"Some of you may have met mathematicians and wondered how they got to be that way." - Tom Lehrer.
"Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science." - Richard Courant and Herbert Robbins in What is Mathematics?
(During a lecture.) "This has been done elegantly by Minkowski; but chalk is cheaper than grey matter, and we will do it as it comes." - Albert Einstein.
"It is a great nuisance that knowledge can only be acquired by hard work." - W. Somerset Maugham (1874-1965)
"But where the senses fail us, reason must step in." - Galileo Galilei (1564-1642)
"If there's no struggle, there's no progress." - Frederick Douglas (1817-1895)
"... the sole object of science is the honor of the human spirit and that under this view a problem of numbers is worth as much as a problem on the system of the world." - Carl Gustav Jacobi (1804-1851)
"What science can there be more noble, more excellent, more useful ... than mathematics." - Benjamin Franklin (1706-1790)
"The modern physicist is a quantum theorist Monday, Wednesday, and Friday and a student of gravitational relativity theory on Tuesday, Thursday, and Saturday. On Sunday he is neither, but is praying to his God that someone, preferably himself, will find the reconciliation between the two views." - Norbert Wiener (1894-1964)
"The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word." Galileo Galilei (1564-1642)
"Alice laughed: 'There's no use trying,' she said; 'one can't believe impossible things.' 'I daresay you haven't had much practice,' said the Queen. 'When I was younger, I always did it for half an hour a day. Why, sometimes I've believed as many as six impossible things before breakfast.'" - Lewis Carroll (1832-1898) in Alice in Wonderland
"Mathematics is not a deductive science -- that's a cliche. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." - Paul Halmos (1916-2006)
"Truth is the most valuable thing we have. Let us economize it." - Mark Twain (1830-1910)
"As God calculates so the world is made." - Gottfried Leibniz (1646-1716)
"Mighty is the charm of those abstractions to a mind beset with images." - William Wordsworth (1770-1850)
"A computer is like an Old Testament god, with lots of rules and no mercy." - Joseph Campbell
"He who seeks for methods without having a definite problem in mind seeks for the most part in vain." - David Hilbert (1862-1943)
"Read Euler, read Euler. He is the master of us all." - Pierre Simon Laplace (1749-1827)
"Let me count the ways." - Elizabeth Barrett Browning (1806-1861)
"Perfect numbers like perfect men are very rare." - Rene Descartes (1596-1650)
"Failure is the path of least persistence.' - Anonymous
"An Englishmen, even if left alone, forms an orderly queue of one." - George Mikes (1912-1987)
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." - Bertrand Russel (1872-1970)
"Sometimes you can see a lot just by looking." - Lawrence Peter "Yogi" Berra (1925-)
"Sixty minutes of thinking of any kind is bound to lead to confusion and unhappiness." - James Thurber (1894-1961)
"To err is human, but to really foul things up requires a computer." - Anonymous
"Never underestimate a theorem that counts something." - John B. Fraleigh (1933-)
"Just the facts, Ma'am." - Joe Friday
"In great mathematics there is a very high degree of unexpectedness, combined with inevitability and economy." - G. H. Hardy (1877-1947)
"The beauty in mathematics is seeing the truth without effort." - George Polya
"He is unworthy of the name of man who does not know the diagonal of a square is incommensurable with its side." - Plato (427-347 BC)
"The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics." - G. H. Hardy (1877-1947) in A Mathematician's Apology
"If I rest, I rust." - Martin Luther (1483-1546)
"An idea is always a generalization, and a generalization is a property of thinking. To generalize means to think." - George Hegel (1770-1831)
"'Mathematizing' may well be a creative activity of man, like language or music, of primary originality ..." - Hermann Weyl (1885-1955)
"I recognize a lion by his paw." - Jakob Bernoulli (1654-1705) after reading an anonymous solution to a problem that he realized was Newton's.
"Life is good for only two things, discovering mathematics and teaching mathematics." - Simeon Denis Poisson (1781-1840)
"Mathematics alone makes us feel the limits of our intelligence." - Simone Weil (1909-1945)
"No human investigation can be called real science if it cannot be demonstrated mathematically." - Leonardo Da Vinci (1452-1519)
"The infinitely competent can be uncreative." - J. E. Littlewood (1885-1977)
"This paper contains much that is new and much that is true. Unfortunately, that which is true is not new and that which is new is not true." - Anonymous Referee's Report
"The King calls me 'my Professor', and I am the happiest man in the world!" - Leonard Euler (1707-1783)
"The profound study of nature is the most fertile source of mathematical discoveries." Joseph Baptiste Fourier (1768-1830)
"In mathematics there are no true controversies." - Karl Friedrich Gauss (1777-1855)
"The gold in `them there hills' is not always buried deep. Much of it is within easy reach. Some of it is right on the surface to be picked up by any searcher with a keen eye for detail and an eagerness to explore. As in any treasure hunt, the involvement grows as the hunt proceeds and each success whether small or great adds the fuel of excitement to the exploration." -- Arnold Ross (1906-2002), Prolog (1978)
"I will a little think." - Albert Einstein
"The physicist cannot simply surrender to the philosopher the critical contemplation of the theoretical foundations; for he himself knows best and feels more surely where the shoe pinches." - Albert Einstein, 1950.
"How does it happen that a properly endowed natural scientist comes to concern himself with epistemology? Is there no more valuable work in his specialty? I hear many of my colleagues saying, and I sense it from many more, that they feel this way. I cannot share this sentiment. ... Concepts that have proven useful in ordering things easily achieve such an authority over us that we forget their earthly origins and accept them as unalterable givens. Thus they come to be stamped as 'necessities of thought,' 'a priori givens,' etc. The path of scientific advance is often made impassable for a long time through such errors. For that reason, it is by no means an idle game if we become practiced in analyzing the long common place concepts and exhibiting those circumstances upon which their justification and usefulness depend, how they have grown up, individually, out of the givens of experience. By this means, their all-too-great authority will be broken." - Albert Einstein. 'Ernst Mach.' Physikalische Zeitschrift 17 (1916): 101, 102 - A memorial notice for the philosopher, Ernst Mach.
"Who will lead me into that still more hidden and dimmer region where Thought weds Fact, where the mental operations of the mathematician and the physical actions of the molecules are seen in their true relation? Does not the way pass through the very den of the metaphysician, strewed with the remains of former explorers?" - James Clerk Maxwell, 1870.
"It behoves us always to remember that in physics it has taken great minds to discover simple things. They are very great names indeed which we couple with the explanation of the path of a stone, the droop of a chain, the tints of a bubble, the shadows in a cup." - D'Arcy Thompson, 1917.
"The foundations of mathematics are an established, flourishing, and fertile branch of mathematics. It is up to the physicists to see that something similar happens with their science." - Mario Bunge, Foundations of Physics, 1967.