It is really pleasing that Nash, the tortured genius, produced such staggering work in pure areas like geometry and PDEs, where he made astonishing advances that cannot be gainsaid.
Because his other, probably even more famous work - the Nash Equilibrium - was an 'advance' of a very dubious kind.
No problem with the maths (not that I am equipped to judge): as with so much in the pseudo-science of 'economics' it's the applications. In the Real World - the one that matters - the simplifying assumptions behind so many theories just do not hold to the necessary degree for the edifices that are constructed on those foundations to be considered safe.
No engineer would be permited to build a bridge on similarly flaky physical principles. But pontificating economists and econometricians, wildly layering unjustified wobbly assumptions one upon another as though they were proper foundation-stones, infect the thought-processes of politicians and regulators. Yes, and sometimes even businessmen, who can frequently be conned into paying tens of thouands for 'forecasts' that are quite literally not worth the paper they are printed on (as a glance at the disclaimers in 6-point at the bottom of the document make clear).
The Nash Equilibrium is mis-applied all over the place: within the models used to generate price forecasts - well, more fools the folk who buy them - but more seriously by regulators who reckon they can thereby 'understand' the markets they intervene in and supervise. The flamboyant Taleb* rants against misuse of the Gaussian, but I'd say misuse of Nash is worse - not least, because it's generally less obvious; embedded deep, unacknowledged, its limitations less well know. And idiot businessmen make speculative decisions that impact their shareholders; but idiot regulators make decisions that affect us all.
Nash's Nobel prize is therefore a rather depressing commentary on the ways of the world. So much the better that he won the great maths prizes as well.
* Don't read Black Swan, he'd gone OTT by then - read Fooled By Randomness