“Deep theorems were scarce and difficult and so became an effective mechanism to identify deep thought. AI has broken this system.”

[This is a guest post by Bryna Kra. This blog post was initially written in a different file format and converted using AI. — T.] For generations, mathematicians have treated the production of theorems as a clear measure of success. The stronger the theorem, the deeper the proof, the more surprising the connections, the greater the achievement. Positions and prizes are based on these theorems and the mathematicians making the breakthroughs set the directions for future research. But theorem production was only part of what we cared about. It was a proxy for something harder to measure: understanding. A major breakthrough meant that years were invested in learning a subject and uncovering hidden aspects, accompanied by work to make the answer apparent to the community. Deep theorems were scarce and difficult and so became an effective mechanism to identify deep thought. AI has broken this system. Artificial intelligence has lowered the cost of producing sophisticated proofs. As the…