Gian-Carlo Rota - Indiscrete thoughts (1997)

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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
We thought that the generalization of the notion of space had ended with topoi, but we were mistaken. We probably know less about space now than we pretended to know fifty years ago. As mathematics progresses, our understanding of it regresses.

Gian-Carlo Rota
The Talmud and the Tao are trainers of scientific minds. A variety of talents is required if the scientific community is to thrive....

Gian-Carlo Rota
The progress of mathematics can be viewed as progress from the infinite to the finite.

Gian-Carlo Rota
Very little mathematics has direct applications - though fortunately most of it has plenty of indirect ones.

Gian-Carlo Rota
Quantum mechanics is the imaginary square root of probability theory.

Gian-Carlo Rota
Group theory, like lattice theory, is the whipping boy of mathematicians in need of concealing their feelings of insecurity.

Gian-Carlo Rota
We take offense at those truths that threaten any of the myths we profess to believe in. Taking offense is an effective way we have of shutting off some unpleasant truth. It works. It enables us to restore a hold on our dearest myths, to last until the next offending myth comes along.

Gian-Carlo Rota
A good teacher does not teach facts, he or she teaches enthusiasm, open-mindedness and values...

Gian-Carlo Rota
Biologists seldom have the mathematical view that is required to spot problems in the mathematics of biology that are staring at them. A biologist will never see anything deeper than binomial coefficients. It is not that the problems aren't there; rather, biologists don't have the view that comes with a solid education in mathematics.

Gian-Carlo Rota
Of all escapes from reality, mathematics is the most successful ever.

Gian-Carlo Rota
Conditional probability tends to be viewed as one technique for calculating probabilities. Actually, there is more to it than meets the eye: it has an interpretation which is ordinarily passed over in silence. Philosophers take notice.

Gian-Carlo Rota
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.

Gian-Carlo Rota
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.

Gian-Carlo Rota
Not only is every mathematical problem solved, but eventually every mathematical problem is proved trivial. The quest for ultimate triviality is characteristic of the mathematical enterprise.

Gian-Carlo Rota
Books on paradoxes in statistics are similar to mystery books. They have a faithful readership, and they follow a rigorous sequence in their presentation, like Greek tragedies.

Gian-Carlo Rota
Mathematics is a cruel profession. Solving a mathematical problem is for most mathematicians an arduous and lengthy process which may take years, even a lifetime. The final conquest of the truth comes, if ever, inevitably tinged with disillusion, soured by the realization of the ultimate irrelevance of all intellectual endeavor.

Gian-Carlo Rota
Mathematical logic deals not with the truth but only with the game of truth.

Gian-Carlo Rota
The snobbish symbol-dropping found nowadays in philosophical papers raises eyebrows among mathematicians, like someone paying his grocery bill with Monopoly money.

Gian-Carlo Rota
The distance between probability and statistical mechanics is diminishing, and soon we won't be able to tell which is which. We will be rid of the handwaving arguments with which mathematically illiterate physicists have been pestering us.

Gian-Carlo Rota
There is nothing deadlier for a mathematician than to be placed in a beautiful office and instructed to lay golden eggs.

Gian-Carlo Rota
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).

Gian-Carlo Rota
Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do.

Gian-Carlo Rota
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 turn elsewhere.

Gian-Carlo Rota
The advice we give others is the advice that we ourselves need.

Gian-Carlo Rota
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 have never decided whether they should feel excited or upset by such events.

Gian-Carlo Rota