Everyone with any interest in probability or combinatorics should take a look at this book, and at least read Chapter 1, on the Buffon needle problem. It gives a beautiful conceptual solution, quite different from the more well-known solution using integrals to get conditional probabilities. I find it hard to imagine anyone reading Chapter 1 and not deciding to read the entire book.

I heard Rota lecture on this material, and the book has much the same feeling as his lectures: it is clear, elegant, and concise, full of illuminating examples. Relatively little background is required, and it should be easily accessible to beginning graduate students (or undergraduates with unusually strong backgrounds).

It was about five years ago. Physics suddenly seemed fascinating but I was struggling with math. My tutor suggested two books for me. One of them was this book. I cannot say this book was particularly helpful but it gave me a good sense of what mathematics is: its people, culture, history, and philosophy. Quite unlike E.T. Bell's Men of Mathematics, this book does not contain romantically presented stories of some math heros. And unlike some popular math books by Ian Stewart, it does not attempt to explain (rather unsuccessfully) some esoteric theories. It is just as the title suggest--what a mathematical experience can be. A book of this kind is rare.

P.S. Now, some five years later, I am not sure if mathematical knowledge maintains a separte existence as Plato had thought, and as the authors believe. (Ref. Plato, Phaedo)

The best book I have read of it's type. Seemlessly incorporating Mathematics, Philosophy and History. Makes one want to really read everything in the Bibliography.

This book was a sheer joy to read and digest. The authors skilfully comingle history, mathematics, philosophy, and biography. The result is a truly fantastic voyage into the meaning and gist of discovery and conjecture. In chapter after chapter important ideas like Fourier analysis, Non-Cantorian Set Theory, and Objects and Structures are scrutinized in a very interesting manner.

The deeper you go into the book the more will you revel in the sheer majesty and scope of the topics. I had to read the chapter on Inner Issues twice to really get everything out of the text. Topics such as Teaching and Learning are very insightful and full of little hidden gems.

If you are prepared to expend some effort and if you wish to know what mathematics "really is like", grab this book. I am sure this will become a permanent treasure in your library and you will peruse it often long into the night.

This book is a pleasure to read, whether or not you're interested in math or philosophy. It stands on the premise that when speaking or writing of science and scientists, we should acknowledge their fallibility and avoid myths. Rota believes the mythification of science and scientists is responsible for many of the flaws in education and science in general.

Accordingly, Rota attempts in this book to show us mathematicians behind the scenes. He exposes the prejudices, mannerisms and also the nice traits of giants such as John von Neumann, Stanislaw Ulam, Willi Feller, Norbert Wiener. His portraits are not based on dull facts, but on lively anecdotes, and you really get a sense of the people he describes. I wish professional biographers took note. Rota also speaks of mathematics and philosophy, again debunking myths and exposing clearly the underlying trends.

As a writer, Rota is fantastic. Through his brief sketches of people, places and events, a connected whole emerges. The clarity of his writing and thought, and his obvious pleasure with words, remind me of Norman Maclean's "A River Runs Through it". A bit like poetry in prose.

Great mathematicians and philosophers can clearly teach us mathematics and philosophy, but I've always thought they could offer more. As critical and itelligent observers, they can draw attention to unsolved problems. As individuals often privy to the greatest genius of their time, they can pass on the odd bits and pieces of wisdom they inevitably pick up, but can't easily fit into any coherent system.

In this book, Gian-Carlo Rota does what I wish more accomplished figures would do: he writes down a motley asortment of wisdoms he collected throughout his life along with a number of pressing questions he never saw answered. True, there is no one overarching theme in his thoughts, nor does he defend any one particular thesis, but few of us have ever synthesized our thoughts into a coherent system.

Like any good educator, Rota doesn't patronize, nor does he dwell on personal reminiscences. "Indiscrete Thoughts" is his way of exiting the scene, leaving behind all the unfinished business of his day for the next generation of mathematicians and philosophers to pick up.

G-C Rota is truly an astonishing writer. His observations are precise and very phenomenological. I could not let go off his book once I started reading it. I truly enjoyed every line of it. It is indeed one of my favorite books.

This is an unusual book on the discipline of mathematics. Don't look here for the usual fluffy collages of fractals, chaos theory and hagiographies.

What this book offers is a collection of essays on the state and nature of mathematics by three top mathematicians. They're honestly worried about the schism between math and science, interested in the effect the computer could have on math, critical about the mathematical establishment. They're completely honest, and their criticisms are incisive and well reasoned. This book is food for thought, and not only about math.

The authors differ in their writing styles. While all three have good essays, Rota is a fantastic writer, and his mixture of serious thought, pith and gossip is completely refreshing. You should also read (before this book) Rota's "Indiscrete Thoughts".

This is a good text for a course in ODE after the computational course is completed. This book covers many topics in ODE, but be careful and watch for errors; especially near the end of the text. Most of the errors come in the excercises. For instance: you are asked to show that "every finite sequence of eigenfunctions of a S-L system is bounded". Duh! This is trivial until one realizes that every infinite sequence is also bounded.