All GIAN-CARLO ROTA Quotes about “Mathematics”

“We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"”
“Every field has its taboos. In algebraic geometry the taboos are (1) writing a draft that can be followed by anyone but two or three of one's closest friends, (2) claiming that a result has applications, (3) mentioning the word 'combinatorial,' and (4) claiming that algebraic geometry existed before Grothendieck (only some handwaving references to 'the Italians' are allowed provided they are not supported by specific references).”
“If we have no idea why a statement is true, we can still prove it by induction.”
“Nature imitates mathematics.”
“God created infinity, and man, unable to understand infinity, had to invent finite sets.”
“THE COMPUTER IS JUST AN INSTRUMENT for doing faster what we already know how to do slower. All pretensions to computer intelligence and paradise-tomorrow promises should be toned down before the public turns away in disgust. And if that should happen, our civilization might not survive.”
“Why is it that Serge Lange's Linear Algebra, published by no less a Verlag than Springer, ostentatiously displays the sale of a few thousand copies over a period of fifteen years, while the same title by Seymour Lipschutz in the The Schaum's Outlines will be considered a failure unless it brings in a steady annual income from the sale of a few hundred thousand copies in twenty-six languages?”
“Stan Ulam was lazy, ... He talked too much ... He was self-centered ... . He had an overpowering personality.”
“Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked askance at this strange habit of mathematicians, which has changed little from Pythagoras to our day.”
“Combinatorics is an honest subject. No adÃ¨les, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't. You get the feeling that the result you have discovered is forever, because it's concrete. Other branches of mathematics are not so clear-cut. Functional analysis of infinite-dimensional spaces is never fully convincing; you don't get a feeling of having done an honest day's work. Don't get the wrong idea - combinatorics is not just putting balls into boxes. Counting finite sets can be a highbrow undertaking, with sophisticated techniques.”
“Theorems are not to mathematics what successful courses are to a meal.”
“The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated.”
“There is something in statistics that makes it very similar to astrology.”
“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, that is what we mean by understanding.”
“[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.”
“Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.”
“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.”
“The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which.”
“The progress of mathematics can be viewed as progress from the infinite to the finite.”
“Our faith in Mathematics is not likely to 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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