The history of mathematics, lacking the guidance of philosophy, [is] blind, while the philosophy of mathematics, turning its back on the most intriguing phenomena in the history of mathematics, is empty.

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

The positive heuristic of the programme saves the scientist from becoming confused by the ocean of anomalies.

Indeed, this epistemological theory of the relation between theory and experiment differs sharply from the epistemological theory of naive falsificationism.

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.

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.