Given a graph, for every pair of vertices s,t find the max flow that can be sent from s to t, if every vertex and edge has unit capacity, and every edge an infinite (very big) negative cost, we’ll get the longest path from s to t. Since MCMF Is P, therefore P=NP. QED
If you can’t find the bug in the previous algorithm, send me my Millennium Prize.
PS. do you know some other P=NP proofs?