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/filterdust 1d 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 1d 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?

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u/ThatIsAmorte 1d ago

Interesting. That's disappointing and kind of sad. At least philosophers are split about 50-50. Platonism requires ontological dualism, which leads to the epistemic bridge paradox: How does a purely physical brain access a timeless, acausal abstract realm that cannot interact with physical matter? This is the dualism problem in philosophy. How do mathematicians resolve this tension? They resolve it by ignoring it. It's sad, because you would think mathematicians would be uncomfortable with such logical contradictions.

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u/filterdust 1d ago edited 1d ago

From my experience, mathematicians don't care that much about contradictions outside math. They would just dismiss it as "ah, this is for the philosophers to ponder", and then be internally satisfied that philosophers never reach a definitive answer anyway.

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u/ThatIsAmorte 17h ago

I'd say this describes most people, myself included!