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> I think one of the greatest difficulties in completely automated mathematics would be the discovery of mostly those things which are interesting. I've been i
by chriswarbo 11y ago
> I think one of the greatest difficulties in completely automated mathematics would be the discovery of mostly those things which are interesting.
I've been investigating this exact issue recently, and you're right.
To me the most promising approach seems to be that of "artificial curiosity", where some traditional AI algorithm is rewarded/biased by an "interestingness measure". These are usually based on subjective information, e.g. how "surprising" an observation is, given what we know.
The key seems to be a balancing act between simplicity and complexity: things which are too simple may be trivial or obvious, and therefore uninteresting; things which are too complex may be unintelligible or arbitrary, and therefore uninteresting. This phenomenon is known in psychology as the "Wundt curve".
- sanxiyn 11y agoYou may enjoy Automated Theory Formation in Pure Mathematics (2012). https://books.google.com/books?id=qJrSBwAAQBAJ https://books.google.com/books?id=qJrSBwAAQBAJ
- chriswarbo 11y agoThanks, I've not managed to get my hands on the book but have read a few snippets. I've certainly read as many of Colton's papers as I can find :) For anyone who's interested, I've got an ever-growing Bibtex file at http://chriswarbo.net/git/writing/branches/master/Bibtex.bib http://chriswarbo.net/git/writing/branches/master/Bibtex.bib which contains many references on this topic (all mixed up with completely unrelated stuff though!).
- iamcurious 11y agoThanks for the link. I'm also working on this. Would love to chat with you (or anybody else reading this), please contact me: juan at juan dot com dot uy