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 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.

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.

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

Man's respect for knowledge is one of his most peculiar characteristics. Knowledge in Latin is scientia, and science came to be the name of the most respectable kind of knowledge.

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.