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nilkn 3 hours ago

An inscrutable 1000-page Lean proof may have low transmissibility amongst humans, yet extremely high transmissibility amongst AI mathematicians.

Probably AI mathematics needs a specially constructed or trained translation or compression system (likely also an AI system) that helps transmit dense Lean proofs back into human-style thinking. We may even see an entire field develop around creating human-comprehensible compressions of vast formal breakthroughs in mathematics. Such an activity would almost certainly be both art and science -- there's some objectivity in that certain abstractions or definitions inherently cover more ground more efficiently, yet there's also a deep creativity and artistry in finding compressions that are adapted to the specific 3+1D spatiotemporal intuition of the human mind. Perhaps with time this will keep a lot of the originality and creativity of research mathematics alive -- maybe with that work having even more centrality than it does today.

Instead of seeing this all as a loss of beauty in mathematics, I choose to see it as the beginning of a new age, which will bring entirely new problems to solve, yet also accelerate discovery at an exponential rate.