A quotation by Roger Bacon
In the mathematics I can report no deficience, except that it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it; if too wandering, they fix it; if too inherent in the sense, they abstract it. So that as tennis is a game of no use in itself, but of great use in respect it maketh a quick eye and a body ready to put itself into all postures; so in the mathematics, that use which is collateral and intervenient is no less worthy than that which is principal and intended.
Quoted in J Fauvel and J Gray, A History of Mathematics: A Reader, 1987.
Et harum scientiarum porta et clavis est Mathematica.
Mathematics is the door and key to the sciences
For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first ... gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, ... It likewise treats of the size and shape of the habitable earth ... All this information is secured by means of instruments suitable for these purposes, and by tables and by canons .. For everything works through innate forces shown by lines, angles and figures.
Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of the world.
Quoted in C B Boyer, A History of Mathematics (New York 1968)
There are four great sciences ... Of these sciences the gate and key is mathematics, which the saints discovered at the beginning of the world.
... mathematics is absolutely necessary and useful to the other sciences.
A little learning is a dangerous thing but none at all is fatal.
Quoted in Des MacHale, Wisdom (London, 2002).
Prudens quaestio dimidium scientiae.
Half of science is asking the right questions.
Neglect of mathematics works injury to all knowledge, since one who is ignorant of it cannot know the other sciences of the things of this world. And what is worst, those who are thus ignorant are unable to perceive their own ignorance and so do not seek a remedy.
The strongest arguments prove nothing so long as the conclusions are not verified by experience. Experimental science is the queen of sciences and the goal of all speculation.