The question
A proof is an argument that shows a mathematical statement must be true. For most of history, proofs were written by people, for people: a reader could follow each step and see why the result holds.
Computers have changed that. In 1976 the four colour theorem, the claim that any map can be coloured with four colours so that no two neighbouring regions match, was proved with heavy computer help, and many mathematicians were uneasy that no person could check every case by hand. Today AI systems are beginning to produce proofs too.
Ajay's argument
Drawing on the mathematician Terence Tao, Ajay argues that a proof nobody understands is not the same as mathematical knowledge. A computer may confirm that something is true, but understanding why it is true is what lets mathematicians build on it, connect it to other ideas and teach it.
It links back to his point about learning. Getting the right answer from an AI is not the same as knowing it yourself.
Decide for yourself
- If a computer checks every step of a proof, should we trust the result even if no one understands it?
- Is knowing that something is true different from knowing why it is true? Give an example from your own studies.
- Would you trust a bridge designed by an AI whose calculations no engineer could follow?