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Fantasia Mathematica

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Clifton Fadiman's classic collection of mathematical stories, essays and anecdotes is now once again available. Ranging from the poignant to the comical via the simply surreal, these selections include writing by Aldous Huxley, Martin Gardner, H.G. Wells, George Gamow, G.H. Hardy, Robert Heinlein, Arthur C. Clarke, and many others. Humorous, mysterious, and always entertaining, this collection is sure to bring a smile to the faces of mathematicians and non-mathematicians alike.

309 pages, Paperback

First published January 1, 1958

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Clifton Fadiman

224Ìýbooks34Ìýfollowers
Clifton Paul "Kip" Fadiman was an American intellectual, author, editor, radio and television personality.

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Displaying 1 - 18 of 18 reviews
Profile Image for Dorothea.
227 reviews76 followers
June 16, 2012
A mixed bag. Some stories are excellent; the poorer ones are at least over quickly. Far too many are sexist. The overall experience for me was that of enduring severe blisters while walking in poorly-fitting shoes up a hill with many beautiful views.

In order:

"Young Archimedes" by Aldous Huxley. Definitely one of the collection's better-written pieces, though rather pathetic; high ratio of not-math to math.

"Pythagoras and the Psychoanalyst" by Arthur Koestler. Meant to be ironic, I think; instead, trite. Also sexist. Mercifully short.

"Mother and the Decimal Point" by Richard Llewellyn. An excerpt from How Green Was My Valley. Charming! Somewhat telling that the joke of the story is Mother's incomprehension of mathematics, yet Mother is probably the most interesting female character in the collection.

"Jurgen Proves It by Mathematics" by James Branch Cabell. Fadiman's summary is apt: "He demonstrates for the beautiful Queen Dolores nine deeply penetrating propositions." The "math" here is really just the cultural symbolism of numbers 1-9, but the double entendres are still funny.

"Peter Learns Arithmetic" by H.G. Wells. A cute excerpt from Joan and Peter about the pedagogy of mathematics.

"Socrates and the Slave" by Plato. From Meno.

"The Death of Archimedes" by Karel ÄŒapek. Archimedes is not interested in glorifying his mathematics with military applications.

"The Devil and Simon Flagg" by Arthur Porges. The Devil can go down to Georgia, but can he prove Fermat's Last Theorem?

"--And He Built a Crooked House" by Robert A. Heinlein. A Californian architect decides that the house of the future should be based on a 3-D representation of a tesseract, with startling results.

"Inflexible Logic" by Russell Maloney. This one is irritating because it's not really about math at all; it's supposed to be comedy about the distress of a mathematician upon observing a phenomenon that apparently defies probability.

"No-Sided Professor" by Martin Gardner. This is ... a slapstick comedy about topography?

"Superiority" by Arthur C. Clarke. Clarke takes a rather long time to make the point that theoretically more powerful weapons can still be tactically weak because of the practical difficulties in implementing them.

"The Mathematical Voodoo" by H. Nearing, Jr. This is a story about a mathematics professor trying unusual methods to inspire confidence in a poor student, with unexpected results, but it's not really a story about math.

"Expedition" by Fredric Brown. A short short story about the "problem" of what ratio of male and female crew members should go on a spaceship. Wins award for most sexism per page. Contains no actual math beyond arithmetic.

"The Captured Cross-Section" by Miles J. Breuer, M.D. Entertaining for its descriptions of how the fourth dimension could appear to us creatures of the third.

"A. Botts and the Moebius Strip" by William Hazlett Upson. Description of a prank achieved by turning an ordinary mechanical belt into a Moebius strip.

"God and the Machine" by Nigel Balchin. Excerpt from Last Recollections of My Uncle Charles. A story about a scientist who hates other humans (including his own family) and devotes his life to creating robots instead. I liked the analysis of the scientist's character, and the description of programming, written in 1951, is historically interesting.

"The Tachypomp" by Edward Page Mitchell. This was first published in 1873, so it's the oldest story in the collection. As Fadiman says, "In its now quaintly old-fashioned way it foreshadows many of the themes and situations that were to be exploited by science-fictioneers more than a generation later" -- such as relative speed (although not quite relativity) and perpetual motion.

"The Island of Five Colors" by Martin Gardner. I loathed this story. Fadiman's description had made me look forward to it: "A tale in which five countries apparently really had common borders--a topological impossibility" because of course I remember that . Then I started reading and discovered that those five countries are actually fictional African tribes. And that this is supposed to be a humorous story. And I kept reading because I was hoping there would actually be some math in the story. And there never really was. And now I never want to read anything else by Martin Gardner.

"The Last Magician" by Bruce Elliott. A stage magician comes to a bad end when he attempts to escape from a real Klein bottle. Not much math. The real drama of the story comes from the narrator's description of the magician's relationship with his assistant, a humanoid, female alien from Mars. The narrator observes that the magician abuses the Martian girl horribly, but -- narrative tragedy! -- there's nothing he can do. The narrator's helplessness here is never explained.

"A Subway Named Moebius" by A.J. Deutsch. The T becomes so complex a closed system that cars begin disappearing into the fourth dimension!

"The Universal Library" by Kurd Lasswitz. A lovely exploration of really large numbers.

"John Jones's Dollar" by Harry Stephen Keeler. It's a fun example of The Importance of Compound Interest, but apart from that, if this is what economic thinking was like in 1927 no wonder the Stock Market crashed.

The remainder of the book is a section called "Fractions," composed of poetry (mostly limericks) and some very short prose. My very favorite is the first one, "A New Ballad of Sir Patrick Spens" by Arthur T. Quiller-Couch:
The King sits in Dunfermline town
Drinking the blude-red wine:
"O wha will rear me an equilateral triangle
Upon a given straight line?
And so on, dramatizing Sir Patrick Spens' inscription of an equilateral triangle within two overlapping identical circles. It is perfect.

This section also contains the only contributions by women, Edna St. Vincent Millay's "Euclid Alone Has Looked on Beauty Bare" and "Plane Geometry," a mathematical filk of "The Jabberwocky" by someone named Emma Rounds. A few of the last limericks are Anonymous, so possibly some of these are by women as well.

As far as I was able to tell (a few of the contributors are obscure enough now that there is little or no biographical information about them online) every named contributor was white. I think the only characters of color (by default of description, anyway, and unless you count the abused Martian girlfriend in "The Last Magician") are the deliberately ridiculously-described islanders in "The Island of Five Colors."

There are lots of white female characters: a few mothers, otherwise wives or girlfriends of mathematicians. Two or three are said to understand mathematics themselves, but in fact play the adoring or tolerant audience for the real, male mathematicians.

This is the case with most female characters in the male-authored 1950s scifi I've read, but I think it's especially painful here because there are so many pieces by so many authors. It's a crushing consensus: we vote that the idea of women being mathematicians themselves is inconceivable, and that wherever women and mathematics coincide, women will come out looking particularly foolish.

My father, a professional mathematician, was eight years old when Fantasia Mathematica was published. When I think about that fact, it brings tears of relief to my eyes to remember how much he always encouraged me to study mathematics. I do not remember a single instance in which he ever suggested that my femaleness had anything at all to do with my aptitude for math -- not when I was frustrated by algebra at age eleven, nor when I told him at age eighteen, upon finishing multivariable calculus, that I was done with it all. (I wasn't.) Thank you, Dad. Thank you, feminism.
Profile Image for J_BlueFlower.
762 reviews8 followers
Shelved as 'looks-interesting'
August 27, 2023
Note to myself:

Notice
"(x + 1)" by Edgar Allan Poe



Contents
"Introduction" by Clifton Fadiman

Odd numbers
"Young Archimedes" by Aldous Huxley
"Pythagoras and the Psychoanalyst" by Arthur Koestler
"Mother and the Decimal Point" by Richard Llewellyn
"Jurgen Proves It by Mathematics" by James Branch Cabell
"Peter Learns Arithmetic" by H. G. Wells
"Socrates and the Slave" by Plato
"The Death of Archimedes" by Karel ÄŒapek

Imaginaries
"The Devil and Simon Flagg" by Arthur Porges
"—And He Built a Crooked House" by Robert A. Heinlein
"Inflexible Logic" by Russell Maloney
"The No-Sided Professor" by Martin Gardner
"Superiority" by Arthur C. Clarke
"The Mathematical Voodoo" by H. Nearing, Jr.
"Expedition" by Fredric Brown
"The Captured Cross-Section" by Miles J. Breuer, M.D.
"A. Botts and the Moebius Strip" by William Hazlett Upson
"God and the Machine" by Nigel Balchin
"The Tachypomp" by Edward Page Mitchell
"The Island of Five Colors" by Martin Gardner
"The Last Magician" by Bruce Elliott
"A Subway Named Moebius" by A. J. Deutsch
"The Universal Library" by Kurd Lasswitz
"Postscript to "The Universal Library"" by Willy Ley
"John Jones's Dollar" by Harry Stephen Keeler

Fractions
"A New Ballad of Sir Patrick Spens" by Arthur T. Quiller-Couch
"The Unfortunate Topologist" by Cyril Kornbluth
"There Once Was a Breathy Baboon" by Sir Arthur Eddington
"Yet What Are All..." by Lewis Carroll
"Twinkle, Twinkle, Little Star" by Ralph Barton
"Mathematical Love" by Andrew Marvell
"The Circle" by Christopher Morley
"The Circle and the Square" by Thomas Dekker
"Euclid Alone Has Looked on Beauty Bare" by Edna St. Vincent Millay
"Euclid" by Vachel Lindsay
"To Think That Two and Two Are Four" by A. E. Housman
"The Uses of Mathematics" by Samuel Butler
"Arithmetic" by Carl Sandburg
"Threes (To Be Sung By Niels Bohr)" by John Atherton
"Plane Geometry" by Emma Rounds
"He Thought He Saw Electrons Swift" by Herbert Dingle
"Fearsome Fable" by Bruce Elliott
"Bertrand Russell's Dream" by G. H. Hardy
"For All Practical Purposes" by C. Stanley Ogilvy
"Eternity: A Nightmare" by Lewis Carroll
"An Infinity of Guests" by George Gamow
"�" by Sir Arthur Eddington
"No Power on Earth" by William Whewell
"(x + 1)" by Edgar Allan Poe
"The Receptive Bosom" by Edward Shanks
"Leinbach's Proof" by Arthur Schnitzler
"Problem from The New Yorker: "Talk of the Town""
"A Letter to Tennyson from Mathematical Gazette"
"A Fable from Mathematical Gazette"
"There Was a Young Man from Trinity" by Anonymous
"There Was an Old Man Who Said, "Do"" by Anonymous
"Relativity" by Anonymous
"There Was a Young Fellow Named Fisk" by Anonymous
Profile Image for Robert.
1,342 reviews3 followers
June 13, 2020
Fun collection of stories, poems and quips turning on some aspect of mathematics. As expected, the stories exploring higher physical dimensions were a struggle to follow, though entertaining when I just relaxed and went with the story rather than trying to envision every aspect of the math. What insight I may have into higher level math mostly comes from my professor friend, Greg Rozenberg, known for publishing around 500+ math and computer science papers, many of which provide theoretical frameworks for using DNA as massive parallel processing computers. I used to edit papers and books for him... at least the American English sections of them! There are several stories based around the Moebius strip... and I even got some ideas for a magic routine (not the old Afghan Bands thing). I've also begun reading Fadiman's Lifetime Reading Plan book.
Profile Image for Warner.
21 reviews7 followers
January 27, 2021
I first bought this in 8th grade and this is at least my third copy, that was 60 years ago.

Delightful, especially if you have a bent for the mathematically obscure, Dr. Slapenarsky proves that the four-color theorem has a six color solution.

And while Fermet's Last Theorem has been solved, it is not the simple solution sought in The Devil and Simon Flagg.

Mr. Fadiman has gifted us with a second volume The Mathematical Magpie, also well worth the read.
Profile Image for Ray Savarda.
461 reviews1 follower
July 19, 2021
A selection of older stories and articles involving mathematics subjects; mostly in fiction.
Interesting to see original works by Aldous Huxley, HG Wells, Karel Capek, Robert Heinlein, Arthur C Clarke, Martin Gardner, and Willy Ley.
Really didn't expect that list of authors in a book published originally in 1958.
12 reviews
December 31, 2023
Some fun stories. Maybe it's because I haven't read in a while (especially old stuff), but most stories seemed dull, curious but uninspired. I also agree with Dorothea's review that it's pretty male and white.

I only read a few stories.
Profile Image for Forrest.
AuthorÌý4 books9 followers
May 2, 2013
This set of short stories and poems on mathematical themes is pleasantly diverting, although many of the stories have not aged particularly well (other reviewers here have pointed out the sexism, which is rampant). Aimed at curious laypersons rather than mathematicians, the stories contain just enough jargon to tickle the synapses but shouldn't intimidate any but the most math-averse.

Science fiction of the 1920s through the early 1950s predominates, and there is an obsession with the Moebius strip, the Klein bottle, and the perils of slipping into the fourth dimension. There are some outliers, though. An excerpt from Plato's "Meno" helps to set the plate, and Aldous Huxley's "Young Archimedes" brings a bit of poignancy while raising the literary bar.

Most of the stories fall short of that mark, and a few are downright terrible. But there are some surrealistic gems, too. I loved Robert Heinlein's "And He Built a Crooked House" and A.J. Deutsch's "A Subway Called Moebius," which offer very similar dilemmas but approach from two delightfully imaginative angles. Russell Maloney's "Inflexible Logic" turns the old saying about monkeys and typewriters on its head, and "The Universal Library" by Kurd Lasswitz anticipates Borges' wondrous "Library of Babel" by several decades -- it's too bad Borges' story hadn't yet been translated into English in 1958; it would have made a perfect addition to this volume.
219 reviews4 followers
July 12, 2012
A collection of short stories and even poems with mathematical themes.

The bad news: The stories feel a bit dated (collected in 1958), and some are slightly sexist (they would have been fine in the 1950's are bit off-kilter in 2012). For the latter reason, it would be hard to recommend these stories, say to my students. I was also underwhelmed by the fact that quite a few of the stories used Mobius strips or Klein bottles for the central idea.

The good news: Some of the stories are fun. A couple outstanding ones include "The Devil and Simon Flagg" by Arthur Porges and "God and the Machine" by Nigel Balchin. The former should be read by any spouse or partner of a mathematician. The latter is a wonderful short sci-fi story about artificial intelligence, written in 1951 and so way ahead of its time. Also worth of special mention, "---And He Built a Crooked House" by Robert Heinlein, a overly familiar story perhaps, but still worth reading again.

Profile Image for Maurizio Codogno.
AuthorÌý55 books144 followers
June 14, 2021
Molto disuguale

Questo libro è probabilmente il primo tentativo che è stato fatto per raccogliere testi letterari sulla matematica, più di sessant'anni fa. Fadiman esplicita subito che le scelte che ha fatto sono secondo i suoi gusti, senza un tema specifico oltre naturalmente a parlare di matematica. Troviamo così una prima parte di brani letterari dove si parla di matematica e matematici; una seconda parte in cui ci si specializza sulla fantascienza matematica, con alcuni racconti che ormai sono dei classici ma allora erano spesso novità, e una sezione finale di epigrammi, limerick e poesie che a mio parere sono la parte più debole dell'opera. Il risultato finale è piuttosto disuguale, ma ci sono indubbiamente alcune gemme, e credo che un letterato possa almeno farsi un'idea di base di come anche la matematica possa fare parte del mondo umanistico.
Profile Image for James Swenson.
493 reviews34 followers
March 12, 2012
A charming collection of stories with mathematical themes. As a topologist, I was pleasantly surprised to find a number of stories inspired by Mobius strips, Klein bottles, and so on. The jewels here are "No-Sided Professor" by Martin Gardner -- for its last line alone; "Superiority" by Arthur C. Clarke; "A. Botts and the Moebius Strip" by William Hazlett Upson; and above all "The Devil and Simon Flagg" by Arthur Porges.

I made my wife put down whatever she had been reading in favor of "The Devil and Simon Flagg" the moment I finished it. If you have any interest at all in mathematics or mathematicians, you should read it, too, right now: the full text is .
Profile Image for Chris.
249 reviews12 followers
June 23, 2010
A curious anthology filled with science fiction type stories, excerpts and even poems that dabble with math. You don't need to know math to enjoy this, but being aware of some math would help with understanding the concepts of some of the stories. If you know about the Mobius strip and the tesseract, you'll enjoy the best stories, especially Robert Heinlein's "And He Built a Crooked House."

Being an anthology, this worked exceptionally well as reading material for my lunch breaks at work.
Profile Image for Cindy Dalfovo.
AuthorÌý2 books6 followers
January 17, 2013
The quality of the short stories are uneven, and the opening one is somewhat of a letdown, even with the beautiful demonstration of Pythagora's theorem. I mean, there are a few pages describing the landscape, and that's hardly interesting when one is eager to read about math...

Of course, some short stories are really nice, especially the ones concerning the Moebius strip and the Klein bottle, and this was a great read. Some made me laugh, some made me think, some were very well written. All in all, a really nice read.
Profile Image for Mallory.
29 reviews7 followers
January 11, 2016
Pretty sexist, probably in part since it was published in the mid-20th century. Also, every other punchline involves a Moebius Strip. Some gems though, including: "Young Archimedes," "Pythagoras and the Psychoanalyst," "Inflexible Logic," "The Universal Library," and "Plane Geometry" (the Jabberwocky in math speak!)
Profile Image for Sally.
1,244 reviews37 followers
April 12, 2008
Like any anthology or collection, you like some of it more than others. I just think the idea of a *math* collection of fiction, poetry and such is just such a cool idea!
Profile Image for YZ.
AuthorÌý7 books101 followers
Read
May 12, 2008
Didn't read all the stories, but definitely thought it was a great idea for an anthology - math stories! Stories about math! C'mon!
Profile Image for S.
236 reviews58 followers
Want to read
November 10, 2012
Mathematical limericks.
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