It Is Not That We

It Is Not That We Propose A Theory And Nature May Shout No; Rather, We Propose A Maze Of Theories, And Nature May Shout Inconsistent.

That Sometimes Clear ... And Sometimes Vague Stuff ... Which Is ... Mathematics.

It Would Be Wrong To Assume That One Must Stay With A Research Programme Until It Has Exhausted All Its Heuristic Power, That One Must Not Introduce A Rival Programme Before Everybody Agrees That The Point Of Degeneration Has Probably Been Reached.

The Classical Example Of A Successful Research Programme Is Newton's Gravitational Theory: Possibly The Most Successful Research Programme Ever.

Mathematics Does Not Grow Through A Monotonous Increase Of The Number Of Indubitably Established Theorems But Through The Incessant Improvement Of Guesses By Speculation And Criticism, By The Logic Of Proofs And Refutations.