This passage was quoted by William Dunham in Euler: The Master of Us All in relation to the criticisms of the great mathematician Leonhard Euler, whose mathematics “did not always display the rigor and precision of today’s.” In introducing the Galileo quote, the author said:

These shortcomings have given ammunition to mathematicians who criticize his work as primitive, intuitive, and decidedly pre-modern. They have a point.

On the other hand, one could reasonably ask whether modern mathematics would even exist without him. It is true that he sometimes proceeded heuristically, relying on intuition as much as logic. But had he been dissuaded by a standard of rigor beyond his reach, would Euler have forgone his remarkable journey? ... Euler took his share of risks, but for this I believe the mathematical world should be ever grateful.

This is worded much too mildly. Euler: The Master of Us All is an overview of this genius’s achievements, and even in this sketchy survey they are shown as fundamental, far-reaching, and vast. If the reader does not fully understand all of the mathematics in this book (as I did not), he will nonetheless be struck with awe at the earthshaking power of this man’s intellect. Euler created a large part of modern mathematics. His thinking was not only as intensive as an electronic microscope, but also as extensive as the Hubble telescope. The publication of Leonhard Euler’s collected works, the Opera Omnia, started in 1911 and “has consumed the remainder of the 20th century [and continues to this day]. To date [1999], six dozen volumes (more or less) have appeared, but the Eulerian gusher has not yet run dry. … A typical volume of the Opera Omnia is large, running from 400 to 500 pages—although some contain over 700.” Topics covered? Algebra, number theory, theory of equations, combinatorics and probability, analysis of infinities, differential calculus, integral calculus, infinite series, integration, geometry, mechanics, theory of machines, naval science, solar and lunar motion, motion of planets and comets, tides and geophysics, optics—and I am leaving a lot out of this list.

I have always liked reading biographies of geniuses, and I was interested in Euler for a long time, but I never pursued the interest until recently. Strange as it may seem, I was partly stopped, not by my intellectual distance from the topic of mathematics, but by a sense of distaste. If I have no photo to look at, I tend to picture people by their names. The name “Euler” for me unaccountably brought to mind a tight-lipped, severe, imperious countenance such as this:

(Prominent Nazi Rosenberg)

I thought for years, “This Euler’s life is bound to be utterly fascinating, and I’ll end up loving him, so one day I suppose I’ll pick up his biography.” But then, last year, when I got into mathematical thinking on a project of my own, I happened to come across an actual likeness of the man:

(Euler)

As though a switch had been thrown, my attitude changed diametrically, and I borrowed Euler: The Master of Us All from my local library. I could not learn enough about the life of the possessor of this immensely sympathetic face, one of the greatest minds who ever lived.

The French mathematician and astronomer Pierre-Simon Laplace once urged: “Read Euler, read Euler, he is the master of us all.” The carping of others about what they see as Euler’s shortcomings, and the answer to them provided by the Galileo quote, evokes a principle upheld by Ayn Rand: that you do not need to know everything to know something. So if you read this book, but grasp only a portion of it, the thing you will know is that that principle is true—in spades.

(Edited by Rodney Rawlings on 9/15, 5:43pm)