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.

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

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.

Research programmes, besides their negative heuristic, are also characterized by their positive heuristic.

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

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.