Science furthers ability, not knowledge. The value of having rigorously pursued a rigorous science for a time does not exactly derive from the results obtained from it: for these will be a vanishingly small droplet in the ocean of things worth knowing. But there will eventuate an increase in energy, in reasoning capacity, in toughness of endurance; one will have learned how to achieve an objective by the appropriate means. To this extent it is invaluable, with regard to everything one will later do, to have once been a person of science.

— Friedrich Nietzsche (1878)

Without mathematical figures there is no mathematical method; and this is a mathematical truth for me, just like the proposition that every quantity is equal to itself: from words and explanations one can extract neither more nor less than whatever one puts into them. The entire certainty of mathematics depends upon the nature of its language; the necessity of all proofs depends upon the poetic license to conceive of metaphysical points, lines, and surfaces that are physically impossible. What Demosthenes calls delivery, Engel calls mimicry, and Batteux calls imitation of beautiful nature — for me, this is language, the instrument and criterion of reason, as Young says. Herein lies pure reason together with its critique, and the eternal boundary disputes will continue for as long as language does not cease to prophesy and to produce knowledge.

— Johann Georg Hamann (1785)