Read This!

The MAA Online book review column

Briefly Noted

July 2003

What hides behind the cute titles is a large collection of mathematical stories, anecdotes, and factoids. Eves clearly had fun collecting these stories. They include many old standards but (given the sheer bulk of the set) most mathematicians will find something here that they didn't know.

Many of the stories are (or try to be, see below) funny. Others are little morality tales, telling us edifying stories about mathematics and how it is done. There are some motivational anecdotes (e.g., according to Hilbert, it takes more imagination to be a mathematician than to be a poet). And there are various historical tidbits based on facts, mostly concerning records in number theory.

Of course, the collection shows its age. Several of the stories seem to be patterned on an old-fashioned Readers Digest sort of humorous anecdote that now falls flat. There is no reason why Eves should not have used this model when he wrote the book. Tapping into contemporaneous tastes and trends certainly is a sound didactical technique. The only problem is that tastes change; what worked very well one or two generations ago might not do the trick today. Finally, none of Eves' accounts on records in mathematics take work that was done after the early 1960s into consideration.

On the other hand, and in contrast with other collections of mathematical anecdotes, there is not a trace of meanness in Eves' stories. We mathematicians seem to be an endearing, if rather exotic, bunch. Or at least we are so in Eves generous eyes.

There are also things that worry us as historians. Eves gives no sources for his stories, so we are left guessing as to where he found them and therefore with no way to verify them. It would have been an herculean task to sift through these stories and assess their historicity, so we could hardly expect the MAA to do that. But readers should be on alert that if some of these stories seem too good to be true, it might well be that the reason is that they are not.

Every community has its shared stories. Many of the stories of the mathematical community can be found in these books. That in itself makes them valuable. Learning such stories is part of what initiates us into the mathematics community. So enjoy, and even pass on, but verify. [Eisso Atzema and Fernando Q. Gouvêa]

Before World War II, the city of Lvov, Poland (now L'viv, Ukraine) was a significant cultural center. Several of the now-famous mathematicians who lived there gathered regularly at a local café to discuss ideas and problems. They recorded their best problems (and solutions, when they had them) in a notebook that came to be known as "The Scottish Book". In The Scottish Café, Susan H. Case uses the story of these mathematicians — and of what happened to them as war approached — as inspiration for a cycle of poems dealing with life in the shadow of great catastrophe.

As the author explains in her note, these poems were written after the September 11 attack. Case uses the story of mathematicians living in Poland as Nazi Germany became more and more of a threat as an indirect way of exploring her own experience of living in New York and wondering whether further attacks were coming. The names are all well known: Banach, Kac, Tarski, Ulam, Orlicz, Schauder, Steinhaus, and several others. Some of their mathematics makes it into the poems, but Case is more interested in their personalities and their reaction to the Nazi threat.

When mathematics does come in, Case does a better than average job of capturing it in her verse. (There is quite a bit of poetry inspired by mathematics out there, but not a lot of it is very successful or very correct!) There is one big mistake, in a poem about the Banach-Tarski paradox: Case says it involves a dissection into an infinite number of pieces, which of course would render the paradox not very paradoxical. But the focus is resolutely on the people, their passion for mathematics and for problems, their lives before the war begins, and what happened to them when catastrophe came.

I hesitate to venture to comment on the poems as poems. Still, at the risk of making a fool of myself, here are a few remarks. Case's open, unpunctuated, verse does a good job of creating an atmosphere of foreboding and of dramatising the mathematical obsession of these men. There are occasional good lines, but the best effects are achieved not with individual lines but with the accumulation of small telling details. There are also occasional clunkers, such as a description of Banach, drinking heavily at a conference in Georgia,

dazzled by the proof in the vodka
the proof in the mathematics

For my money, this isn't brilliant poetry, but it's competently done and captures with nostalgia, respect and horror a significant moment in the history of twentieth century mathematics. [Fernando Q. Gouvêa]

As readers of Greg Chaitin's article know, it's zeta function time. Mathematicians who read one of the recent popular accounts of the Riemann Hypothesis might be interested in learning more. So Dover's decision to republish Aleksandar Ivic's The Riemann Zeta Function makes good business sense. It is also to be welcomed because this is a useful book.

There are not all that many books that focus exclusively on the Riemann zeta function. H. M. Edwards' Riemann's Zeta Function, also from Dover, comes to mind first. Edwards focuses on Riemann's original paper, using it as a springboard to develop the modern theory. I am aware of two other books: a more recent (1988) treatment by S. J. Patterson and and updated classic by E. C. Titchmarsh (revised by D. R. Heath-Brown). Ivic's book dates back to 1985, so it does not include the most recent results (e.g., there is nothing about random matrices), but it does offer a thorough treatment of the theory.

I'm not enough of an expert to offer advice on which of these books is the best reference on the zeta function. (The best entry point for the non-specialist is probably a broader book on analytic number theory, from which one might proceed to one of these books.) As a part-time historian, I tend to lean towards Edwards, but Ivic covers much more ground. In any case, I'm delighted to see this affordable Dover edition of a book that had been out of print. [Fernando Q. Gouvêa]

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