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.

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

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.

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.

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.

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

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.