John_Baez

He didn't get into the news because he didn't solve a problem for which a famous mathematician (Ronald Graham) had offered a prize. Also, it's somewhat more exciting to use a huge calculation to answer a yes-or-no question that anyone can understand, rather than to count a huge number of fairly obscure gadgets: semigroups of size 10.

(Personally I love semigroups, and I think it's cool that you counted all the ones of size 10. But any story about them in the popular press would focus on the sheer size of the calculation rather than what it actually achieved.)

It turns out this only pushes back the problem. You can write down second-order axioms for arithmetic which have a unique model, but in a model of a second-order theory predicates are interpreted as sets. So, you need to choose a version of set theory, to know what a model actually is. Suppose you choose ZFC (the usual axioms of set theory). Unfortunately this itself has infinitely many models!

I explained this in a bit more detail here:

https://johncarlosbaez.wordpress.com/2016/04/02/computing-th...