As a boy in high school, more than thirty years ago, I read E.T.Bell's "Men of Mathematics." Bell's book celebrates the lives of some twenty odd mathematicians. The biographies were inspiring, but the mathematical content of the book was hardly illuminating. So much more, therefore, is the pleasure of Professor Dunham's little book.

     Professor Dunham writes eight chapters, each devoted to one aspect of Euler's multifaceted work. Each describes no more than two or three problems that Euler attacked, successfully or not so successfully, but always with the greatest courage and cunning. In each chapter, a prologue and an epilogue provide an account of some antecedent, and some subsequent developments.

    Each chapter is written with transparent simplicity and goodwill. I think that this book is accessible, down to the very last morsel, to anyone with a modest preparation in calculus. I was caught up enough to follow every argument, down to the every last letter ---except, I should confess, in the chapter on geometry where Euler's direct and brutal attack on the problem of the "Euler line" (the line on which the orthocenter, the  centroid, and the circumcenter of a triangle lie) made me skim a page or two, and follow only the gist, minus the details, of his arguments.

    My most favorite chapter is the third, "Euler and Infinite Series." The chapter opens with the state of the art in Euler's day, with Jacob Bernoulli's account of his successes and his failures. Of the latter the most vexing was Bernoulli's failure to sum the series 1 + 2^-2 + 3^-2 + 4^-2 + ... . Bernoulli could show easily that this series converges. But to what? He issued a general call for help. At twenty-four years of age Euler showed how to rapidly estimate the value of the series to any desired accuracy. At twenty-eight years of age, in 1735, Euler gave a closed-form formula, proving that the series sums to p² / 6. Jacob Bernoulli did not live to see his nemesis slain. Euler went on to derive, by way of a trivial corollary, a beautiful formula familiar earlier (1655) to Wallis and Newton:

    What can one say of Euler's felicity with infinite series? Here in the clear light of Professor Dunham's projector we see the heroic Euler, striding forth without fear, right through the flames that had in moments incinerated the giants that ventured before him. And from almost nothing at all we see Euler create structures of astonishing and eternal beauty. And just in case there is any doubt, Euler returns again and again with a new proof, and another, to demonstrate with repeated stabs of his blood-stained sword that the demon he had slayed was truly dead and  gone.

    Perhaps even more astonishing than his battle with infinite series, was Euler's originality in founding the discipline of analytic number theory, and in his imaginative application of infinite polynomials to the art of counting the variety of certain combinatorial patterns. To these subjects too Professor Dunham devotes separate chapters. 

    Euler's collected works occupy seventy two hefty volumes (but not in English), and more are in the pipeline. The compilation and printing of these is funded by the Swiss government. Of all the world's filthy and ill-gotten gains that find shelter in Swiss banks --- the money stolen by the wealthy and the powerful from the most wretched and vulnerable of the world  --- it is heartening to know that at least some of the proceeds from that loot are being invested by the Swiss in this imposing monument to human intellect.

    Professor Dunham concludes that "there is fertile ground for a number of sequels." To this I say: please give us more. There must be a million like me, I'm sure, whose thirst for this sort of books will never be slaked.