Quotations in English (and in some other languages)

• Everyone has a way of teaching that is beneficial to a part of the group and negative to the other part.

  Yves Meyer (Abel Laureate 2017) in an interview in Newsletter of the European Mathematical Society, September 2017.

• Referring to a Bourbaki in a military tone still means "disorderly and untended" even today.

  from Panorama Bourbaki, Luzern, Switzerland

• And then the big reveal: The woman wasn’t really sick at all! Instead this quick-thinking traveler had Seen Something, and so she had Said Something. That Something she’d seen had been her seatmate’s cryptic notes, scrawled in a script she didn’t recognize. Maybe it was code, or some foreign lettering, possibly the details of a plot to destroy the dozens of innocent lives aboard American Airlines Flight 3950. She may have felt it her duty to alert the authorities just to be safe. The curly-haired man was, the agent informed him politely, suspected of terrorism.
  The curly-haired man laughed. He laughed because those scribbles weren’t Arabic, or another foreign language, or even some special secret terrorist code. They were math. Yes, math. A differential equation, to be exact.

  from an article Ivy League economist ethnically profiled, interrogated for doing math on American Airlines flight in the Washington Post, May 7, 2016.

• Du siehst, mein Sohn,
  zum Raum wird hier die Zeit.

  Gurnemanz talking to Parsifal in first act of opera Parsifal by Richard Wagner

• Les plus dangereux de nos calculs sont ceux que nous appelons des illusions.

  La Prieure au deuxième tableau de l'acte premier de l'opéra Dialogue des Carmélites par Francis Poulenc

• Ce que nous appelons hasard, c'est peut-être la logique de Dieu.

  Soeur Constance au 1.interlude du deuxième acte de l'opéra Dialogue des Carmélites par Francis Poulenc

• Der liebe Gott würfelt nicht.

  Albert Einstein

• S'incomincia per cantare             Sing to start
  E si canta per finire                     and sing to end

  Text of the poem Uno by Guiseppe Ungaretti. It became part of the song cycle Tempo e Tempi by Elliott Carter.

• RYAN: You can cut tax rates by 20 percent and still preserve these important preferences for middle-class taxpayers...
  BIDEN: Not mathematically possible.
  RYAN: It is mathematically possible. It's been done before. It's what we're proposing.
  BIDEN: It has never been done before.

  Debate on October 11, 2012 between US vice presidential candidates Joe Biden (Democrats) and Paul Ryan (Republicans).

• One of the very first popularizers, M. Faraday, arrived at the conclusion that “Lectures which really teach will never be popular; lectures which are popular will never teach.” This Faraday effect is easy to explain: according to N. Bohr, clearness and truth are in a quantum complementarity relation.

  Vladimir Arnold in an interview in 1990 which appeared in the Russian magazine Kvant. The English translation of part of this interview was included in Tribute to Vladimir Arnold, Notices Amer. Math. Soc., March 2012.

• In the broad light of day mathematicians check their equations and their proofs, leaving no stone unturned in their search for rigour. But, at night, under the full moon, they dream, they float among the stars and wonder at the miracle of the heavens. They are inspired. Without dreams there is no art, no mathematics, no life.

  Michael Atiyah in “The art of mathematics”, Notices Amer. Math. Soc., January 2010 (originally in French in the book Les Déchiffreurs, translated in English as the book The Unravelers).

• Although several of the essays in this collection are by sociologists, none addresses the central question of the sociology of mathematics: why is it that mathematicians are such nice people? We are no respecters of persons (in that curious phrase that means we do respect persons but pay little attention to the trappings of age, position, or prestige), we take equal delight in fierce competition and collaborative effort, and we are quick to say “I was wrong.”   …   How does one explain that we are so lovable? Is there something in the nature of mathematics that attracts gentle souls? Possibly, but another explanation is more convincing. We are singularly blessed in that the worth of a mathematical work is judged largely by whether the proof is correct, and this is something on which we all agree (eventually).

  Edward Nelson in Review of “18 Unconventional Essays on the Nature of Mathematics”, American Mathematical Monthly, November 2007.

• At the time, I had grown dissatisfied with the usual vehicles for recording and communicating mathematics. One issue has been that the informal drawings and diagrams that mathematicians often use when talking with each other are quite often missing from papers and books. When I was an undergraduate and graduate student, I enjoyed learning to study mathematics in a slow, laborious, step-by-step process, but as my study of mathematics progressed, I went through many experiences of struggling to digest laborious sequential arguments, finally catching on to whole-brain, instantaneous ways to understand the concepts and saying to myself, "Oh, is that what they were talking about? Why didn't they say so?" I started to realize that written mathematics is usually a highly denatured rendition of what sits inside mathematicians' heads. It's a hard task that often never happens to translate a detailed step-by-step proof or description into a conceptual understanding, far harder than to translate from concept to details. We've all also noticed that in seminar talks and even in informal one-on-one explanations of mathematics, it's common for one person to talk completely past another. Why is it so hard to communicate mathematics effectively?
  I had the ambition to try to communicate on a more conceptual level, paying attention not only to the logical aspects of what is correct but also to the psychological aspects of how we can hold it in our heads and understand it. The geometric modules of our brains are the parts most severely neglected in most mathematical writing. Many papers, even about geometry and topology, lack the figures, or they have figures that are poor or mistaken.

  William P. Thurston in 2005 Book Prize, Notices Amer. Math. Soc., April 2005, pp. 449-450.

• Undoubtedly philosophers are in the right when they tell us, that nothing is great or little, otherwise than by comparison.

  Jonathan Swift, Gulliver's travels, Part II. A voyage to Brobdingnag.

• My opinion of the value of democracy in the running of an academic department has been monotonically decreasing throughout my career.
  But here is the fundamental rule. The head who acts more like a chair and the chair who acts more like a head will be more successful than one who tries to live in a pure state.

  John B. Conway, On being a department head, a personal view, American Mathematical Society, 1996.

• There are trivial truths and there are great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.

  Attributed to Niels Bohr.

• There are three kinds of researchers: Those who can do math and those who cannot.

  Attributed to Tom Rusk Vickery.

• The importance of the full linear group GL(n) lies in the fact that any group Γ of linear transformations is a subgroup of GL(n) ... . One should, however, not overemphasize this relationship; for after all each group stands in its own right and does not deserve to be looked upon merely as a subgroup of something else, be it even Her All-embracing Majesty GL(n).

  Hermann Weyl in The Classical Groups, end of Chapter IV.

• The great, wide-stretching earth and the all-embracing sky—the birthright of us all—are what I care most to look at.

  George Eliot in George Eliot's Life as related in her Letters and Journals, Vol. II, Chapter VIII, April 12, 1858.

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Last modified: 20 February 2024 10:50:11