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.

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

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

The proving power of the intellect or the senses was questioned by the skeptics more than two thousand years ago; but they were browbeaten into confusion by the glory of Newtonian physics.

In degenerating programmes, however, theories are fabricated only in order to accommodate known facts

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

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