Titlebook: Discrete Thoughts; Essays on Mathematic Mark Kac,Gian-Carlo Rota,Jacob T. Schwartz Book 1992Latest edition Springer Science+Business Media

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Combinatorics.—or, as it is coming to be called, combinatorial theory — is both the oldest and one of the least developed branches of mathematics. The reason for this apparent paradox will become clear toward the end of the present account.

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Economics, Mathematical and Empirical., mathematics has shaped our world in fundamental ways. What is the practical value of mathematics? What would be lost if we had access only to common sense reasoning? A three-part answer can be attempted:

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Complicating Mathematics., the Swiss historian Jakob Burckhardt, who, unlike most historians, was fond of guessing the future, once confided to his friend Friedrich Nietzsche the prediction that the Twentieth Century would be “the age of oversimplification.”

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The Future of Computer Scienceze to grow in an astounding way, confronting workers in the field with a continually widening range of opportunities. For example, discs have led to databases, communication technology has led to ARPANET, and microchips to interest in distributed computing.

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Discrete Thoughtsrophe theory for instance, and then turn out to resemble a three-dollar bill. Others, like dynamic programming, have to overcome a questionable background before they are reluctantly recognized to be substantial and useful. It is a tough world, even for the judgement-pronouncers.