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.

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.

There is no falsification before the emergence of a better theory.

Einstein's results again turned the tables and now very few philosophers or scientists still think that scientific knowledge is, or can be, proven knowledge.

That sometimes clear ... and sometimes vague stuff ... which is ... mathematics.

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.