Do you believe P=NP?  

I've seen some mathematicians say that if P=NP their work would be worthless and restricted to enunciating theorems. They seem to believe that there exist an almost philosophical impediment to P=NP. Do you agree with that? Does the possibility of P=NP bother you?



Do you believe P=NP?
Contrary to a popular misunderstanding: if P = NP, then the proof of any statement $A$ can be found by an algorithm in time polynomial *in the length of the shortest proof of $A$*, not in the length of $A$ itself. Moreover, the exponent of the polynomial could easily be so large as to make this algorithm practically worthless. But most importantly: the shortest, machine-generated, proof of some theorem is highly unlikely to be the most elegant, illuminating, or just human-comprehensible, proof. Thus this idea that under P = NP, mathematics would be reduced to “enunciating theorems”, is completely misguided.


