I'm currently an undergrad whose been amazed by what Turing has done for the world. I know there are plenty of other amazing individuals, but Turing's work specifically has always sounded the most interesting to me and I'm finally at the point where I can understand some of it. So my question is,...
agreed w DR about splitting this. fyi a neat crosscutting book (as you ask for) is the Turing Omnibus by Dewdney. the best book on P/ NP for beginners is now by Fortnow, "The golden ticket"... also drop by Computer Science Chat for this type of wondering... — vzn9 hours ago
@yuval and, so what? (am anticipating your answer already & my counter response...) — vzn1 hour ago
@vzn Its target audience is people not willing to make the effort to actually study the area. — Yuval Filmus19 mins ago
@yuval ?!? / sigh duly noted the questioner says he has some mathematical maturity, but lets not imagine that every meaningful pov on the field has math formulas. its written by a top expert of the field (fortnow) with excellent credentials, and is a breakthru book in the sense that its mass market and covers (previously) abstruse complexity theory and broad areas as a popular science survey. reading it is indeed studying the area (but ofc maybe not the way a hardcore insider at IAS might)... wondering if you have looked at all! (ofc let the experts disparage it in private...) — vzn14 mins ago
@vzn I haven't looked at the book, but I'm confident that reading the book is not studying the area. It's probably more like studying anecdotes about the area. In order to make progress you have to delve deeper than that. — Yuval Filmus11 mins ago
the questioner is an undergraduate and said nothing about "making progress" a concept/ agenda/ desire that sounds vaguely affiliated with research(er)s / PhDs; my original comment/ not an answer was near offhand/ throwaway on this post that is 1v )( away from being closed... note also that Turing remarkably wrote nothing whatsoever about time/ space complexity theory! although godel did mention it in his "lost letter"... the questioner does not seem to realize that... he mentioned math in the paragraph wondering about TMs, not in the 2nd part query about complexity theory... — vzn9 mins ago
> By contrast, in some versions of type theory, theorems and SETS are on equal footing. They are “types” — a new kind of mathematical object. A theorem is the type whose elements are all the different ways the theorem can be proved.
@vzn It's a quote from your link, to which I replied. (I knew about inhabited types before, but I didn't think of them as the collection of different proofs.)
@ThomasKlimpel worth reading for me or worth reading for you or worth reading for somebody else? sure post refs! am a big fan of curry-howard correspondence & auto thm proving myself, planning to do another post on auto thm proving incl Voevodsky who is apparently a real math rock star in the news lately :)
its a tricky area, not all mathematicians are enthusiastic about ATP, but proof verification might be an awesome "stealth-back-door" way/ route to penetrate into that field.
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