Quotes by Gian-Carlo Rota

Gian-Carlo Rota

[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.

Mistake

Science

Two

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 often than not a way of making sure that our minds are not playing tricks.

Frustration

Hard Work

Science

A technique is a trick that works.

Technique

Tricks

Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.

Age

Forever

Ideas

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. 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.

Cutting

Ideas

Math

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).

Three

Two

Writing

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 the cows will scatter all over the field. The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture.

Moving

Order

Science

God created infinity, and man, unable to understand infinity, had to invent finite sets.

Education

Men

Statistics

How did he do it? He must be a genius!

Genius

If we have no idea why a statement is true, we can still prove it by induction.

Ideas

Mathematics

Prove It

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Achievement

Advice

Age

Astrology

Challenges

Civilization

Concerts

Cutting

Dollars

Education

Errors

Fields

Fifteen

Forever

Frustration

Genius

Giving

Hard Work

Ideas

Indirect

Infinite

Jobs

Lasts

Law

Littles

Math

Mathematician

Mathematics

May

Meals

Mean

Men

Mistake

Motivation

Moving

Navigation

Needs

Order

People

Personality

Philosopher

Progress

Promise

Prove It

Real

Running

Science

Scylla

Self

Statistics

The Future Blueprint

Tool

The Home Therapist: Anti Anxiety

Tool

The Autobiography

Tool

The Behaviour Diary

Tool

The Dating Diary

Tool

The Relationship Therapist

Tool

Quotes by Gian-Carlo Rota

Gian-Carlo Rota

[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.

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 often than not a way of making sure that our minds are not playing tricks.

A technique is a trick that works.

Are mathematical ideas invented or discovered? This question has been repeatedly posed by philosophers through the ages and will probably be with us forever.

God created infinity, and man, unable to understand infinity, had to invent finite sets.

How did he do it? He must be a genius!

If we have no idea why a statement is true, we can still prove it by induction.

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The Home Therapist: Anti Anxiety

The Autobiography

The Behaviour Diary

The Dating Diary

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