(source) 
GianCarlo Rota
(27 Apr 1932  18 Apr 1999)

Science Quotes by GianCarlo Rota (13 quotes)
A mathematicians 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.
— GianCarlo Rota
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.
— GianCarlo Rota
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.
— GianCarlo Rota
Mathematics is the study of analogies between analogies. All science is. Scientists want to show that things that dont look alike are really the same. That is one of their innermost Freudian motivations. In fact, that is what we mean by understanding.
— GianCarlo Rota
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.
— GianCarlo Rota
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 constantly present in your mind, although by and large they will lay in a dormant state. Every time you hear or read a new trick or a new result, test it against each of your twelve problems to see whether it helps. Every once in a while there will be a hit, and people will say, How did he do it? He must be a genius!
— GianCarlo 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.
— GianCarlo 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.
— GianCarlo Rota
The progress of mathematics can be viewed as progress from the infinite to the finite.
— GianCarlo Rota
The results of mathematics are seldom directly applied; it is the definitions that are really useful. Once you learn the concept of a differential equation, you see differential equations all over, no matter what you do. This you cannot see unless you take a course in abstract differential equations. What applies is the cultural background you get from a course in differential equations, not the specific theorems. If you want to learn French, you have to live the life of France, not just memorize thousands of words. If you want to apply mathematics, you have to live the life of differential equations. When you live this life, you can then go back to molecular biology with a new set of eyes that will see things you could not otherwise see.
— GianCarlo Rota
Theorems are not to mathematics what successful courses are to a meal.
— GianCarlo Rota
We often hear that mathematics consists mainly of proving theorems. Is a writer's job mainly that of writing sentences?
— GianCarlo 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.
— GianCarlo Rota
See also:
 27 Apr  short biography, births, deaths and events on date of Rota's birth.
 Indiscrete Thoughts, by GianCarlo Rota and Fabrizio Palombi.  book suggestion.