2023-05-10 15:00:17
CLike everyone else, mathematicians are wondering if ChatGPT will transform their business in depth. The first tests are inconclusive and encourage some to reject this tool altogether. It is true that there are disturbing errors.
When I asked GPT for some examples of important theorems, he first explained to me that the question was delicate, because not everyone agrees on the meaning of the word “important” in this context, but that he was going to give me three examples which seemed to him to be consensual. It was a great start.
The first two examples were completely on point, but the third made me jump. Admittedly, it was a fundamental theorem, but GPT attributed it to Jean-Pierre Serre in 1974, whereas any mathematician, even a beginner, knows that it is due to Evariste Galois in… 1832. All this had the look serious, and an uninformed reader would have been misled.
When I asked for a proof of the Pythagorean theorem, I received a perfectly written proof, like a rigorous proof. GPT lowered a height of the right-angled triangle to decompose it into two smaller right-angled triangles, and it then applied… the Pythagorean theorem to each of them!
A vicious circle in a demonstration is of course unacceptable. How could an artificial “intelligence” “imagine” such a fallacy? Perhaps by looking for his “ideas” on a website, somewhere on the web, which would contain lists of false evidence, intentional or not. Let’s teach our students not to be fooled by these perfectly written but completely false demonstrations, sometimes in a more subtle way.
However, the baby should not be thrown out with the bathwater. On the one hand, there is no doubt that GPT will progress very quickly. I did not hesitate, for example, to sharply criticize his proof of the Pythagorean theorem, and I dare to hope that he will not commit this gross error again. But, above all, we must learn to use it as an assistant, who knows many things.
Finding analogies
The mathematical literature becomes so immense that it is almost impossible to find one’s way through it. Avalanches of increasingly long and increasingly technical articles flood the preprint databases every day. GPT could help us summarize works in order to select those that deserve further examination. Above all, it will soon allow us to look for analogies.
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