Mathematical Quotes

• There can never be surprises in logic.

  Ludwig Wittgenstein

  Math, Logic, Surprise

  Ludwig Wittgenstein (2016). “Tractatus Logico Philosophicus”, p.28, Clube de Autores

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• The understanding of mathematics is necessary for a sound grasp of ethics.

  Socrates

  Understanding, Sound, Ethics

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• The only way to learn mathematics is to do mathematics.

  Paul Halmos

  Learning, Math, Way

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• Each problem that I solved became a rule, which served afterwards to solve other problems.

  Rene Descartes

  Success, Witty, Humorous

  "Discourse on the Method". Book by Rene Descartes (Part 2), 1637.

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

  Carl Friedrich Gauss

  Time, Math, Science

  "The Mind and the Eye: A Study of the Biologist's Standpoint". Book by A. Arber, 1954.

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• Mathematics is not a deductive science - that's a cliché. 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

  Math, Science, Errors

  "I Want to be a Mathematician: An Automathography". Book by Paul Halmos, 1985.

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• I know that two and two make four - and should be glad to prove it too if I could - though I must say if by any sort of process I could convert 2 and 2 into five it would give me much greater pleasure.

  Lord Byron

  Math, Two, Giving

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• The mathematician has reached the highest rung on the ladder of human thought.

  Havelock Ellis

  Math, Science, Ladders

  havelock ellis (1923). “the dance of life”

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• The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas, like the colours 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

  Beauty, Beautiful, Math

  A Mathematician's Apology ch. 10 (1940)

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• As for everything else, so for a mathematical theory: beauty can be perceived but not explained.

  Arthur Cayley

  Beauty, Math, Theory

  Arthur Cayley (1895). “The Collected Mathematical Papers of Arthur Cayley”

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• We must admit with humility that, while number is purely a product of our minds, space has a reality outside our minds, so that we cannot completely prescribe its properties a priori.

  Carl Friedrich Gauss

  Humility, Math, Reality

  Letter to Friedrich Wilhelm Bessel, 1830.

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• Mathematics is the only good metaphysics.

  Lord Kelvin

  Math, Numbers, Metaphysics

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• The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.

  Charles Caleb Colton

  Math, Magnificence, Study

  Charles Caleb Colton (1824). “Lacon, Or, Many Things in a Few Words: Addressed to Those who Think”, p.164

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• Nature is an infinite sphere of which the center is everywhere and the circumference nowhere.

  Blaise Pascal

  Nature, Math, Garden

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• Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascods, so pages of formulae will not get a definite result out of loose data.

  Thomas Huxley

  Work, Data, May

  "Geological Reform". Quarterly Journal of the Geological Society of London, Volume 25, 1869.

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• 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 Russell

  Fake People, Math, Talking

  "Mathematics and Metaphysicians" (1901)

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• Mathematicians have tried in vain to this day to discover some order in the sequence of prime numbers, and we have reason to believe that it is a mystery into which the human mind will never penetrate.

  Leonhard Euler

  Believe, Math, Order

  "Calculus Gems: Brief Lives and Memorable Mathematics". Book by George F. Simmons, 1992.

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• Science without religion is lame, religion without science is blind.

  Albert Einstein

  Love, Life, Motivational

  "Science, Philosophy, and Religion" (1940).

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• A mathematician, like a painter or poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas.

  G. H. Hardy

  Education, Math, Unique

  G. H. Hardy (2012). “A Mathematician's Apology”, p.84, Cambridge University Press

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• If I am given a formula, and I am ignorant of its meaning, it cannot teach me anything, but if I already know it what does the formula teach me?

  Saint Augustine

  Math, Ignorant, Doe

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• Measure what is measurable, and make measurable what is not so.

  Galileo Galilei

  Math, Statistics, Metrics

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• All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon.

  Roger Bacon

  People, Brain, Facts

  1267 OpusMajus, pt.4, ch.1 (translated by Robert Belle Burke, 1928).

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• A mathematician is a blind man in a dark room looking for a black cat which isn't there.

  Charles Darwin

  Inspirational, Cat, Science

  Quoted in John D Barrow Pie in the Sky, Counting, Thinking and Being (1992).

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• Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform.

  Bertrand Russell

  Math, Conformity, Regions

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• Mathematics is written for mathematicians.

  Nicolaus Copernicus

  Mathematics, Mathematician, Written

  Nicolaus Copernicus (1939). “On the Revolutions of the Celestial Spheres ...”

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