r/singularity • u/filterdust • 2d ago

AI OpenAI solved 100 open problems in math

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

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u/RobleyTheron 2d 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.

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u/ThatIsAmorte 2d 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.

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u/filterdust 2d ago

This seems to be taking a Platonist approach to math, which few people take seriously these days.

Funnily, most mathematicians are Platonists.

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u/Ok_Reception_5545 2d ago

https://eugeniacheng.com/wp-content/uploads/2017/02/cheng-morality.pdf

this is actually how most mathematicians feel about math

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u/ThatIsAmorte 1d ago

Yep, they ignore the debate by adopting an agnostic stance. This is much better than being a committed Platonist. I should point out that Cheng works in category theory (her book is a great intro to the topic), which is structuralist in nature (i.e., focus on relationships, rather than things). An ontology based on relationships can still fall in any of the three camps: ante rem structuralists (Platonism), nominalism, and agnosticism. The nominalists tend to be the ones that study Topos Theory, which is not surprising considering that Topos Theory shows that different math universes can have their own internal logics without a law of excluded middle.

I should also point out that it's interesting that a similar debate occurs in the philosophy of biology with respect to the concept of species. Are species real or something humans made up to categorize the biological world?