Collected Quotes of Gian-Carlo Rota
A mathematician's work is mostly a tangle of guesswork,
anology, wishful thinking and frustration, and proof,
far from being the core of discovery,
is more often than not a way of making sure that
our minds are not playing tricks.
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A technique is a trick that works.
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Are mathematical ideas invented or discovered?
The question has been repeatedly posed by philosophers through the ages and will probably be with us forever.
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If we have no idea why a statement is true, we can
still prove it by induction.
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How did he do it?
He must be a genius!
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It is a common public relations gimmick to give the
entire credit for the solution of famous problems to
the one mathematician who is responsible for the last step.
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Making mathematics accessible to the educated layman,
while keeping high scientific standards,
has always been considered a treacherous navigation
between the Scylla of professional contempt
and the Charybdis of public misunderstanding.
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Mathematicians - for what they do - are really poorly rewarded.
And it's a very competitive field, almost as bad as being a concert
pianist.
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Mathematicians also make terrible salesmen.
Physicists can discover the same thing as a mathematician and say
"We've discovered a great new law of nature. Give us a billion dollars."
And if it doesn't change the world, then they say,
"There's an even deeper thing. Give us another billion dollars."
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Mathematics is the study of analogies between analogies.
All science is. Scientists want to show that things
that don't look alike are really the same.
That is one of their innermost Freudian motivations.
In fact, this is what we mean by understanding.
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Our faith in Mathematics is not likely to be wane if
we openly acknowledge that the personalities of even
the greatest mathematicians may be as flawed as those
of anyone else.
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The advice we give others is the advice that we ourselves need.
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The apex of mathematical achievement occurs when two or more fields
which were thought to be entirely unrelated turn out to be closely interwined.
Mathematicians have never decided whether they should feel excited or upset by such events.
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The lack of real contact between mathematics and biology
is either a tragedy, a scandal or a challenge,
it is hard to decide which.
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The progess of mathematics can be viewed as progress from the infinite to the finite.
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The one contribution of mine that I hope will
be remembered has consisted in just pointing out
that all sorts of problems of combinatorics
can be viewed as problems of location of the
zeros of certain polynomials and in giving
these zeros a combinatorial interpretation.
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Theorems are not to mathematics what successful courses are to a meal.
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[In mathematics] There are two kinds of mistakes.
There are fatal mistakes that destroy a theory.
But there are also contingent ones.
Which are useful in testing the stability of a theory.
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There is something in statistics that makes it very similar to astrology.
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We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
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