Using Kepler's discovery of planetary motion as a historical analog, the conversation posits that AI has drastically lowered the cost of generating hypotheses. This shifts the primary challenge in science from creative ideation to the rigorous verification and evaluation of a flood of new, often low-quality, ideas.
Terence Tao frames AI's current strength as its ability to explore a vast 'breadth' of possibilities, such as systematically applying every known mathematical technique to a problem. However, it lacks the human expert's 'depth' of understanding, intuition, and ability to invent entirely new concepts when existing methods fail.
Mathematics has traditionally been an almost purely theoretical discipline. Tao predicts AI tools will revolutionize the field by enabling an 'experimental' side, allowing for large-scale data gathering and analysis to identify patterns and test the efficacy of different problem-solving approaches at scale.
Despite impressive successes on specific problems (like some Erdős problems), current AI models have a very low success rate (1-2%) on truly hard, open problems. Tao points to a key limitation: their inability to build cumulatively on partial progress within a single problem-solving session, as they lack a persistent state of understanding.
Keep pulling the thread on Terence Tao.