The pendulum of mathematics swings back and forth towards abstraction and away from it with a timing that remains to be estimated. — Gian-Carlo Rota Copy Share Image
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 cows, moving slowly in the direction they are being driven towards. If we make one point, we have a good chance that the audience will take the right direction; if we make several points, then… — Gian-Carlo Rota Copy Share
God created infinity, and man, unable to understand infinity, had to invent finite sets. — Gian-Carlo Rota Copy Share Image
Philosophers and psychiatrists should explain why it is that we mathematicians are in the habit of systematically erasing our footsteps. Scientists have always looked… — Gian-Carlo Rota Copy Share Image
The lack of real contact between mathematics and biology is either a tragedy, a scandal or a challenge, it is hard to decide which. — Gian-Carlo Rota Copy Share Image
The apex of mathematical achievement occurs when two or more fields which were thought to be entirely unrelated turn out to be closely intertwined.… — Gian-Carlo Rota Copy Share Image
[In mathematics] There are two kinds of mistakes. There are fatal mistakes that destroy a theory, but there are also contingent ones, which are… — Gian-Carlo Rota Copy Share Image
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… — Gian-Carlo Rota Copy Share
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… — Gian-Carlo Rota Copy Share Image
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… — Gian-Carlo Rota Copy Share Image
If we have no idea why a statement is true, we can still prove it by induction. — Gian-Carlo Rota Copy Share Image
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.… — Gian-Carlo Rota Copy Share Image
![“[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.” quote by Gian-Carlo Rota](https://sms4smile.com/quotes/img-quotes/cbc/gian-carlo-rota-19795_failure_in-mathematics-there-are-two-kinds-of-mi_493803.jpg)
