The life of Alan Turing (1912–1954) is as compelling a tale as the history of mathematics can boast. It is the story of genius, of courage, and of utter tragedy.

This is the subject of David Leavitt’s book, *The Man Who Knew Too Much: Alan Turing and the Invention of the Computer*, published by Norton in 2006. Leavitt did significant research for this volume and now and then was able to turn a phrase with the best of them. In its review, *American Scientist* described the work as a “commendable job,” and the *New York Times* used adjectives like “skillful” and “literate.”

Clearly, Leavitt’s book has its fans. But I am writing for MAA Reviews, and so I find it appropriate to address the *mathematical* content of the book. And, on this front, *The Man Who Knew Too Much* is a nightmare in print.

Leavitt’s math errors are frequent and egregious. For instance, on p. 129 he defines the zeta function as follows: \[ \zeta(x) = 1 + \frac12 + \frac1{3^{\mathrm{x}}} + \dots \frac{1}{\mathrm{nx}}\dots .\]

Here is an expression with *four* glaring errors. First, Leavitt italicizes “*x*” on the left side of the equation but not on the right. Second, he forgets the exponent “*x*” above the “2” in the second term on the right side, even though he puts an exponent “x” above the “3” in the third. Next, he fails to surround the final fraction by “+” signs, before and after. Finally, that final fraction should be \(\frac{1}{n^x}\) rather than \(\frac{1}{\mathrm{nx}}\), which is a very different thing.

Matters are equally garbled in a footnote on p. 220, where Leavitt addresses the four-color theorem that, he says, had been “proven in 1997.” According to him, the theorem states that, when coloring a map, “… you will need a minimum of four colors if no two adjoining regions are to be the same color.”

Now, think about this for a moment. If we had a map of the four adjacent U.S. states Illinois, Indiana, Ohio, and Pennsylvania, we could color them with just two colors: Illinois in red, Indiana in blue, Ohio in red, and Pennsylvania in blue. No two adjoining regions would be the same color, yet we would have colored our map with fewer than the “minimum of four colors” that Leavitt claimed was necessary.

The actual four-color theorem guarantees that a *maximum* of four colors will do the job for any planar map. And it was proved in 1976. So, Leavitt not only confused “minimum” and “maximum,” but got the date wrong by almost two decades. This is laughably bad.

For another example, consider Leavitt’s discussion of Mersenne primes on p. 234. He there credits Julia Robinson with proving that “ \(2_{521}-1\)” is a prime. Hmmm. It made me wonder if he would write the Pythagorean theorem as “\(a_2+b_2=c_2\).” And it was Raphael Robinson, not his wife Julia; his paper is easily found online.

The effect of such mathematical sloppiness is to erode confidence in everything else. If the author couldn’t tell the difference between an exponent and a subscript, or couldn’t state the four-color theorem correctly, or couldn’t copy down the equation of the zeta function, then what else did he get wrong? This sort of thing destroys credibility in a jiffy.

Leavitt is a novelist, not a mathematician, so some people might overlook these infelicities. But I doubt that readers would be as forgiving if I published a book on baseball in which I described a game that was won “by two free throws scored on penalty kicks at the 18th hole.” Anyone seeing such a sentence would conclude immediately that I had never played an inning of baseball. In like manner, anyone reading Leavitt will readily conclude that the author has never done a lick of mathematics.

There might be readers who enjoy this book. But from a mathematical viewpoint, David Leavitt is the man who knew too little.

William Dunham is currently Research Associate in Mathematics at Bryn Mawr College. He is the author of many books, and most recently was one of the editors of *The G. H. Hardy Reader*.