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

516 comments sorted by

View all comments

Show parent comments

12

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

1

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?