One of my favorite math reference books is the monumental Mathematics: from the Birth of Numbers, by Swedish writer Jan Gullberg, illustrated by Jan's son Per, as well as other members of his family. Gullberg was not a mathematician; he was a surgeon, who also wrote on scientific and medical topics. This grand compendium, published in 1996, was recommended to me by one of my Friendly Scientists who unfortunately is no longer with us. Charles Sheffield, who died in 2002, was both a scientist and a science fiction writer. When I told Sheffield, at a convention in 2001, that I was studying mathematics, he immediately cited me the Gullberg title, and said that this book would last me a lifetime. It's not something you read sequentially, like a novel; it's a reference book, where you look up what you need, when and where you need it.

It has an excellent chapter on logarithms and their origins. Mathematics, like music and costuming, is one of those fields of human endeavor where the past is everpresent, and where practitioners willingly attend to details of tradition that may go back thousands of years. Gullberg recounts the work of seventeenth-century Scottish mathematician John Napier. Though he's credited with the invention of logarithms, he actually must share that credit with one of his English contemporaries, Henry Briggs. It is Napier, though, whose name appears with logarithms based on the number e even though the books say that he didn't invent this form. The logarithm chapter of the Gullberg book shows a somewhat poorly printed facsimile page of Napier's book A Description of the Admirable Table oe Logarithmes, With a declaration of the most plentiful, easy, and speedy vie thereof in both kindes of Trigonometrie, as also in all Mathematicall calculations.

Currently I'm learning to identify the parts of logarithms, the characteristic and the mantissa. Gullberg, always ready to deliver fascinating mathematical and linguistic tidbits, writes:

Mantissa is a late Latin word of Etruscan origin, meaning "addition" or "makeweight" — that is, something added to make up the weight; it later came to acquire also the meaning of "appendix."

It is the decimal, or non-integer, part of a logarithm. See what I mean about ancient traditions!

And so I have finally been introduced to e. Even Gullberg is hard to understand when he talks about the derivation of e, or why logarithms using it are called natural. As with other transcendental numbers, golden ratios, and other ancient mathematical realities, I must accept these as features of the world without asking too many questions, at least for now. Repeat after me the hopeful, eschatological prayer of the aspiring mathematician/scientist: "Its usefulness and value will be revealed to me in the future."

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