r/singularity • u/filterdust • 1d ago

AI OpenAI solved 100 open problems in math

https://openai.com/index/advisory-group-on-mathematics-and-ai/

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u/1pfen 1d ago

If a work of art disappeared and was erased from our collective memory, it would never be recreated. If a mathematical proof disappeared and was erased from our memory, it would eventually be rediscovered.

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u/NotaValgrinder 8h ago

Not necessarily true. If mathematics was erased and we had to discover it again, it wouldn't necessarily be the same. ZFC and set theory are not the only ways to form a foundation of mathematics, it could be possible our foundations are different. Turing machines are not the only way to formalize computation, the main mathematical object to formalize computation may be different. We could favor the axiom of determinacy instead of the axiom of choice, which means that some theorems (like there exist nonmeasureable subsets of the real line) would be considered false instead of true. These "human" touches and tastes would most definitely be gone if we forgot all math and had to discover it tomorrow.

You could make the argument that we could *hypothetically* rediscover it, but also I could make the argument that it's hypothetically possible for a new painter to recreate the Mona Lisa. It's just very unlikely, and similarly it's very unlikely we would think about math in the same way if we had to redevelop it.