Favorite quotations about mathematics and science

Below I have collected some of my favorite quotations. I also provide the original references of them.

“Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.”

“Remote from human passions, remote even from the pitiful facts of nature, the generations have gradually created an ordered cosmos, where pure thought can dwell as in its natural home, and where one, at least, of our nobler impulses can escape from the dreary exile of the actual world.”

Bertrand Russell (1872–1970)

[See the essay Study of Mathematics from 1907.]

“the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and there is no rational explanation for it. ...it is not at all natural that ‘laws of nature’ exist, much less that man is able to discover them... The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.”

Eugene Wigner (1902–1995)

[See The Unreasonable Effectiveness of Mathematics in the Natural Sciences which is the written version of a lecture given at New York University in 1959.]

“Life is good only for two things: to do mathematics and to teach it.”

« La vie n'est bonne qu'à deux choses: à faire des mathématiques et à les professer »

Siméon Denis Poisson (1781–1840)

[Attributed to Poisson by François Arago (1786–1853) in his Collected works of Arago Vol II in page 662.]

“I don't know what I may seem to the world; but as to myself, I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.”

Sir Isaac Newton (1624–1727)

[First appeared in 1820 in the book Anecdotes, Observations and Characters, of Books and Men by Rev. Joseph Spence (1699–1768) and there attributed to Newton by Michel de Ramsay lovag (1686–1743). The original quotation can be found in pages 158–159. There is a detailed discussion about the origin of the quoation on this website.]

« L'étude approfondie de la nature est la source la plus féconde des découvertes mathématiques. ...L'analyse mathématique... semble être une faculté de la raison humaine destinée à suppléer à la brièveté de la vie et à l'imperfection des sens. »

“Profound study of nature is the most fertile source of mathematical discoveries. ...Mathematical analysis... seems to be a faculty of the human mind destined to supplement the shortness of life and the imperfection of the senses.rdquo;

Joseph Fourier (1768–1830)

[Written in 1822 in the Preface of Fourier's Théorie analytique de la chaleur in page xiii and page xv. In the English translation it can be found in az idézetek a page 7 and page 9.]

“It is true that Fourier had the opinion that the principal object of mathematics was public use and the explanation of natural phenomena; but a philosopher like him ought to know that the sole object of the science is the honor of the human spirit and that under this view a problem of [the theory of] numbers is worth as much as a problem on the system of the world.”

« Il est vrai que M. Fourier avait l'opinion que le but principal des mathématiques était l'utilité publique et l'explication des phénomènes naturels; mais un philosophe comme lui aurait dû savoir que le but unique de la science, c'est l'honneur de l'esprit humain, et que, sous ce titre, une question de nombres vaut autant qu'une question du système du monde. »

Carl Gustav Jacob Jacobi (1804–1851)

[From a letter written by Jacobi in 1830 to Adrien-Marie Legendre (1752&ndas1833). The original text begins on the bottom of this page and ends on the next page. The words of Jacobi later became the motto of the Bourbaki group.]

“Mathematics is a part of physics. Physics is an experimental science, a part of natural science. Mathematics is the part of physics where experiments are cheap.”

« Les mathématiques font partie de la physique. La physique est une science expérimentale, une des sciences naturelles. Les mathématiques, ce sont la partie de la physique où les expériences ne coûtent pas cher. »

Vladimir Arnold (1937–2010)

[From Arnold's paper On teaching of mathematics, see also the French translation.]

„Jacobi szerint a matematika legcsodálatosabb összefüggése, hogy ugyanaz a függvény írja le egy egész számnak négy négyzetszám összegeként való előállíthatóságát, és az inga mozgását.”

“Jacobi noted as mathematics' most fascinating property, that in it one and the same function controls both the presentations of a whole number as a sum of four squares and the real movement of a pendulum.”

« Jacobi affirmait que c'était le plus grand attrait de la mathématique que de voir apparaître la même fonction dans la représentation d'un nombre entier comme somme de quatre carrés et et dans le mouvement du pendule. »

Vladimir Arnold (1937–2010)

[From Arndold's paper On teaching of mathematics. There is no reference whether Carl Gustav Jacob Jacobi (1804–1851) had this opinion or not.]

“Our brain has two halves: one is responsible for the multiplication of polynomials and languages, and the other half is responsible for orientation of figures in space and all the things important in real life. Mathematics is geometry when you have to use both halves.”

Vladimir Arnold (1937–2010)

[The last paragraph from the interview with Arnold.]

“Calculation replaces while geometry stimulates thinking.”

Jakob Steiner (1796–1863)

[The quotation is from the book A Concise History of Mathematics by Dirk Jan Struik (1894–2000).]


„Data aequatione quotcunque fluentes quantitates involvente, fluxiones invenire; et vice versa.

“Given an equation involving any number of fluent quantities to find the fluxions, and vice versa.”

Sir Isaac Newton (1624–1727)

[The quoation is known as Newton's anagram.]

“It is useful to solve differential equations. Differential equations are the language in which the laws of nature are expressed.”

Vladimir Arnold (1937–2010)

[The modern translation of Newton's anagram according to Arnold. Mentioned in the preface of his books Ordinary Differential Equations and Geometric Theory of Differential Equations.]

“But then the rigorous logic of the matter is not plain! Well, what of that? Shall I refuse my dinner because I do not fully understand the process of digestion?”

Oliver Heaviside (1850–1925)

[From Heaviside's book Electromagnetic theory in Part II in page 9.]

“Mathematics is an experimental science, and definitions do not come first, but later on.”

Oliver Heaviside (1850–1925)

[From Heaviside's paper On operations in physical mathematics in page 121.]

“Opportunity is missed by most people because it is dressed in overalls and looks like work.”


[Erroneously attributed to Thomas Alva Edison (1847–1931), see the discussion.]

“Mathematics is a dangerous profession; an appreciable proportion of us go mad, and then this particular event would be quite likely.”

John Edensor Littlewood (1885–1977)

[From Littlewood's autobiography A Mathematician's Miscellany in page 104.]

“Mathematicians grow very old; it is a healthy profession. The reason you live long is that you have pleasant thoughts. Math and physics are very pleasant things to do.”

Dirk Jan Struik (1894–2000)

[In Struik's biography at Tufts University. Struk died at age 106.]

“You cannot overestimate the stupidity of your audience. Insist on the obvious and glide nimbly over the esssential.”

„Du kannst deine Hörer nicht dumm genug einschätzen. Bestehe auf dem Selbstverständlichen und husche über das Wesentliche hinweg.“

Ernst Zermelo (1871–1953)

[Mentioned as Zermelo's principles in the book Mathematical Discovery of George Pólya (1887–1985) .]

“One can always find imbeciles to prove theorems.”

René Thom (1923–2002)

[Mentioned as Thom's principle in the interview with Arnold.]

“If I feel unhappy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy.”

Alfréd Rényi (1921–1970)

[Mentioned by Paul Turán (1910–1976) in a paper published in 1970 in the Hungarian journal “Matematikai lapok”.]

“...mathematics has the dubious honor of being the least popular subject in the curriculum... Future teachers pass through the elementary schools learning to detest mathematics. They drop it in high school as early as possible. They avoid it in teachers' colleges because it is not required... They return to the elementary school to teach a new generation to detest it.”

Time Magazine, June 18, 1956.

[Written in an article Time Magazine. It was mentioned in the preface of the book How to sole it by George Pólya (1887–1985).]

“Everyody writes and nobody reads.”

Lipót Fejér (1880–1959)

[Paul Erdős (1913–1996) mentions it in an interview.]

“Every human activity, good or bad, except mathematics, must com to an end.”

Paul Erdős (1913–1996)

[Mentioned by Bollobás Béla (1943–) in the paper az Paul Erdős and his mathematics.]