In my experience accessibility and understandability have to balance theorem proving.
This book is well on it's way to becoming a modern classic even if it is somewhat dated
in it's material. Robert Osserman is recognized as a great teacher of mathematics
by many in the mathematics community. But his approach has come between
the seeker of knowledge and his goal of understanding and mastery of the subject.
It is not his fault as in a peer review he would be generally
rewarded for his approach as he has been in his paper
publishing. But I can see grad students rushing to resell this book
as it has a limited amount of useful reference information
and very few of the actual definitions of the curves talked about.
The references are classic and many of the people are dead or retired by now.
It is access to the actual formulations for the minimal surfaces and explanations that
help in understanding the material not by theorem proving ,
but by visualization and explanation that are needed.
In that: this book fails. But compared to many other such mathematics books , it is actually superior!

Osserman's survey is both an excellent starting point for beginners and a reference for some interesting problems in the subject (although it was written some years ago!). Weiesrtrass' classical representation of minimal surfaces, their topology...how can all these be in such a small book?

The hype on the back cover, from the publisher, likens this book to the "literary bestsellers" of Watson and Thomas. However, the great shame is that this book won't last. Ultimately, the book is quite exasperating, not for the conceptual challenges it poses, but for the sloppiness of the writing a key junctures: often it is quite impossible to understand what is meant from what is written. On at least three occasions, I am certain that Osserman used inappropriate words. I entirely blame the editors for this failure. It is a shame because it ultimately renders the book incomprehensible to the non-specialist. I would recommend Brian Greene's recent book over this one, though the subject matter differs somewhat: Greene takes in string theory and the unified field challenge, while Osserman focuses on multidimensional space and cosmogony. Maybe it is worth reading Osserman to get a sense of the art of such books, to appreciate the quiet brilliance of Lewis Thomas. Sort of like drinking bad wine in order to really appreciate the good.

bmaddox
dobbs ferry ny

This is a marvelous little tour through the development of geometry and its ties with our ever-evolving conception of space. In fact, what tickled my cortex most here was Osserman's adeptness at conveying the strength of this tie. One feels a definite Yin-Yang interplay here, an enlightening example of how ideas are born of real-life problems, the solutions to which beget further physical inconsistencies that in turn spawn further ideas, and so on, and so on. And after being guided through the history of this mathematical development, it becomes easily clear as to why it is so difficult (in fact practically meaningless) for us to visualize a shape for our Universe. You understand why it is pointless to use conventional three-dimensional thought (what we all live with day-to-day) as a lever to comprehend the bigger picture. All of this is sewn so well into this neat little pocketbook, that it is practically a reference you wish to carry with you at all times. He misses the mark in at least one place when he stretches his discussions to include and touch upon other branches of science. His comment that our ability to see in a narrow swatch of the electromagnetic spectrum is a "quirk of physiology" is an air ball demonstrating his ignorance of photochemistry. But such shortcomings, which are extremely few, do not taint the grand picture that he has painted for us. The style is very approachable and I would highly recommend this work to anyone who seeks to grasp the whole enchilada.

Very readable. The emphasis is on helping the non-mathematical reader understand modern cosmology without the need for math. While reading this I had the sense that I was getting closer to visualizing the fifth dimension, but of course that is only an illusion.

Repeated here is the idea that there is something amazing about the ability of mathematics to describe the universe. Mathematics is amazing, no doubt about that, but our amazement ought to be tempered with the realization that the knowledge and extent of mathematics has grown along with our knowledge of the universe around us; and that the mathematics of the Greeks, for example, would not adequately describe the universe as it is known today. This makes me suppose that along with the incredibly vast areas of the universe unknown to us, there is also the vast extent of mathematics not yet even dreamed of by even our best mathematicians. Something to look forward to.