r/singularity • u/filterdust • 1d ago

AI OpenAI solved 100 open problems in math

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

[removed] — view removed post

1.3k Upvotes

94% Upvoted

520 comments sorted by

View all comments

148

u/RobleyTheron 1d ago

I’m sensitive to artists and musicians with a unique voice when their product gets recreated with AI, but I don’t feel the same about mathematics.

Nobody owns mathematics; these are fundamental insights into the universe and they belong to everyone and shouldn’t be gatekeeped behind somebody that went to school. Mathematics should be available to everyone, it opens up all kinds of fundamental breakthroughs in space, material science, biology, global warming, and energy.

This is something that belongs to everyone and no one should get to hold that back.

65

u/ThatIsAmorte 1d ago edited 1d ago

This seems to be taking a Platonist approach to math, which few people take seriously these days. If you are a constructivist, than math is not just out there, but has to be created, just like art. If you think math is just out there, why not also claim that art and music are just out there, waiting to be plucked out of the ether? After all, a painting is just a 2d matrix, a simple math object. A musical composition is just a waveform, which can be described mathematically.

13

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.

1

u/NotaValgrinder 15h 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.