Mathematicians Confront AI. The Proofs Were Never The Point. The Handwringing Is Telling.
Dr Henry Bradford writes in The Guardian that recent AI breakthroughs in mathematics have surpassed what he would have believed possible mere months ago, forcing the field to ask whether its purpose is theorem-proving or something deeper. He now considers it foolhardy to bet against AI achieving superhuman capabilities across all areas of mathematical thought in the coming years. The question, he insists, is what society actually values in human intellect.
This illustrates a concept I like to call the substitution trap. When a machine matches humans at a cognitive task, the real question is never whether the task survives. It is whether the task was ever the point. Mathematics, it turns out, may have been valued for the beauty of human struggle rather than the correctness of output. The mechanism here is teleological displacement: AI forces a field to rediscover its actual purpose by automating away its stated one.
Dr Henry Bradford authored the piece in The Guardian dated 27 August 2026, reflecting on AI breakthroughs that even months earlier he would have found incredible.
- Open a consumer AI assistant and ask it to prove something elementary, like the infinitude of primes. Read the proof and notice whether you feel admiration for the reasoning or nothing at all.
- Now attempt to write your own proof of the same theorem by hand, using only pencil and paper. Observe the difference in what you value about each effort.
- Write one sentence describing what you think mathematics is for. That sentence is your answer to Bradford's question, and it probably has nothing to do with the proof itself.