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Beyond Einstein

David E. Rowe, Tilman Sauer, and Scott A. Walter, editors
Publication Date: 
Number of Pages: 
Einstein Studies 14
[Reviewed by
Michael Berg
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As so many of those of my generation, or the one or two preceding mine, in those halcyon days when the public’s exposure to the lives of scientists and mathematicians occurred almost entirely through books and articles, my first awareness of the mystique of the titans of exact science came courtesy of Albert Einstein. I guess he still holds the record for biographies and biographical articles written about a scientist. Accordingly, before I even knew that there were such things are research mathematicians, I learned that Einstein had performed acts of scientific magic, using only paper and a fountain pen — what an attractive image to a kid of fourteen or so. I figured that the thing to do was to become a theoretical physicist. The books and articles I went on to read, not just about Einstein but also about Heisenberg, Fermi, Bohr, Dirac, and Pauli — I recall Gamow’s book Thirty Years that Shook Physics: The Story of Quantum Physics — , conspired to enchant me: equations, diagrams, and mysterious symbols provided my imagination with all the fuel to spur me on to commit to study first physics, then, a little later, mathematics — just mathematics. The transition to these purer realms came about courtesy of my early discovery that the only part of physics that I could relate to was its mathematics: here was the true home of mysterious (and irresistible) equations, diagrams, and symbols. I haven’t looked back in five decades.

But physics has regrouped, so to speak, in that now more than ever (at least in modern reckoning) its interactions with mathematics are striking and deep. The interplay between low-dimensional topology and quantum field theory comes to mind, but there’s a lot more. The book under review has to do with that “a lot more.” It is marvelous indeed that it’s about none other than the redoubtable Albert Einstein.

The subtitle is given as “perspectives on geometry, gravitation, and cosmology in the twentieth century,” and the book under review is a compendium of articles written around these themes. The book contains seventeen such articles, presented in 2008 at a conference in Mainz. It is launched under the auspices of the Einstein Studies Series, whose objective is “to build … a thriving international scholarship focused on Einstein.” Evidently it has succeeded in spades.

The book is subdivided into five parts, respectively, “Mathematical and Physical Underpinnings of Spacetime,” “Testing General Relativity and Rival Theories,” “Geometry and Cosmology, Past and Present,” “Mathematical Motifs in General Relativity and Beyond,” and “Quantum Gravity, Conformal Boundaries, and String Theory.” Hilbert appears in Chapter 3 (Part I). Chapter 7 (Part II) talks about the fifth force in physics (its appearance, disappearance, current status). Hermann Weyl occurs in Chapter 11 (Part III). Chapter 13 (Part IV) is devoted to nothing less than the Poincaré Conjecture and Perelman’s proof thereof; and Chapters 15 and 17 (Part V) hit, respectively, quantum field theory in curved spacetime and string theory and the geometry of spacetime. So this book sports many very tantalizing offerings even for us mathematicians.

Michael Berg is Professor of Mathematics at Loyola Marymount University in Los Angeles, CA.

See the table of contents in the publisher's webpage.