• Racine carrée de 2, c’est 1,414 et des poussières… Et quelles poussières ! Des grains de sable qui empêchent d’écrire racine de 2 comme une fraction. Autrement dit, cette racine n’est pas dans Q. — Rationnel mon Q: 65 exercices de styles, Ludmilla Duchêne et Agnès Leblanc (2010)
• The square root of 2 is 1·414 and dust… And what dust! Grains of sand that stop you writing the root of 2 as a fraction. Put another way, this root isn’t in Q [the set of rational numbers].
“A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence.” — Howard Whitley Eves (1911-2004)
“Film is one of the three universal languages. The other two: mathematics and music.” — Frank Capra (1897-1991)
“Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.” — Bertrand Russell, An Outline of Philosophy (1927), ch. 15, “The Nature of our Knowledge of Physics”
“If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.” — John von Neumann
This quote is popular on web pages about von Neumann, and about computing and mathematics generally. It is apparently not from a published work of von Neumann’s, but Franz L. Alt recalls it as a remark made from the podium by von Neumann as keynote speaker at the first national meeting of the Association for Computing Machinery in 1947. The exchange at that meeting is described at the end of Alt’s brief article “Archaeology of computers: Reminiscences, 1945–1947”, Communications of the ACM, volume 15, issue 7, July 1972, special issue: Twenty-fifth anniversary of the Association for Computing Machinery, p. 694. Alt recalls that von Neumann “mentioned the ‘new programming method’ for ENIAC and explained that its seemingly small vocabulary was in fact ample: that future computers, then in the design stage, would get along on a dozen instruction types, and this was known to be adequate for expressing all of mathematics…. Von Neumann went on to say that one need not be surprised at this small number, since about 1,000 words were known to be adequate for most situations of real life, and mathematics was only a small part of life, and a very simple part at that. This caused some hilarity in the audience, which provoked von Neumann to say: ‘If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is.’ ”
• Source of John von Neumann quote
“In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug. Chess sometimes plays a similar role. In their unhappiness over the events of this world, some immerse themselves in a kind of self-sufficiency in mathematics. (Some have engaged in it for this reason alone.)” — Stanislaw Ulam (1909-84)
• Matematyka jest najpotężniejszym intelektualnym wehikułem, jaki kiedykolwiek został skonstruowany, za pomocą którego uciekamy przed czasem, lecz nie ma powodu przypuszczać, że mogłaby kiedyś umożliwić tego rodzaju ucieczkę, jaką ucieleśnia pogoń za Absolutem. — Leszek Kołakowski
• Mathematics is the most powerful intellectual vehicle that has ever been constructed, by means of which we flee ahead of time, but there is no reason to suppose that it could someday enable the kind of escape embodied by the pursuit of the Absolute. — Leszek Kołakowski
• φασὶ γοῦν Ἵππαρχον τὸν Πυθαγόρειον, αἰτίαν ἔχοντα γράψασθαι τὰ τοῦ Πυθαγόρου σαφῶς, ἐξελαθῆναι τῆς διατριβῆς καὶ στήλην ἐπ’ αὐτῷ γενέσθαι οἷα νεκρῷ. — Κλήμης ὁ Ἀλεξανδρεύς, Στρώματα.
• They say, then, that Hipparchus the Pythagorean, being guilty of writing the tenets of Pythagoras in plain language, was expelled from the school, and a pillar raised for him as if he had been dead. — Clement of Alexandria, The Stromata, 18.104.22.168.3-4
• Mathematik ist die Wissenschaft von dem, was an sich klar. — Carl Jacobi (1804-51).
• “Mathematics is the science of that which is clear by itself.” — Carl Jacobi.
• Apud me omnia fiunt Mathematicè in Natura — René Descartes (1596-1650).
• For me, all things in nature occur mathematically. — Correspondence with Martin Mersenne (1640).