There is no proof in science and we observe it doesn't suffer from wholesale collapse. Things being proved in mathematics are unlikely to be wildly wrong even

There is no proof in science and we observe it doesn't suffer from wholesale collapse. Things being proved in mathematics are unlikely to be wildly wrong even without proof. Fermat's theorem being an example of one that took a very long time to be proved and basically nothing changed when it was. We were already convinced it was true by brute force failure to find a counter example. This lack of proof but search for counter-example is basically the scientific method. Is A equivalent to B? Prove it? Or write a for-loop and test it for values you care about. If you think you've proved it you probably write the for loop anyway (where such a thing is feasible). So do we actually /need/ proof in math at all or is it just good fun and properly satisfying for mathematicians? Perhaps these are two extremes and case-by-case we could plot them somehwere between the two. Some right up hard against one side or the other. So is P=NP? There is no proof. You probably aren't going out on a massive limb to have a view on the matter without it.