The article doesn't really tell us much about the "why" unfortunately. Diophantine equations are introduced but all the interesting stuff is promised in future articles which haven't come yet. All the reader can take from this is that these equations lead to some "profound hidden structures" without a good idea what they are.

I get that it's hard to wrap one's head around the Langlands program but I'd love to see at least more exposition on the following statement:

>inventing the Euclidean algorithm is essentially equivalent to inventing unique prime factorization