I spent from 1961 to 1965 on the subject NP versus P, and in 1966 made the conjectures NP≠P and NP≠NP∩coNP=P. The "Traveling Salesman Problem" is the NP predicate:
TSP(G,T)=[there is a tour in G cheaper than tour T in G].
I became excited in 1961 to show that TSP(G,T) is coNP by finding an NP description of a set of inequalities whose solution set is the convex hull of all the 0,1 incidence vectors of tours in G. I failed, and so in 1966 I conjectured that TSP is not in P. The ideas did however show various other problems to be in P including the "Chinese Postman Problem". I will also explain how current cryptography challenges "NP∩coNP=P".
This talk is also invited to be a public lecture in the 9th Shanghai Conference on Combinatorics.