Poetry of the Universe: A Mathematical Exploration of the Cosmos

This is a charming book, with a graceful pace and engaging illustrations. The transparency and accessibility of this book are a gift to the reader, who is brought through complex material in a gentle way. I suspect that technically advanced readers may find some of the material fairly elementary, but may still find pleasure in the beauty of this book. I should here confess that as a math major I took a course from Professor Osserman on linear algebra about 30 years ago. His teaching style then mirrored his writing style in this book--calm, understated, confident. Additionally, I probably never thanked him at the time for giving me a great math experience during that course. (For non-mathematicians who haven't had such an experience, let me assure you that there is exhilaration in struggling with an initially complicated mathematical idea that suddenly becomes crystal clear.)So, belatedly, if you're reading this review, Professor, THANK YOU!

This is a story of shape and form. The Poetry of the Universe answers two related questions: What is the shape of the universe and what do we mean by the curvature of space? During the great period of global exploration the Europeans placed rigorous demands on maps, demands that stretched the capabilities of mathematicians. Robert Osserman offers a striking parallel between that endeavor and our modern efforts to unravel the form and structure of the universe. Osserman's description of the evolution of abstract geometries is fascinating. We learn about the remarkable contributions of the combined genius of Euler, Gauss, Lobachevsky, Bolyai, Riemann, Minkowski, and Einstein to our new understanding of cosmology. Gradually, Osserman brings us full circle from the problem of representing a spherical (or elliptical) earth on a Euclidian flat map to the more difficult problem of representing an expanding universe characterized as a hypersphere. This is a good little book and I can recommend it to a wide audience. Osserman conveys the beauty and excitement of mathematics without delving into equations. In parallel, he provides expanded footnotes in an appendix for the mathematically inclined. I suggest reading the appendix after completing each chapter, mathematically inclined or not. In keeping with his title, he offers pertinent, often poetic quotes in each chapter such as: Euclid alone has looked on Beauty bare. Pure mathematics is, in its way, the poetry of logical ideas. The most distinct and beautiful statement of any truth must take at last the mathematical form. (By Edna St. Vincent Millay, Albert Einstein, and Henry David Thoreau.)

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 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.

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.

Robert Osserman does a wonderful job of covering the evolution of Mathematics from early studies in Greece to modern day Cosmology around the world. This is a superb introduction to many of the different paths in Mathematics. Available and accessible to any level of study in math, Osserman keeps the equations down to a bare minimum and focuses more on the thought processes behind the theory as well as some of the socio-political factors surounding their introduction into the Mathematical Community. Illustrations help to explain the words and give a good mental picture of the abstract thought in the book.Highly reccomended to anyone with an interst in Mathematics and who may be looking for a way to break into higher level subjects such as Relativity, Non-Euclidean Geometry and the Structure of the Universe.