> A sense of wonder (sometimes jocularly or cynically > abbreviated to 'sensawunda') is an emotional reaction > to the reader suddenly confronting, understanding, or > seeing a concept anew in the context of new > information. [1]

I was unfamiliar with this concept! I can surely relate to the feeling though, especially in the context of seeing the beauty of a solution to a problem, maths or otherwise.

[1]: http://en.wikipedia.org/wiki/Sense_of_wonder

My only real interest in number theory is applied number theory; i.e. the basis of many schemes of asymmetric cryptography.

Well… the weak Goldbach conjecture has been known for a couple hundred years and my understanding is it's one of those things we've suspected was true but just never found a solid way to prove that it was so.

This is a neat result, but no one's surprised, per se.

Being able to prove can also bring new pieces of mathematics.

I mostly just meant "any results in the space at all" might change things, and really can only change things for the worse (if you have deployed cryptosystems).

There are 2 mostly distinct branches of number theory additive and multiplicative. Integer factorization is related to multiplicative number theory, but not really additive (as far as is known). This is a result in additive number theory so you shouldn't be any more concerned than say if a major problem in graph theory or differential equations was solved.

The fact that the security of a cryptosystem can only degrade over time is what I find so interesting about them. You can't just plug in a cryptosystem and forget about it. If you want real security you will regularly have to make changes.