I have complied as a PDF file a collection of over 200 of Gian-Carlo Rota's delightful telegraphic reviews, along with a fascinating review by Gian-Carlo of the Schaum's Outline Series books in mathematics. I have also included his article entitled The Lost Café about his friend Stanislaus Ulam. (All of this material appeared in the 1990's in my newsletter The Bulletin of Mathematics Books.)
Below is an excerpt from the my Forward to this document, along with excerpts from the Schaum's review, a few telegraphic reviews and an excerpt from The Lost Café.
If, after reading the excerpts, you are interested in the entire PDF file (of 72 pages), I am making it available for $12.00. Just click the PayPal button below. Once payment is made, I will email you the PDF file and a password to unlock the file.
Sometime in 1992, frustrated with how difficult it was to obtain good information on what advanced mathematics books were being and had been published in the various fields in which I was interested, I decided to publish a newsletter that addressed this frustration. I called it The Bulletin of Mathematics Books.
The publication lasted 15 years, through 58 issues, until I was forced to shut it down in 2007 due to lack of publisher interest and support.
Briefly, each issue of the Bulletin contained a list of the latest releases in intermediate and advanced mathematics books from most of the world's leading publishers of such books. Also, each issue contained one or two comprehensive lists of books in one or two chosen fields, such as group theory, logic or partial differential equations. These lists were populated by a database of over 10,000 mathematics titles that I had rather painfully assembled in 1992 by contacting various publishers.
Perhaps the most unique feature of my newsletter was the contribution of my friend and colleague Gian-Carlo Rota. This contribution consisted of two things. First, there was a series of telegraphic reviews of mathematics books. These are short but highly entertaining book reviews that only Gian-Carlo could have written. (Anyone who knows Gian-Carlo's writing style will instantly know this to be true.) One feature of these reviews is worth singling out. Gian-Carlo loved the Schaum's Outline Series and did a special rather extensive review of that series, included herein.
The second part of Gian-Carlo's contribution was a column entitled Indiscrete Thoughts. As it turned out, this column consisted solely of a single serialized article entitled The Lost Café, a tribute to his close friend Stanislaus Ulam.
While my newsletter will never rise like the Phoenix out of its ashes, it seems appropriate at this time to resurrect Gian-Carlo's wonderful telegraphic reviews and to republish The Lost Café. I hope you enjoy this content as much as I do.
Gian-Carlo Rota was an Italian mathematician and philosopher with unusual gifts for mathematical research, as well as for teaching and writing. Gian-Carlo earned his undergraduate degree at Princeton and his Ph.D. at Yale, graduating summa cum laude. He trained originally as a functional analyst, but then switched to combinatorics. His series of ten papers entitled "Foundations of Combinatorics" written in the 1960s has been credited with upgrading combinatorics from a peripheral field into a main-line branch of mathematics. Some of his strongest combinatorial work includes the development of incidence algebras (which generalize the theory of Möbius inversion), the location of zeros of polynomials, the theory of matroids and the finite operator calculus. He also contributed to the theory of Baxter algebras and to invariant theory.
Gian-Carlo spent most of his career as a professor at MIT, where he was the only person ever to be appointed both Professor of Applied Mathematics and Professor of Philosophy. (He was the Norbert Wiener Professor of Applied Mathematics at MIT.) Gian-Carlo taught a variety of mathematics classes as well as classes in philosophy. He was a member of the Heidegger circle and also an expert on the phenomenology of Edmund Husserl. Two of the philosophy classes he taught regularly were entitled "Being and Nothingness" and "Being and Time."
Gian-Carlo held four honorary degrees: from the University of Strasbourg, France (1984); the University of L'Aquila, Italy (1990); the University of Bologna, Italy (1996); and Brooklyn Polytechnical University (1997). He was elected to the National Academy of Sciences in 1982.
From 1966 until his untimely death in 1999, Gian-Carlo consulted at the Los Alamos National Laboratory primarily during the summer months, where he was able to spend time with his close friend Stanislaw Ulam. He also spent many Januaries consulting at the University of Southern California, where his friend Marc Kac taught.
When you travel to Naples, Zimbabwe, Bombay, or Dresden, and you visit the foremost scientific bookstores of such places, you will not find on the shelves any items of the Springer Grundleheren series (as was the case in the golden times of Courant and Hilbert), nor any of the soi-disant thorough textbooks by Serge Lang, nor even any volume of the Graduate Textbooks in Mathematics (Springer's flagship series), much less any of the numerous publications of the American Mathematical Society. Such books are totally unknown in Togo or Guyana, two countries that, we rashly surmise, are probably not to be found in the mailing list of the Springer Newsletter (but, we should add, two countries that are well within the reach of the present Newsletter [Gian-Carlo is referring to The Bulletin of Mathematics Books, ed.]). What you will find instead in every scientific bookstore, whether in Santiago or in Islamabad, is a shelfful of firmly bound, elegantly printed volumes of what in this country is known as the Schaum's Outlines. A wide selection of titles from this series is likely to be the backbone of every scientific bookstore's sales, whether in Nigeria or in Indonesia, in Ecuador or Greece. The individual volumes may be purchased at a price affordable to college students, either in the original English, or in bilingual editions (indispensable to those ambitious young men and women who are eager to pursue their graduate studies in the U.S., with an eye on an eventual green card), brilliantly translated by mathematicians of high local renown, into one of a great many colorful and poetic languages of the world: Swahili, Urdu, Papiamento, Cantonese, Basque and even Esperanto.
Advances in Number Theory, F. Q. Gouvea and N. Yui, editors, Oxford University Press, 1993, 534pp.
Advances in number theory probably take more "Sitzfleisch" than advances in any other branch of mathematics. The techniques are complex, sophisticated, pedigreed, and take years to master. The results are more often than not elegant, understandable by any educated mathematician, and frighteningly difficult to prove. The advances are so refined that they are at times wholly imperceptible to anyone not in the thick of research. Every mathematician should be proud to be counted in the same community with those hardest-working of all mathematicians, the number theorists. The present volume bears witness to their indefatigable work.
Algebraic geometry and its applications, B.L. Bajaj, Ed., Springer-Verlag, 1994, 536pp.
This is an excellent source for several reasons: (1) it gives equal time to most of the current trends in algebraic geometry; (2) it does not disdain applications; (3) it does not turn its nose up at combinatorics; (3) it revises several old problems; (4) it gives new and elegant proofs of some classical theorems; (5) it presents commutative rings in a non-obnoxious way; (6) it celebrates the anniversary of one of the great mathematicians of our time, namely, S. Abhyankar; (7) it admits that algebraic geometry may, just may, have something to do with computer science. A refreshing departure from the usual monograph on algebraic geometry.
Algebraic K-Theory, V. Srinivas, Birkhauser, 1991, 314pp.
Although the author does his best to explain the difficult topic of K-theory, perhaps the central chapter of today's algebra, to an audience of mathematicians steeped in commutative algebra, homological algebra, algebraic topology, algebraic geometry and category theory, and although the author amply succeeds in his avowed purpose (a success for which he should be warmly congratulated), nevertheless, the overwhelming majority of research mathematicians (that is, 99.99% of them) will feel that they have been left out on page one. It would have cost little to have prefaced the book with a Reader's Digest Condensed Version of the material, which explained in the language of the ordinary research mathematician what is going on in K-theory. Or shall we conclude that such an exposition is impossible? We strongly surmise that it is possible, but the author would be permanently exiled from the community of K-theorists if he dared do such a thing, that is, if he dared betray to the non-initiated the holy secrets of the theory. Let us hope a disrespectful engineer or physicist will come along soon, who will break the pledge of omertà and finally tell us what K-theory is really about.
An Introduction to Sato's Hyperfunctions, M. Morimoto, American Mathematical Society, 1993, 272pp.
Sato's theory of hyperfunctions is one of the most original contributions to mathematics in the last fifty years; although motivated by Schartz's theory of distributions, it goes much deeper and much farther. It is also difficult to learn, partly because it demands of the reader a background in several complex variables and in homology theory, and partly because it is hard to find in it a purely algebraic underpinning to hang onto. But the theory is here to stay, and it is wiping out its competitors one by one. If philosophers of science were doing their duty, instead of writing books on the philosophy of quantum mechanics, they would give a philosophical treatment of the theory of hyperfunctions. But is there any living philosopher of mathematics who is competent enough to carry out this task? No.
One morning in 1946, in Los Angeles, Stanislaw Ulam, a newly appointed professor at the University of Southern California, awoke to find himself unable to speak. A few hours later, he underwent a dangerous surgical operation after the diagnosis of encephalitis. His skull was sawed open and his brain tissue was sprayed with antibiotics. After a short convalescence, he managed to recover apparently unscathed.
In time, however, some changes in his personality became obvious to those who knew him. Paul Stein, one of his collaborators at the Los Alamos Laboratory (where Stan Ulam worked most of his life), remarked that, while before his operation Stan had been a meticulous dresser, a dandy of sorts, afterwards he became visibly sloppy in the details of his attire, even though he would still carefully and expensively select every item of clothing he wore.
Soon after I met him in 1963, several years after the event, I could not help noticing that his trains of thought were not those of a normal person, even for a mathematician. In his conversation he was livelier and wittier than anyone I had ever met, and his ideas, which he spouted out at odd intervals, were fascinating beyond anything I have witnessed before or since. However, he seemed to studiously avoid going into any details. He would dwell on any subject no longer than a few minutes, then impatiently move on to something entirely unrelated.
Out of curiosity, I asked John Oxtoby, Stan's collaborator in the thirties (and, like Stan, a former Junior Fellow at Harvard), about their working habits before his operation. Surprisingly, Oxtoby described how at Harvard they would sit for hours on end, day after day, in front of the blackboard. Since the time I met him, Stan never did anything of the sort. He would perform a calculation (even the simplest) only when he had absolutely no other way out. I remember watching him at the blackboard, trying to solve a quadratic equation. He furrowed his brow in rapt absorption, while scribbling formulas in his tiny handwriting. When he finally got the answer, he turned around and said with relief: I feel I have done my work for the day.
The Germans have aptly called Sitzfleisch the ability to spend endless hours at a desk, doing gruesome work. Sitzfleisch is considered by mathematicians to be a better gauge of success than any of the attractive definitions of talent with which psychologists regale us from time to time. Stan Ulam, however, was able to get by without any Sitzfleisch whatsoever. After his bout with encephalitis, he came to lean on his unimpaired imagination for his ideas, and on the Sitzfleisch of others for technical support. The beauty of his insights and the promise of his proposals kept him amply supplied with young collaborators, willing to lend (and risking to waste) their time.