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A nice easy explanation of the abc conjecture, pointed out by +Nic Johns.  It's clear, and I also like James Grime's style of explaining math in a cramped bedroom with bizarre decorations, writing equations on brown wrapping paper on his bed.  This is the life you choose when go into math.   :-)
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Mme Amy
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Speaking of conjectures, one leaps to certain conjectures about a person who's bedroom is decorated with pigeon wall paper and mannequins. 

But it is interesting what he's talking about.
 
Just a typical math grad student.  But this guy's actually on the faculty at Cambridge University.  I guess property is so expensive there that junior faculty can only afford to live in garrets.
Mme Amy
 
I just love geeks.  I married one.  They're weird in a fun way.

It helps that I'm a nerd, too.  ;)
 
The example he chose on the left is one that's a bit trivial for the purposes of demonstrating that the factors of all the terms multiply to a greater product than c. I mean, c in this case has no repeating factors, so of course its factors multiplied by any positive number greater than 1 are going to have a product that will be greater than itself.

Let him choose a new example for the rad(abc) > c example, where c has repeating factors. It won't change anything, but it'll be a slightly less self-evident example.
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