This week, the uncheckable proof that's stumping mathematicians.

Looking at it, you feel a bit like you might be reading a paper from the future or from outer space.

And the latest science from Comet 67P.

We are very glad that we have a very strange, dark shape, a comet.

And it's very odd, and we are very happy.

Plus toggling REM sleep on and off.

And it's Nobel Prize Week so stay tuned to hear who won what.

This is the nature podcast for October 8th, 2015.

I'm Kerry Smith.

And I'm Adam Levy.

Jackson et al famously claimed in their 1970 thesis

that ABC is as easy as one, two, three.

Well, Michael Jackson and his colleagues

can't have been talking about

the infamous ABC conjecture. This fiendish

maths problem is the subject of a feature this week written by Davdey Castelvecci. It's one of

those ideas that could shake the foundations of things you thought you knew about, like addition

and multiplication. It's called the ABC Conjecture because it hasn't got a proof yet.

Well, actually, that's not quite true. One man has written a proof, but it's so complicated

that even mathematicians in his own field are struggling to verify whether he's right. But before we

get to that, let's start with the problem.

The ABC conjecture asks what happens when we add two whole numbers together.

...