share of the time and energy is devoted to assimilating other people's mathematics or re-assimilating one's own.
This activity of digestion is essential, and all the more so with the arrival of artificial intelligence. But perhaps the effect of artificial intelligence that is at once the most satisfying and the most unpleasant is the correction of human mathematics, present and, above all, past.
Mathematicians are under no obligation to use artificial intelligence to produce more and faster; they can also use it to take the time to produce better work and correct what already exists.
The artificial intelligence revolution is driven essentially by American and Chinese industry. The situation in Europe is dismal. A lack of long-term vision and globalising economic liberalism have all but wiped out its digital industry, and we should probably not count on herbivorous Polytechnique graduates to rebuild it.
For several decades now, Europeans have been on the receiving end of wave after wave of innovation, confining themselves to regulating it with a barrage of laws, charters, and self-righteous petitions. But by being creative only in regulation, they are engineering their own decline. The issue of wealth creation in Europe is on the verge of supplanting that of wealth distribution. Deindustrialisation in Europe is, unfortunately, a problem on a massive scale, extending beyond the digital sector.
Artificial intelligence is likely to share the fate of most technologies: commoditisation. Initially driven by monopolies, they eventually become commonplace. The ground gained by cheap, open Chinese models relative to closed, cutting-edge American models seems to point in this direction.
The sustainability of artificial intelligence is all the more pressing a question because it heightens the pressure on resources and is not immune to the crises of capitalism, which are bound to hit it. Even so, the fact that artificial intelligence can surpass human intelligence will remain, and the commoditisation of the technologies underpinning it could make it sustainable fairly quickly.
This increasingly computerised world is also increasingly fragile and increasingly evil. When will we see vast communities of resisters who have pulled the plug once and for all on that fruit of the devil, computing? Yet they will not escape perversion, a human passion.
Artificial intelligence of course affects all of society and all disciplines, particularly the neighbouring disciplines of theoretical physics and computer science, perhaps even more strongly than mathematics. The organisation of science had already reached a considerable degree of absurdity and mediocrity, and the explosive arrival of artificial intelligence forces us to reinvent the way knowledge is accumulated and disseminated.
The medium- and long-term effect of artificial intelligence on the number of mathematicians is a legitimate yet navel-gazing concern, one that can naturally cause anxiety. From society's point of view, mathematicians are not an end in themselves; rather, they are a means of developing knowledge, keeping it alive, and passing it on. Our collective social responsibility is to move with the times and put an appropriate form of organisation in place, and that is not straightforward.
My personal dream is that mathematicians should embrace artificial intelligence as a continuation of their history, and establish free and open-source artificial intelligence models that could play a universal role similar to that of arXiv. Such open models could be regarded as large-scale research facilities. European mathematicians may be even better placed than others to carry such a universal project forward.