Here is an article that talks about how two of the most intransigent maths problems might have been solved. I have only one complaint about this article: the way it exaggerates the threat to the security of our online transactions because of the danger to internet cryptography posed by one of these solutions. I agree that the author has qualified this prediction with a big if, but the fact that people have been trying in vain for millennia to find order in the sequence of prime numbers reassures me that our cryptography systems will be safe for a while longer. I am not a mathematician, but I think it will not be that easy to take advantage of this proof and exploiting it (though the Russian mafia have been known to employ serious hackers, I think such an exploit will be beyond them - for the time being at least).