My favorite irrationality of sqrt(2) proof is the paper: Robert Gauntt & Gustave Rabson, The irrationality of \sqrt{2}, American Mathematical Monthly 63(4) (1956) 247. Almost the entire paper: "a^2=2b^2 cannot have a non-zero solution in integers because the last non-zero digit of a square, written in the base three, must be 1, whereas the last non-zero digit of twice a square is 2." On May 29, 2018, at 12:59 PM, Mike Stay <metaweta@gmail.com<mailto:metaweta@gmail.com>> wrote: My favorite irrationality proof is one I heard from John Baez. Suppose the cube root of two were not irrational; then there would be two positive integers p, q such that p/q = ∛2. Multiplying both sides by q and cubing, we get p³ = 2q³ = q³ + q³, which has no solutions in the positive integers by Fermat's Last Theorem! On Tue, May 29, 2018 at 10:17 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: Wow! That was quick work; thanks! Here's the passage in question (from Lehman-Haupt's 1992 review of Jerry King's book "Ruminations of a Mathematics Lover"): "Moreover, he flops as a priest of mathematics, failing as he does to convey the esthetics of his subject. He stakes his case on a proof of the irrationality of the square root of 2, but this reader did not feel any mysterious resonance in his logic, which throws one tiny monkey wrench in his thesis that the beauty of math is accessible to each of us." (Do any of you know this book? Did you like/dislike it?) Jim On Tue, May 29, 2018 at 12:05 PM, Lucas, Stephen K - lucassk < lucassk@jmu.edu<mailto:lucassk@jmu.edu>> wrote: Check out this New York Times article from 1992. https://urldefense.proofpoint.com/v2/url?u=https-3A__www.nytimes.com_1992_05... times-ruminations-of-a-mathematics-lover.html On May 29, 2018, at 11:57 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com><mailto:j amespropp@gmail.com<mailto:amespropp@gmail.com>>> wrote: Thanks! Couldn't find the question there, so at least I'm asking something I haven't asked before. It's possible that the person in question was Christopher Lehmann-Haupt. Jim Propp On Tue, May 29, 2018 at 11:20 AM, Tom Duff <td@pixar.com<mailto:td@pixar.com><mailto:td@pixar. com>> wrote: I believe everything is in https://urldefense.proofpoint.com/v2/url?u=https-3A__ mailman.xmission.com_cgi-2Dbin_mailman_private_math-2D&d=DwICAg&c= eLbWYnpnzycBCgmb7vCI4uqNEB9RSjOdn_5nBEmmeq0&r=vge6KOo90zMf7Wx14WFtiQ&m= H1Qo6za3ir2-GZIcigqCHlVwryzc_8UKd-R4ZVhLwoM&s=ggyncGT05kVjYANDno93M0If3vu- YDf1Jj2oyhZsFHY&e= fun.mbox/math-fun.mbox You may have to remember your math-fun password to get it. On Tue, May 29, 2018 at 8:14 AM, James Propp <jamespropp@gmail.com<mailto:jamespropp@gmail.com>> wrote: Some fancy-pants literary intellectual like Louis Menand or Anatole Broyard once unabashedly professed a failure to see the beauty in the proof of the infinitude of the primes (or maybe it was the proof of the irrationality of the square root of two). Does anyone know the quote I'm thinking of? I apologize if I've asked this before, especially if it was in the past five years. (Is there a single document somewhere out there that has absolutely everything that's ever been posted to math-fun?) Thanks, Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__ mailman.xmission.com_cgi-2Dbin_mailman_listinfo_math-2Dfun&d=DwICAg&c= eLbWYnpnzycBCgmb7vCI4uqNEB9RSjOdn_5nBEmmeq0&r=vge6KOo90zMf7Wx14WFtiQ&m= H1Qo6za3ir2-GZIcigqCHlVwryzc_8UKd-R4ZVhLwoM&s=iSUimRMwTuCn5epaCxfT_BIvie- ptuDdYT2rpoGmIT4&e= _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__ mailman.xmission.com_cgi-2Dbin_mailman_listinfo_math-2Dfun&d=DwICAg&c= eLbWYnpnzycBCgmb7vCI4uqNEB9RSjOdn_5nBEmmeq0&r=vge6KOo90zMf7Wx14WFtiQ&m= H1Qo6za3ir2-GZIcigqCHlVwryzc_8UKd-R4ZVhLwoM&s=iSUimRMwTuCn5epaCxfT_BIvie- ptuDdYT2rpoGmIT4&e= _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com><mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__ mailman.xmission.com_cgi-2Dbin_mailman_listinfo_math-2Dfun&d=DwICAg&c= eLbWYnpnzycBCgmb7vCI4uqNEB9RSjOdn_5nBEmmeq0&r=vge6KOo90zMf7Wx14WFtiQ&m= H1Qo6za3ir2-GZIcigqCHlVwryzc_8UKd-R4ZVhLwoM&s=iSUimRMwTuCn5epaCxfT_BIvie- ptuDdYT2rpoGmIT4&e= _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg... -- Mike Stay - metaweta@gmail.com<mailto:metaweta@gmail.com> https://urldefense.proofpoint.com/v2/url?u=http-3A__www.math.ucr.edu_-7Emike... https://urldefense.proofpoint.com/v2/url?u=http-3A__reperiendi.wordpress.com... _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com<mailto:math-fun@mailman.xmission.com> https://urldefense.proofpoint.com/v2/url?u=https-3A__mailman.xmission.com_cg...