Public

Faster-than-light neutrinos? Boring... let's see something

"I am writing up a proof that Peano arithmetic (P), and even a small fragment of primitive-recursive arithmetic (PRA), are inconsistent. This is posted as a Work in Progress at http://www.math.princeton.edu/~nelson/books.html

A short outline of the book is at:

http://www.math.princeton.edu/~nelson/papers/outline.pdf

The outline begins with a formalist critique of finitism, making the case that there are tacit infinitary assumptions underlying finitism. Then the outline describes how inconsistency will be proved. It concludes with remarks on how to do modern mathematics within a consistent theory."

Thanks to +David Roberts and +Andres Caicedo for pointing this out.

*really*revolutionary. Edward Nelson, a math professor at Princeton, is writing a book called*Elements*in which he claims to prove the**inconsistency of arithmetic**. He writes:"I am writing up a proof that Peano arithmetic (P), and even a small fragment of primitive-recursive arithmetic (PRA), are inconsistent. This is posted as a Work in Progress at http://www.math.princeton.edu/~nelson/books.html

A short outline of the book is at:

http://www.math.princeton.edu/~nelson/papers/outline.pdf

The outline begins with a formalist critique of finitism, making the case that there are tacit infinitary assumptions underlying finitism. Then the outline describes how inconsistency will be proved. It concludes with remarks on how to do modern mathematics within a consistent theory."

Thanks to +David Roberts and +Andres Caicedo for pointing this out.

*I have no idea if Nelson's proof is correct!*He has, however, done good mathematics in the past: in his PhD thesis he was the first to rigorously construct an interacting quantum field theory.View 23 previous comments

- I forget how 'Hot Rock' goes... but I've read pretty much all his stuff.Sep 29, 2011
- It's about an orphaned planet which was dislodged from its Sun, and spent the next few billion years hurtling through space alone. Yet, mysteriously, its surface is still warm, and indeed supports simple life. This turns out to because... [that's as far as I've got].Sep 29, 2011
- Gee, I don't think I've read this one! Don't give it away.Sep 29, 2011
- +Terence Tao "but personally I think that the FTL neutrino confirmation will arrive first" -- well, yeah....Oct 3, 2011
- But Nelson had the coolest sentence in the copyright page of his book: "All numbers in this book are fictitious, and any resemblance to actual numbers, even or odd, is entirely coincidental."Oct 5, 2011
- It's a nice read. I got it as a gift. +David BarzagaJan 16, 2014