Will Intellectual Bulldozers Solve Math?

under science research AI chronicle AI chronicle   Read time: 3 min.

An AI has just disproved an 80-year-old mathematical conjecture, where the best human minds failed for decades. It is a feat that invites us to rethink, well beyond mathematics, what artificial intelligence really changes about our professions.

An AI overcomes a central Erdős conjecture

Imagine n points placed on a plane. How many pairs of points can be separated by a distance of exactly 1? In 1946, the mathematician Paul Erdős conjectured that this number of pairs could not grow beyond a certain limit. Eighty years later, an AI has just disproved this conjecture by constructing, for a given n, a set of points containing more such pairs than Erdős believed possible.

This result is striking: it concretely demonstrates that an AI can solve problems on which the best mathematicians stumbled for decades. It is part of a broader trend: AIs are gradually becoming capable of handling complex formal problems, and computer scientists like me are turning to them more and more.

How does an AI achieve such results? It draws on encyclopedic knowledge: the entirety of mathematical publications, public computer code, and results from sometimes distant fields. Here, for example, tools from number theory were brought to bear on a geometry problem. The AI can also tirelessly explore leads that each have only a small chance of succeeding, something a human would not do for lack of time or motivation. This power is multiplied when the AI is paired with an automatic verification program, able to validate or invalidate each lead in real time. In the Erdős case, the AI proposed a first draft of the construction; mathematicians at OpenAI then refined it and verified it.

An AI is to the intellect what a bulldozer is to a construction site: remarkably powerful for certain tasks, but incapable of carrying out every step needed to build a house. A construction project requires plans upstream and finishing work downstream. Likewise, all mathematical research begins with something the AI does not do: asking the right question. Erdős was famous for precisely that, his ability to formulate questions that seemed simple but profoundly pushed back the frontiers of mathematics.

Yet asking a structuring question earns no prize. The rewards go to those who prove difficult theorems, the most visible and most glorified task. When AI excels at that task, it would be tempting to conclude that it is “doing the math” for us. That would be a mistake. The real question lies elsewhere: how do we reassess what truly matters in intellectual work, now that some of its steps can be automated? This question applies to every profession. Just as we do not measure the progress of a construction project by the cubic meters of earth a bulldozer has moved, we cannot judge the progress of intellectual work by the number of lines of code or pages of reports produced, because thanks to AI, volume has become easy.

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