This is the only biography of Leonhard Euler currently available in English, and it would be worth having for that reason alone. Originally published in German in 1995, it has been translated into English as part of the celebration of Euler's tercentenary in 2007. The book a good introductory biography of Euler, and it is handsomely produced, with nice paper and lots of illustrations. It is a welcome addition to the literature on Euler.

Fellmann has chosen to make this a non-technical biography. There are no mathematical details and no formulas. Short accounts of Euler's work are included, but few details are given. Even then, the sections that go into Euler's work are marked with asterisks so that readers who are not willing to delve into specifics can skip them. With non-technical readers in mind, Fellmann privileges those aspects of Euler's work that are more accessible, so his music theory gets much more attention than his work on elliptic integrals and his lunar theory and optics more than the geometry or number theory.

The real emphasis falls on Euler the man. Fellmann, who is one of the editors of the volumes of Euler's correspondence in the *Opera Omnia*, makes very good use of that correspondence and of other manuscript material to give us an inside look at Euler and those with whom he interacted. The attention lavished on each of Euler's colleagues, family members, and friends is a function of what material is available. Thus, there is very little on Euler's wife, because there is very little information about her anywhere. (Fellmann quotes Otto Spiess: "Since neither Euler nor anybody else speaks about her, she must have been (according to a known proverb) a fine woman!" I have no idea which proverb Spiess had in mind.) On the other hand, we get good descriptions of life in both the St. Petersburg and the Berlin academies, since there is extensive correspondence and other materials on them and on Euler's life within them.

Fellmann has a light touch, and manages to do quite a lot in little space. The book is much shorter than its 133 pages of main text suggest, but it does manage to give us a sense of the man and his life, and at least a glimpse of his work. Euler's work may well strike the reader as monumental and inaccessible; alas, it is hard to avoid this! One gets the feeling that Fellmann likes Euler, rather than only admiring him; he comes off as an interesting, well-adjusted, happy man.

The illustrations are wonderful. They range all the way from the standard portraits of Euler (with, thank goodness, proper information on their dates and authors) to portraits of his son and his mathematical associates, engravings of the places where Euler lived, reproductions of pages from his letters, and even a (very bad) drawing by one of Euler's sons that may be a representation of his parents. (If so, it contains the only known image of Euler's wife.)

Given those virtues, it is disappointing that more care was not taken with the translation, which would have benefited from some careful copyediting. There are many, many instances of translator-English, in which the German syntactic structure has been preserved in English words. Such sentences sometimes just sound weird, and sometimes come close to being incomprehensible. (In the examples that follow, I've refrained from attempting to reproduce the small caps used for each and every proper name. They annoy me and they're hard to do in html. Readers should take them for granted.)

For example, speaking of Peter the Great's wish to secure "hegemony in the Baltic area",

An essential preliminary step for this was the citadel built by Tsar Peter I (the Great) with an incredible expenditure of energy at the swampy mouth of the Neva river. From the very beginning, it carried Peter's name as the Russian metropolis and was built according to his own plans — with the aid of many foreign architects, engineers, and technicians — following a strict geometric pattern, starting in 1703 with the colossal bastion "Peter and Paul", and engaging hundreds of thousands of "work slaves."

That is (barely) English, but it is fairly strange English. I wonder whether most English readers will figure out that "the Russian metropolis" that "carried Peter's name" is St. Petersburg, that "Peter and Paul" is a cathedral, and that "work slaves" are serfs. But it gets worse. For example, consider this:

In the financial affair around David Koehler in connection with the calendar sales — it has already been described repeatedly — Euler has undoubtedly put himself in a spot, and the loss of competency resulting from it, combined with the not particularly fortunate activity of the congenial Johann Heinrich Lambert, has finally put the lid on it.

Anyone who can figure *that* out has my deepest admiration. I'll limit myself to pointing out that the "calendars" in question were almanacs, that the "has been described repeatedly" means that others have written about it (it is not discussed at all in this book), and that the mixture of tenses is found throughout the book. What is meant by describing Lambert as "congenial" and what put the lid on what is anyone's guess.

There are many, many such examples. Sometimes the translators choose the wrong English word. Sometimes they have the wrong word order. Not common in English are sentences like this one. Common they are in this book, though.

Then there is the place where St. Petersburg (always, by the way, referred to as "Petersburg", except when quoting from others) is described as the "Venice of the Nord". Or when Fellmann is made to say that London and Paris had "scientific academies of high and highest niveau." (It makes me wonder whether there was an intermediate version in French!)

And finally:

… since nowhere more than in the realm of mathematics are valid the words of Johannes: "The spirit goes where it wants to go."

I'm probably just being naïve, but I have to admit that it pains me that educated folks can fail to recognize a well-known Biblical quotation (from John 3:8) and as a result introduce a mysterious "Johannes" (in small caps!). *O tempora! O mores!*

Fellmann's book deserved better than this. It is a good read, a light appetizer for a full-blown biography of the great man. Let's hope someone will write one soon.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME. As his students know well, he is a stickler for good English prose.