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.

Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime.

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.

One may rationally stick to a degenerating research programme until it is overtaken by a rival and even after. What one must not do is to deny its poor public record... It is perfectly rational to play a risky game: what is irrational is to deceive oneself about the risk.

The great scientific achievements are research programmes which can be evaluated in terms of progressive and degenerative problemshifts; and scientific revolutions consist of one research programme superceding (overtaking in progress) another. This methodology offers a new rational reconstruction of science.

Philosophy of science without history of science is empty; history of science without philosophy of science is blind.