Terence Tao on Nostr: Another role that mathematical negative results can play is to focus attention on the ...

Another role that mathematical negative results can play is to focus attention on the minimal component of a proposed technology that is in conflict with such results. For instance, regardless of whether the law of conservation of energy holds or not, it is a mathematical theorem (assuming additivity of energy) that if a machine fails to conserve energy, then at least one of its components must do so as well. And so, if forced to evaluate some complex "Rube Goldberg" design of a perpetual motion machine, it becomes natural to insist that the inventor identify at least one atomic component of this machine that violates this law. (There is a similar technique when reading papers claiming to prove a difficult result: see https://terrytao.wordpress.com/advice-on-writing-papers/on-the-strength-of-theorems/ ) (6/7)