Gian-Carlo Rota Quotes

20 quotes in 429 categories

• 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.…
• [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…
• Richard Feynman was fond of giving the following advice on how to be a genius. You have to keep a dozen of your favorite problems…
• 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…
• The progress of mathematics can be viewed as progress from the infinite to the finite.
• Theorems are not to mathematics what successful courses are to a meal.
• We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?"
• Every lecture should state one main point and repeat it over and over, like a theme with variations. An audience is like a herd of…
• God created infinity, and man, unable to understand infinity, had to invent finite sets.
• How did he do it? He must be a genius!
• The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined. Mathematicians…
• The advice we give others is the advice that we ourselves need.
• There is something in statistics that makes it very similar to astrology.
• Running overtime is the one unforgivable error a lecturer can make. After fifty minutes (one microcentury as von Neumann used to say) everybody's attention will…
• 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…
• Combinatorics is an honest subject. No adèles, no sigma-algebras. You count balls in a box, and you either have the right number or you haven't.…
• If we have no idea why a statement is true, we can still prove it by induction.
• Nature imitates mathematics.
• 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…
• A mathematician's work is mostly a tangle of guesswork, analogy, wishful thinking and frustration, and proof, far from being the core of discovery, is more…

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