This is a fascinating book, even though there isn't much mathematics in it. (*Love with Mathematics* might have been a better title.) It gives us a glimpse of life and courtship in the 1920s, shows what it was like to be a creative engineer at the time, and tells us a little bit about mathematical education and how mathematics was understood.

The first main character in the story is Barnes Wallis, a talented young engineer who was pretty much self-taught and was working on the development of airships (i.e., Zepellin-style dirigibles). Barnes' father, having lost his first wife, remarried, and so Barnes got to know the family of Arthur Bloxam, brother to his father's new wife. Arthur Bloxam's daughter Molly is the other main character of the story.

Barnes met Molly in 1922, when he was 34 and she was 17. He seems to have fallen in love instantly. He was about to leave England, however, the airship job having (temporarily, as it turned out) disappeared. He decided to strike up a correspondence with Molly. Of course, this required obtaining her father's permission. This was granted, but conditions were imposed: it was to be a pen friendship only, nothing that would pose a threat to Molly's college career (which she was about to start at University College in London) nor to "her open-minded contact with men her own age."

So began a long courtship by correspondence. In the early phase, perhaps in order to have an excuse for writing, Barnes offered to help Molly with her mathematics. As a result, the letters include lessons in calculus, some elementary trigonometry, and a very little bit of physics.

These initial letters are fascinating. Both writers work under serious restrictions as to what they might say, and so both spend lots of time telling each other how wonderful the other's last letter was and encouraging each other to continue writing. Barnes is a good teller of stories, and keeps things interesting.

As the courtship evolved, Molly's father became more and more concerned. He seems to have felt Molly was too young for this sort of thing, and worried that Barnes' age and experience would allow him to convince her to make a decision too early and too easily.

Still, about halfway through the book Mr. Bloxam accepts the fact that Barnes really is courting his daughter, and relaxes the rules a little. He allows Barnes to express his feelings, but not Molly! She is to withhold any hint of how she feels, any decision, until her 19th birthday. So we are treated to a rather strange correspondence. Barnes' letters become little more than repeated protestations about how much he loves her (and therefore make for much less interesting reading). Her replies are, as her father stipulated, guarded, though there are ample hints about how it all ends.

Of course, Barnes gets the girl in the end, and the author, his daughter, tells us a little — very little — about their life together.

So what's interesting? First of all, these are two interesting people. Were it not for that, the book would be unreadable. Barnes is smart but unsure of himself, especially at first. Molly is sensitive but intelligent. We grow to like them... and to share their impatience with the rules under which they find themselves.

Second, the book gives a fascinating glimpse of life in the 1920s. Because Barnes and Molly must write without talking about feelings, they tell each other what they are doing, and so we see what it was like to be an engineer, the ups and downs of the airship business (we don't quite get to see the final down, but there are hints), and the difficulties of university. We learn a little about courtship and what it entails, and come to realize that the restrictions imposed by Arthur Bloxam actually helped these two young people get to know each other quite well before making their final decision.

Finally, there are a few interesting bits in the mathematics. The notation for limit was apparently "Lt." Barnes uses bars over expressions where we would put them in parentheses. Molly seems to have no trouble following an exposition that, though witty, is fairly serious. We find out that Molly's pre-university mathematical education was pretty dismal, contra all the legends about the good old days.

Barnes argues, at one point, that 0 is not simply "nothing", not a number in the sense that 2 is a number, but rather a code for a variable that becomes arbitrarily small. In other words, he takes 0 and ∞ as dual concepts. And we get some nice quotes. Here is Barnes writing about a temporary teaching job he had (I have preserved Barnes' idiosyncratic spelling and punctuation):

I've been getting so cross with some of my people — I thumped a desk today. People seem so __stupid__ about maths. I don't mind how much explaining I do, or what pains I take to make them understand, but inattention and wilful stupidity I cannot tolerate.

Or, getting ready to explain some calculus to Molly:

...perhaps it is best to say that I do not propose to give the full mathematical treatment of the subject — I do not see that that is at all necessary (also it is rather difficult). The calculus is a very beautiful and simple means of performing calculations, which either cannot be done at all in any other way, or else can only be performed by very clumsy, roundabout, and approximate methods. No one would suggest that you must be able personally to manufacture a needle, before you are allowed to sew, or that I must be able to make a watch, before I am allowed to tell the time, — these things are tools, or instruments, put at our disposal by the accumulated experience of our forefathers, and we are quite justified in making such use of them as our skill and ingenuity can contrive. So with the calculus — it is a mental tool left at our disposal by the great mathematicians of the past.

Here he is meditating on how hard it is to make trigonometry fun:

Somehow one can not make any fun out of trig. its all so matter of fact — its difficult to say just what I mean — Calculus is an art — it endows you with wonderful powers; you can let your imagination go to all sorts of lengths and not pass out of the realm of reality — Calculus is like chocolate meringues — elementary trig is like very thick stale bread and margarine. It improves a lot later on, and like everything else, merges into calculus...

At the end, the reader feels happy for Barnes and Molly, and perhaps wishes to know more. I was a little frustrated to find no explanation at all of the "bouncing bomb" business from the subtitle, and no account of what happened to Barnes' airships. But that frustration only shows how well I got to know and like these people, and underscores that this curious book is well worth reading.

Fernando Q. Gouvêa is the Secret Master of MAA Reviews, the editor of FOCUS online, and Professor of Mathematics at Colby College in Waterville, ME. He thinks trigonometry is more like rice cakes and calculus is more like rice and beans. It is number theory that is chocolate meringues, while history of mathemaitcs is regular meringues.