Starting from literally nothing, it derived all of the geometric propositions in Euclid’s Elements in a matter of seconds. Then it proceeded to produce a number of geometric theorems of human interest that were never noticed by any previous Euclidean geometers, classical or modern.
Where do you get these detailed claims about the program? I don’t see anything like them in the book or here or here
Starting from literally nothing, it derived all of the geometric propositions in Euclid’s Elements in a matter of seconds.
Where do you get these detailed claims about the program?
Just to point out the obvious, your first link certainly does say that
Once you know the ansatz, you can have the machine, discover from scratch all the statements of any bounded complexity, and prove them at the same time, either rigorously (time permitting) or semi-rigorously (if a polynomial of degree 10^100 vanishes at 10^6 random values it is most likely identically zero, just like Rabin’s pseudo-primes). This is what Shalosh B. Ekhad, XIV, did in its 2050 PLANE GEOMETRY TEXTBOOK. What is so nice about it is that it is written in a precise, and hence completely formally correct programming language, Maple, but the names of the definitions are English based. Also each statement doubles as the proof, ready to be executed by Maple. So we have a text that is even more formally correct than any logocentric human proof (recall that Bill Thurston said that a computer program is much more formally correct than a human proof), yet just as much fun to read, and in which once you read the statement, you already have the proof (modulo running it on Maple, but I already did, so you can trust me and not run it again).
Oh, yeah, I missed that Zeilberger used the phrase “from scratch,” so that explains why JH says “from literally nothing” (though I disagree), but why did you quote the rest of the passage? Do you think it suggests any other of JH’s claims?
I quoted the rest so that it was clear that the key phrase ‘from scratch all the statements’ was referring to a computational, implemented, software package for Euclidean / plane geometry in particular.
Where do you get these detailed claims about the program? I don’t see anything like them in the book or here or here
Just to point out the obvious, your first link certainly does say that
Oh, yeah, I missed that Zeilberger used the phrase “from scratch,” so that explains why JH says “from literally nothing” (though I disagree), but why did you quote the rest of the passage? Do you think it suggests any other of JH’s claims?
I quoted the rest so that it was clear that the key phrase ‘from scratch all the statements’ was referring to a computational, implemented, software package for Euclidean / plane geometry in particular.