However http://xkcd.com/955/ applies in spades here. While it would be really interesting if Peano arithmetic is inconsistent, it is also really unlikely. For those who don't know the Peano axioms, see http://en.wikipedia.org/wiki/Peano_axioms.
Of those axioms, nobody has any trouble with any axiom other than the last one. Which is induction. His claim boils down to stating that allowing proof by induction leads to contradictions. But there is a pretty big tower of theorems needed to get there. Most people's guess is that he has made a mistake. If he hasn't, then it is still far more likely that some theorem in that tower is wrong than that induction leads to contradictions.
However if he proves to be right, in that tiny sliver, this will be really cool.
Now for the people who think I'm wrong, anyone want to wager $200 on the outcome? :-)
I'll wager $200, but first I need to know the odds offered. Also, I will want my payment even if you can prove that $5 == $200 (1 to 1 odds assumed) if Peano arithmetic is inconsistent.
However http://xkcd.com/955/ applies in spades here. While it would be really interesting if Peano arithmetic is inconsistent, it is also really unlikely. For those who don't know the Peano axioms, see http://en.wikipedia.org/wiki/Peano_axioms.
Of those axioms, nobody has any trouble with any axiom other than the last one. Which is induction. His claim boils down to stating that allowing proof by induction leads to contradictions. But there is a pretty big tower of theorems needed to get there. Most people's guess is that he has made a mistake. If he hasn't, then it is still far more likely that some theorem in that tower is wrong than that induction leads to contradictions.
However if he proves to be right, in that tiny sliver, this will be really cool.
Now for the people who think I'm wrong, anyone want to wager $200 on the outcome? :-)