We often hear that mathematics consists mainly of "proving theorems." Is a writer's job mainly that of "writing sentences?" Gian-Carlo Rota More Quotes by Gian-Carlo Rota More Quotes From Gian-Carlo Rota 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. Gian-Carlo Rota cutting math ideas Why is it that Serge Lange's Linear Algebra, published by no less a Verlag than Springer, ostentatiously displays the sale of a few thousand copies over a period of fifteen years, while the same title by Seymour Lipschutz in the The Schaum's Outlines will be considered a failure unless it brings in a steady annual income from the sale of a few hundred thousand copies in twenty-six languages? Gian-Carlo Rota fifteen science years If we have no idea why a statement is true, we can still prove it by induction. Gian-Carlo Rota prove-it mathematics ideas 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. 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The audience will lose interest and everyone will go back to the thoughts they interrupted in order to come to our lecture. Gian-Carlo Rota order science moving 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. Gian-Carlo Rota philosopher littles science [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. Gian-Carlo Rota mistake two science 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. 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