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I was studying philosophy of AI when a question came to my mind.

I'd like to write an essay (both informative and argumentative) about the state of the art in Artificial Intelligence advancing the mathematical knowledge. Therefore, I'd like to get references about:

  1. examples of intelligent systems displaying mathematical creativity;
  2. characterisations of the kind of (human) intelligence involved in mathematical discovery;
  3. the transition from proof-checkers and proof-finders to theorem-inventors machines, from a historical, algorithmic and structural point of view;
  4. areas of mathematics in which AI systems are most likely to thrive;
  5. the possibility for systems to internalise features like intuition, mathematical taste, geometric visualisation and more generally informal aspects related to the production of knowledge.

These are only some extemporaneous ideas, any further insight is welcome. Also brilliant and authoritative points of view about the (human) mathematical creation (e.g. Hadamard's one) may enlighten the matter. I know it is vast but I'll be really thankful to those who will contribute.

Disclaimer

  • This question is not answerable by "opinions", being a reference request and not a personal enquiry.
  • A similar question has been closed for "not being about Mathematics" on the Mathematics Stack Exchange, where people seem to be really jealous of their own borders.
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  • $\begingroup$ So, what is your question? I only see one question here and it's in the title. Are you asking if AI is capable of mathematical creation? After reading your post, it doesn't seem that you're looking just for that. You're looking for reference that describes different things about how AI can be applied to math. Anyway, although I find this post interesting, it might be too broad, because you may be asking for many things. So, if you can ask a specific question, then maybe it's not broad. $\endgroup$
    – nbro
    Commented May 20 at 12:15
  • $\begingroup$ @nbro It’s a reference request in order to get information to elaborate on the initial question. I did not insist on that since I am not looking for people’s views (as I’ve spelled out) but for references on the topic. I can see no contradiction or omission. The question is broad because the topic is. $\endgroup$ Commented May 20 at 12:50
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    $\begingroup$ I've not read it, except the first few lines, but maybe take a look at this paper Advancing mathematics by guiding human intuition with AI and the references there. Feel free to provide an answer to your own question, if you find it and nobody answers it meanwhile ;) $\endgroup$
    – nbro
    Commented May 21 at 14:21
  • $\begingroup$ @nbro Thank you! I’ll read it soon $\endgroup$ Commented May 21 at 16:49

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