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This book is an English translation of a collection of papers in Russian from a conference held in Moscow and St. Petersburg in 1983, 200 years after Euler's death. Two of the Russian papers in the collection are themselves translations from the German. The present English translation appears in 2007, 300 years after his birth. We speak of the "Age of Euler". A justification of this term is provided by a list of scientific terms connected with Euler s name and his many contributions to pure mathematics, well-known in the mathematical community and, in part, covered in this volume. What makes this collection remarkable, though, is the extensive treatment of Euler's contributions outside pure mathematics--to astronomy, celestial mechanics, ballistics, history of science, instruments and technology, physics, mechanics, hydromechanics, mechanics of elastic systems, variational principles of mechanics, and a mathematical theory of music. In addition to this survey of his contributions to science, we find here material otherwise very difficult to find detailed accounts of Euler's family life and the careers pursued by his children and grandchildren. Readers otherwise well-informed about Euler and his work will find here much to enhance their appreciation of this extraordinary scientist and human being. For significant and factual knowledge of Euler's contributions to science past and present, this book is easily the best available choice. ... Read more

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Customer Reviews (2)

Judenfrei Mathematics - Self-Destructive Russian Anti-Semitism
Written in the late 1970s, this disturbing essay on Russian anti-Semitism provides - in hindsight - a clear example of one of the many corrupting, self-destructive forces that operated within the Soviet bureaucracy and contributed to the eventual collapse of the Soviet empire. The author, Grigori Freiman, was a noted mathematician, a professor, and a member of the Communist Party. His samizdat essay was a plea for fairness and justice in the selection of Jewish candidates for advance training in mathematics. He also warned that Russian anti-Semitism was undermining the future of mathematics in the Soviet Union.

Samizdat refers to the self-publishing of underground literature in Russia under Communism. A copy of Grigori Freiman's samizdat essay reached the United States in 1978. Southern Illinois University Press in 1980 published this small book, It Seems I Am a Jew, in cooperation with the Committee of Concerned Scientists. Melvyn Nathanson prepared the introduction as well as translated Freiman's essay into English.

It Seems I Am A Jew is less than 100 pages (even including the forward, introduction, and a three part appendix). The essay itself is riveting, and most readers will likely read this disturbing essay in a single sitting. I highly recommend Freiman's remarkable essay to a wide audience that includes essentially any reader interested in history, concerned with the current political situation in Russia, or concerned with injustice wherever it occurs.

The appendix will appeal more to readers that have an interest in mathematics. Extremely difficult test questions were reserved for Jewish students (and sometimes for testing non-Russians from the more distant Soviet republics).These questions were designed to ensure that all Jewish candidates failed, even Jewish winners of the Soviet Union's Mathematics Olympiad.By the late 1970s the mathematics section of the Soviet Academy of Sciences had nearly achieved the goal of Judenfrei mathematics.

Ethnic profiling
The memoir of a Jewish mathematician. Freiman recalls the special obstacles he and other Jewish students of mathematics faced in the USSR. To get a doctorate in mathematics one had to pass an oral exam given by a member of the anti-semetic Stekov Institute. Only it seems if you were Jewish you got an especially difficult and in most cases impossible exam to pass. Because the exam was oral with no paper record of the questions asked, the examiner could easily fail the Jewish students by asking research level questions. A grim reminder of the policies of a terrible regime. ... Read more

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This significantly expanded second edition of Riemann, Topology and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Gttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics.

Special attention is paid in part one to new results on the Riemann-Hilbert problem and, in part two, to recent discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, 'fake' differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today his name appears prominently throughout the literature. The references to the literature have been substantially updated in this new edition. ... Read more

Customer Reviews (2)

Some nice insights, but very uneven (3.5 stars)
This book is worth reading for its second (stand-alone) half, about topology and physics. Michael Monastyrsky (MM) relies mainly on words to convey the big picture of many connections between the two topics. I had a number of "aha" moments while reading it, which had eluded me despite having struggled through some more formal introductions to T&P. Chapter 9's discussion of the relationship between homology and homotopy and later chapters about liquid crystals and topological particles were especially enlightening.

That said, I think it would be difficult to have those moments if you hadn't already had at least an introduction to algebraic topology (e.g., Michael Henle's wonderfully clear "A Combinatorial Introduction to Topology," from Dover). The treatment gets more abstruse in the later chapters, where it feels like MM was rushing. E.g., the chapter on braids and knots, which should be relatively intuitive to understand, struck me as quite abstract even though I'd already read a couple of books on the subject. And the discussions of magnetohydrodynamics and "What's next?" (at the end) were more like catalogues of topics than anything you could learn from. MM is also sometimes quite rambling, such as in his long chapter on gauge fields, inmore than 80% of which he doesn't discuss topology at all.

The rambling tendency is even more evident in the Riemann part of the book. E.g. Dirichlet doesn't make an appearance in the chapter entitled "Riemann and Dirichlet" until, again, 80% of the way through the chapter; and in the 2-page chapter "Last Years", MM jumps from Riemann's marriage and illness in 1862 to June 28, 1866, then to early 1866, then to June 14 and finally to Riemann's death on July 20 (@75-76). Even though Riemann's accomplishments are extremely interesting, there's something flat and dull about the writing style in this part of the book, so much so that I'd lost interest on two previous attempts to read it. But the main flaw in this section is that MM seems unsure of what level of readership he's aiming for. E.g., on one hand MM feels readers need to be told that "shock waves are formed when high-speed aircraft break the sound barrier, when atomic bombs explode, and so forth" (@69), but on the other hand if you don't have any prior background in complex analysis you will be lost. (It also doesn't hurt to have encountered monodromy mappings previously (@56)).

A few more diagrams would have been helpful especially in the Riemann section, and throughout the book it would have been nice if the diagrams had been re-drawn from the Russian edition: some of them are quite murky, and one or two of them don't seem to match the revised text. All in all, I give "Riemann" barely a 3, and "T&P" a 4, for an average of 3.5 stars.

Excellent
This is a translation of two quite small Russian books. The first is a biography of Riemann, the second a review of "Geometrical" physics, recently updated. Even the biography includes some mathematicswhich I did not fully understand, but it is a great introduction, and it'sgood to get your feet a little wet! The book is small and very readable. Irecommend it to students interested in understanding the relationshipsbetween physics, mathematics, and geometry. A gentle introduction to the"technical" journey. ... Read more