Indiscrete Thoughts

Gian - Carlo Rota

Reuben Hersh

If you're about to buy this book, you're in for a treat.

I first met Gian-Carlo in the late 70's in Las Cruces, New Mexico. He was there to lecture on his mathematical specialty, combinatorics - how to count complicated finite sets, and extensions of that problem. I repeated inaccurately what I had heard from my honored mentor, Peter Lax of New York University.

"A lecture by Rota is like a double martini!"

It was true. Even to one innocent of combinatorics, his lectures were a delightful combination, both stimulating and relaxing.

There are mathematicians who give great lectures, but write dull, ponderous books. There are some who write beautiful books and give dull lectures. (No names will be mentioned). Gian-Carlo gives brilliant lectures, and his writing is as good. He loves contradiction. He loves to shock. He loves to simultaneously entertain you and make you uncomfortable.

His personal history is rare. He was born in Italy of an architect father who was a leading member of Mussoliniís secret hit list. Educated first in Ecuador, then at Princeton and Yale. Started research in a "hot" specialty, functional analysis. Underwent an epiphany and conversion to discrete math-the hard-nosed, down-to-earth stuff-but done from the abstract, high level view point of functional analysis. Developed a major interest in the thought of Husserl, Heidegger and Sartre - phenomenology. With it, a distaste for "analytic philosophy," the ruling trend in Anglo-America.

When he started to teach phenomenology at M.I.T, students wanted "philosophy credit" for his course. The M.I.T. philosophers (analytic, of course) said, "Never," and offered to quit en masse. Jerry Wiesner, the President, told them, "Go ahead, that will help my budget." They didn't quit. Gian-Carlo's students get philosophy credit.

His large Cambridge apartment has enough bookshelves for many a library, but books are all over everything. I'm not sure he sleeps. Certainly he keeps late hours, reading, writing, doing email, talking on the phone, and thinking.

He has a talent for friendship. Some of my warmest memories are dinners at the home of Stan and Francoise Ulam in Santa Fe, with Gian-Carlo and Mark Kac.

He did me a great service, for which I'd like to thank him again. My first piece on the philosophy of mathematics was rejected, on the advice of a prestigious Harvard philosopher. Gian-Carlo immediately printed it in Advances in Mathematics, an absolutely tip-top high-class journal published by Academic Press under the founding editorship of G.-C. Rota. Later he started a second organ, Advances in Applied Mathematics. His journals' editorial boards boast the highest conceivable quality and prestige. I once mentioned a difference of opinion with the editor at a journal where I was a board member. Gian-Carlo said, "if anyone on my board gave me trouble, I would kick him out." This book ends with some truly inimitable book reviews from the Advances.

Before that come three main parts: Persons and Places, Philosophy, and Indiscrete Thoughts.

In Persons and Places you'll meet great names. You'll learn not only about their contributions, but also about their kindness, their egos, their absurdities. Most mathematicians know Artin, Church, Feller, Lefschetz and Ulam only as names on a book or paper. Gian-Carlo presents vivid, startling images of them, as live human beings, like us! What a shock! What a liberation! I don't know another since Plutarch who attains this balance: deep appreciation of their accomplishments, and honesty about the embarrassing qualities of great men of science.

After the suave raconteur of Persons and Places, Gian-Carlo the phenomenologist may come as a shock. The reader may feel lost for a moment. But, as Richard Nixon said in another connection, "When the going gets tough, the tough get going." Phenomenology is one of the seminal forms of thought of our age. You'll make faster headway with Gian-Carlo than with other writers on the subject. And you can look forward to the easy delights of Indiscrete Thoughts coming next.

But you're within your rights if you decide to take phenomenology in small doses. The chapter on mathematical beauty is recommended. Everyone knows that in mathematics, beauty is the highest desideraturn. But the few attempts to explain what's meant by "mathematical beauty" have been feeble and unconvincing. Gian-Carlo has a new answer. "Beauty in mathematics is enlightenment." When we are enlightened, we think, "How beautiful." This insight is both enlightening and beautiful!

Indiscrete Thoughts is strong medicine. His thoughts about mathematics are usually startling and provocative. His messages to and about mathematicians are provocative beyond indiscretion. Gian-Carlo never pulls his punches. I advise discretion in reading these indiscretions. A few every few hours. Gulping them at one sitting is not recommended.

Whatís the thread tying together Gian-Carlo the memoirist, the aphorist, and the phenomenologist? He strives to keep his eyes wide open and then tells it the way he sees it, without pretense, and often without prejudice. Always with wit and flair.


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