It went/goes something like this:

"It [the abc conjecture] resembles a false proposition in that A GREAT DEAL of results would follow from its veracity".

I may have read it in the comments of a discussion on Mochizuki's papers on IUT sometime in 2012; the thing is that I don't recall if it was on MO or on a blog post (maybe one by J. Ellenberg?) mentioned in actual MO thread.

Does any of you remember reading this witty remark once? If so, could you please tell me where I can find it?

Let me thank you in advance for your attention and support.


  • 6
    Why post this at meta and not at MO? Meta is for discussing how the MO site works, its policies, etc. – Todd Trimble Mar 23 '17 at 10:42
up vote 8 down vote accepted

I think the remark you want is on page 361 of the Princeton Companion to Mathematics.

Edit in response to a comment - the paragraph in question follows:

The ABC conjecture has many other marvelous consequences; for a delightful survey, see Granville and Tucker (2002). In fact the ABC conjecture and its generalizations can be used to prove so many things that I have joked that it is beginning to resemble a false statement, since a false statement implies everything. But probably the ABC conjecture is true. Indeed, though a bit harder to see, the Erdős-Ulam probabilistic argument can be modified to provide heuristic evidence for it, too.

  • 1
    Yes, this is just what I was looking for. Thanks a lot for your support! – José Hdz. Stgo. Mar 20 '17 at 23:06
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    It would be good if you write down what it is.... – Praphulla Koushik Sep 21 at 10:04
  • Hello, thanks for edit.. When I first clicked on that link which says page 361, it did not show any thing.. That is why I asked... Now it is showing correctly... May be I went to next page and did not realize so I saw some blank page in with some note written in Chinese.. – Praphulla Koushik Sep 22 at 6:44
  • @PraphullaKoushik Sorry, I had linked to the Japanese (not Chinese) Google Books site. – S. Carnahan Sep 23 at 1:58
  • The selection of pages that are and are not shown in google books seems unpredictable. Today I was not able to see the quote, but I was able to see the author. Tomorrow, or for someone else, this may be different so I will record the author's name here: Carl Pomerance. – Vincent Sep 24 at 14:25

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