Favorite Math Quotes

If you enjoy the quotes found on this site, you can find many more at the following site:

Furman University - Mathematical Quotations Server

"Mathematics is not a careful march down a well cleared highway, but a
journey into a strange wilderness, where explorers often get lost." 

W. S. Anglin

"I had a feeling once about Mathematics - that I saw it all. Depth beyond depth was revealed to me - the Byss and Abyss. I saw - as one might see the transit of Venus or even the Lord Mayor's Show - a quantity passing through infinity and changing its sign from plus to minus. I saw exactly why it happened and why the tergiversation was inevitable but it was after dinner and I let it go."

Sir Winston Spencer Churchill,  (1874-1965)

"A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence."

Howard W. Eves

"One is hard pressed to think of universal customs that man has successfully established on earth. There is one, however, of which he can boast the universal adoption of the Hindu-Arabic numerals to record numbers. In this we perhaps have man's unique worldwide victory of an idea."

Howard W. Eves

"Since you are now studying geometry and trigonometry, I will give you a problem. A ship sails the ocean. It left Boston with a cargo of wool. It grosses 200 tons. It is bound for Le Havre. The mainmast is broken, the cabin boy is on deck, there are 12 passengers aboard, the wind is blowing East-North-East, the clock points to a quarter past three in the afternoon. It is the month of May. How old is the captain?"

Gustave Flaubert (1821-1880)

"God does arithmetic."

Karl Friedrich Gauss (1777-1855)

"I have had my results for a long time: but I do not yet know how I am to arrive at them."

Karl Friedrich Guass

"It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment. When I have clarified and exhausted a subject, then I turn away from it, in order to go into darkness again; the never-satisfied man is so strange if he has completed a structure, then it is not in order to dwell in it peacefully, but in order to begin another. I imagine the world conqueror must feel thus, who, after one kingdom is scarcely conquered, stretches out his arms for others."

Karl Friedrich Gauss (1777-1855)

"Finally, two days ago, I succeeded - not on account of my hard efforts, but by the grace of the Lord. Like a sudden flash of lightning, the riddle was solved. I am unable to say what was the conducting thread that connected what I previously knew with what made my success possible."

Karl Friedrich Gauss (1777-1855)

"The mathematician requires tact and good taste at every step of his work, and he has to learn to trust to his own instinct to distinguish between what is really worthy of his efforts and what is not."

J. W. Glaisher

"There are no deep theorems -- only theorems that we have not understood very well."

Nicholas P. Goodman

"I remember one occasion when I tried to add a little seasoning to a review, but I wasn't allowed to. The paper was by Dorothy Maharam, and it was a perfectly sound contribution to abstract measure theory. The domains of the underlying measures were not sets but elements of more general Boolean algebras, and their range consisted not of positive numbers but of certain abstract equivalence classes. My proposed first sentence was: "The author discusses valueless measures in pointless spaces." "

Paul R. Halmos
I want to be a Mathematician, Washington: MAA Spectrum, 1985, p. 120.

"To be a scholar of mathematics you must be born with talent, insight, concentration, taste, luck, drive and the ability to visualize and guess."

Paul R. Halmos

"The fact is that there are few more "popular" subjects than mathematics. Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances may suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity."

Godfrey H. Hardy (1877 - 1947)

"One of the big misapprehensions about mathematics that we perpetrate in our classrooms is that the teacher always seems to know the answer to any problem that is discussed. This gives students the idea that there is a book somewhere with all the right answers to all of the interesting questions, and that teachers know those answers. And if one could get hold of the book, one would have everything settled. That's so unlike the true nature of mathematics."

Leon Henkin

"We are servants rather than masters in mathematics."

Charles Hermite (1822-1901)

"Mathematics is often erroneously referred to as the science of common sense. Actually, it may transcend common sense and go beyond either imagination or intuition. It has become a very strange and perhaps frightening subject from the ordinary point of view, but anyone who penetrates into it will find a veritable fairyland, a fairyland which is strange, but makes sense, if not common sense."

E. and Newman, J. Kasner

Mathematics and the Imagination, New York: Simon and Schuster, 1940.

When asked what it was like to set about proving something, the mathematician likened proving a theorem to seeing the peak of a mountain and trying to climb to the top. One establishes a base camp and begins scaling the mountain's sheer face, encountering obstacles at every turn, often retracing one's steps and struggling every foot of the journey. Finally when the top is reached, one stands examining the peak, taking in the view of the surrounding country side and then noting the automobile road up the other side!

Robert J. Kleinhenz

"What we know is not much. What we do not know is immense."

Pierre-Simon de Laplace (1749 - 1827)
(Allegedly his last words.)
DeMorgan's Budget of Paradoxes.

"All great theorems were discovered after midnight."

Adrian Mathesis

"We arrive at truth, not by reason only, but also by the heart."

Blaise Pascal (1623-1662)

"Through space the universe grasps me and swallows me up like a speck; through thought I grasp it."

Blaise Pascal (1623-1662)

"Mathematical discoveries, small or great are never born of spontaneous generation. They always presuppose a soil seeded with preliminary knowledge and well prepared by labor, both conscious and subconscious."

Jules Henri Poincaré (1854-1912)

"One of the endearing things about mathematicians is the extent to which they will go to avoid doing any real work."

Matthew Pordage

"The simplest schoolboy is now familiar with facts for which Archimedes would have sacrificed his life."

Ernest Renan

"Although this may seem a paradox, all exact science is dominated by the idea of approximation."

Bertrand Russell (1872-1970)

"The desire to understand the world and the desire to reform it are the two great engines of progress."

Bertrand Russell (1872-1970)

"The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities."

G. Sarton

"Though this be madness, yet there is method in't."

William Shakespeare (1564-1616)

"I am ill at these numbers."

William Shakespeare (1564-1616)

"The mathematician is fascinated with the marvelous beauty of the forms he constructs, and in their beauty he finds everlasting truth."

J. B. Shaw

Henry John Stephen Smith (1826 - 1883)
[His toast:]
"Pure mathematics, may it never be of any use to anyone."

"Every mathematician worthy of the name has experienced ... the state of lucid exaltation in which one thought succeeds another as if miraculously... this feeling may last for hours at a time, even for days. Once you have experienced it, you are eager to repeat it but unable to do it at will, unless perhaps by dogged work..."

Andre Weil (1906 -1998)
The Apprenticeship of a Mathematician.

"[Mathematics] is an independent world. Created out of pure intelligence."

William Wordsworth  (1770 - 1850)

If you enjoyed the quotes found on this site, you can find many more at the following site: