Quotes on Mathematics
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
— Charles Caleb Colton (1820), English writer, clergyman, composer of aphorisms
Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.
— William P. Thurston (2009), influential American mathematician, Fields medalist, educator, reformer
Mathematics is no more the art of reckoning and computation than architecture is the art of making bricks or hewing wood, no more than painting is the art of mixing colors on a palette, no more than the science of geology is the art of breaking rocks, or the science of anatomy the art of butchering.
— Cassius Jackson Keyser (1907), American mathematician, educator, author, popularizer of math
To some extent the whole object of mathematics is to create order where previously chaos seemed to reign, to extract structure and invariance from the midst of disarray and turmoil.
— Philip J. Davis & Reuben Hersh (1980), American mathematicians, educators, popularizers of math, co-authors of The Mathematical Experience
For what would mathematics be without the imagination of its devotees…There never was a discovery made without the urge of imagination—of imagination which broke the roadway through the forest in order that cold logic might follow.
— David Eugene Smith (1934), American mathematician-historian, educator, translator, one of the founding fathers of mathematics education as a separate discipline
The greatest perfection of mental economy is attained…in mathematics…Strange as it may sound, the power of mathematics rests upon its evasion of all unnecessary thought and on its wonderful saving of mental operations. When we employ the multiplication table in multiplying numbers of several places
and so use the results of old operations of counting instead of performing the whole of each operation anew
…we see in this simply a feeble reflexion of the intellectual activity of a Lagrange or Cauchy, who, with the keen discernment of a great military commander substituted for new operations whole hosts of old ones.
— Ernst Mach (1883), influential Austrian physicist, scientific philosopher, namesake of the Mach number used in fluid dynamics
The mystery, as well as the glory of mathematics, lies not so much in the fact that abstract theories do turn out to be useful in solving problems but in the fact—wonder of wonders—a theory meant for one type of problem is often the only way of solving problems of entirely different kinds, problems for which the theory was not intended.
These coincidences occur so frequently, that they must belong to the essence of mathematics. No philosophy of mathematics can be excused from explaining such occurrences.
— Gian-Carlo Rota (1997), influential Italian-American mathematician, educator, philosopher, author
Mathematical analysis is as extensive as nature itself…It brings together phenomena the most diverse, and discovers the hidden analogies which unite them.
If matter escapes us, as that of air and light…, if bodies are placed far from us in the immensity of space… at depths [inside the solid earth] which will be always inaccessible, mathematical analysis can yet lay hold of the laws of these phenomena.
…and what is still more remarkable, it follows the same course in the study of all phenomena; it interprets them by the same language…
— Joseph Fourier (1822), influential French mathematician, physicist, educator, author, administrator
Is mathematical analysis then…only a vain play of the mind?...Far from it; without this language most of the intimate analogies of things would have remained forever unknown to us; and we should forever have been ignorant of the internal harmony of the world...
— Henri Poincaré (1906), influential French mathematician, physicist, philosopher, educator, author of The Future of Mathematics
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that don’t look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
— Gian-Carlo Rota (1997), influential Italian-American mathematician, educator, philosopher, author
The real purpose of mathematics is to be the means to illuminate reason and to exercise spiritual forces.
— Attributed to August Leopold Crelle (1780 - 1855), German mathematician, educator, autodidact, founder of Crelle’s Journal
I hold that the study (of mathematics) began because it was useful, it continues because it is useful, and it is valuable to the world because of the usefulness of its results.
The pure mathematician must allow me to go on thinking that, if his discoveries were not being utilized continually, his study would long ago have degenerated into something like what the Aristotelian dialectic became in the fourteenth century.
— John Perry (1901), Irish engineer, mathematician, education reformer