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Fantasia Mathematica

Clifton Fadiman
Publication Date: 
Number of Pages: 
[Reviewed by
Allen Stenger
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This 1958 fiction and verse collection was very impressive in its day, but has not aged well. I remember reading it 50 years ago, and I loved it then, but re-reading it today was painful at times. Literary styles have shifted a good bit in the past 60 years, and stories today are much more character driven, even in the science fiction genre (which most of these stories were selected from). The stories here tend towards the mad-scientist model. Their mathematical content is usually based on Moebius bands or Klein bottles, or sometimes tesseracts (hypercubes), all of which have drifted out of the public consciousness. The fiction tends to be jokes rather than stories.

The book is divided into three parts. “Odd Numbers” are mainstream stories (usually a fragment of a longer work) that have some mathematical content. “Imaginaries” takes up most of the book and consists of science fiction stories with a mathematical premise. “Fractions” are single-page pieces, mostly verse (including limericks), about a mathematical concept.

There were a few stories that I still enjoyed today. William Hazlett Upson’s “A. Botts and the Moebius Strip” is about how to circumvent the military bureaucracy and get things done, and does have good character development (in addition to a starring role for the Moebius strip). H. Nearing, Jr.’s “The Mathematical Voodoo” will appeal to every teacher who struggles with eager but inept students, but has no explicit mathematical content. Edward Page Mitchell’s “The Tachypomp” (written in 1873) is a mad-scientist story but has lots of interesting ideas and is well-written. It deals with a method for making railroad cars move arbitrarily fast, and was only slightly spoiled by our later knowledge that the theory of relativity rules this out. Arthur Porges’s “The Devil and Simon Flagg” is a classical twist on the “making a pact with the devil” story, and was only slightly spoiled by Fermat’s Last Theorem having been proved since it was written.

I think the “Fractions” section has held up better than the rest. There are a lot of classical pieces here (for example, from Edna St. Vincent Millay, Vachel Lindsay, and Andrew Marvell), and parodies of classical pieces. The mathematics is more varied, and often written by scientists rather than professional writers. George Gamow’s “An Infinity of Guests” is about the Hilbert Hotel. C. Stanley Ogilvy’s “For All Practical Purposes” is a clever take on Zeno’s Paradox. G. H. Hardy’s “Bertrand Russell’s Dream” retells Russell’s nightmare about the fate of the last surviving copy of Principia Mathematica.

Fadiman’s 1962 sequel (now out of print), The Mathematical Magpie, has the same nature but more variety in the formats, including some songs and some cartoons. Despite being only four years newer it has held up better over time. A more recent collection that I have not seen but is well-regarded is William Frucht’s Imaginary Numbers: An Anthology of Marvelous Mathematical Stories, Diversions, Poems and Musings.

Allen Stenger is a math hobbyist and retired software developer. He is an editor of the Missouri Journal of Mathematical Sciences. His personal web page is His mathematical interests are number theory and classical analysis.

Part 1. Odd Numbers
Part 2. Imaginaries
Part 3. Fractions