It is true that Fourier had the opinion that the principal aim of mathematics was public utility and explanation of natural phenomena; but a philosopher like him should have known that the sole end of science is the honor of the human mind, and that under this title a question about numbers is worth as much as a question about the system of the world.
Source: N. Rose Mathematical Maxims and Minims, Raleigh NC:Rome Press Inc., 1988.
The most distinctive characteristic which differentiates mathematics from the various branches of empirical science, and which accounts for its fame as the queen of the sciences, is no doubt the peculiar certainty and necessity of its results.
Carl G. Hempel
Source: "Geometry and Empirical Science" in J. R. Newman (ed.) The World of Mathematics, New York: Simon and Schuster, 1956.
The value of dissent is not purely negative; it does more than protect us from error. It often points to the truth. One could make a good case for the proposition that the heroes of science, the arts, and the professions have been dissenters.
There is only one nature - the division into science and engineering is a human imposition, not a natural one. Indeed, the division is a human failure; it reflects our limited capacity to comprehend the whole.
The study of logic becomes the central study in philosophy: it gives the method of research in philosophy, just as mathematics gives the method in physics. . . . All this supposed knowledge in the traditional systems must be swept away, and a new beginning must be made. . . . To the large and still growing body of men engaged in the pursuit of science, . . . the new method, successful already in such time-honored problems as number, infinity, continuity, space and time, should make an appeal which the older methods have wholly failed to make. The one and only condition, I believe, which is necessary in order to secure for philosophy in the near future an achievement surpassing all that has hitherto been accomplished by philosophers, is the creation of a school of men with scientific training and philosophical interests, unhampered by the traditions of the past, and not misled by the literary methods of those who copy the ancients in all except their merits.
Bertrand Russell (1872 - 1970)
Source: Our Knowledge of the External World, as a Field For Scientific Method in Philosophy