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