a list compiled by Alex Kasman (College of Charleston)

 ...
 The Brink of Infinity (1936) Stanley G. Weinbaum (click on names to see more mathematical fiction by the same author)
 Highly Rated!

 Contributed by Fred Galvin A mathematics professor is kidnapped by a madman with a grudge against mathematicians, who threatens dire consequences unless the prof can solve a math riddle he has concocted: by asking ten questions, the prof has to guess the mathematical expression the madman has in mind. The answer is "infinity minus infinity". No fantastic elements, but I consider it honorary sf, being a story by a prominent sf author in an sf pulp.

Published in Thrilling Wonder Stories, December, 1936.

This story by pulp SF author Stanley G. Weinbaum was published posthumously. As Fred Galvin explains above (thanks Prof. Galvin for sending me this story!), it is not science fiction but rather a straight-forward thriller a la Steven King's "Misery". A math professor, thinking that he has been hired by a chemist to run some statistical analyses on experimental data, is surprised to learn that he is the experiment. The chemist, angry at mathematicians because a miscalculation by one resulted in him being crippled in an explosion, wishes to separate the real mathematicians from the bogus ones who -- in his opinion -- deserve to die. To test whether the protagonist is a real mathematician, he must guess the mathematical expression that the kidnapper is thinking of by asking ten questions.

Much of the math in the story is wrong. For instance:

 (quoted from The Brink of Infinity) "I trust you have used your time well," he sneered. "At least, I have my first question," I responded. "Good, Dr. Aarons! Very good! Let us hear it." "Well, I continued, "among numbers, expressions of quantity, mathematicians recognize two broad distinctions -- two fields in which every possible numerical expression may be classified. These two classifications are known as real numbers on the one hand, including every number both positive and negative, all fractions, decimals, and multiples of these numbers, and on the other hand the class of imaginary numbers, which include all producs of operations on the quantity called `e', otherwise expressed as the square root of minus one." "Of course, Dr. Aarons, that is elementary!" "Now then - is this quantity of yours real or imaginary?" He beamed with a sinister satisfaction. "A very fair question, sir! Very fair! And the answer -- may it assist you -- is that it is either."

Now, the most obvious problem with this quote is that `e' is not the symbol for the square root of negative one (at least not the standard one). Probably what was meant was `i', and the author merely got confused with the transcendental real number `e' (the base of the natural logarithm). Moreover, I am bothered by the whole gist of this discussion. I do not think any reasonable mathematician would claim that all numerical quantities are either real or imaginary. For one thing, most complex numbers (take a generic one of the form a+bi where a and b are real numbers) are neither real nor imaginary. In particular, they are only real or imaginary if a or b happen to be zero. (Technically, this becomes apparent if one takes his use of the word `field' to be literal. The real numbers are a field, but the imaginary numbers are not a field since they are not closed under multiplication: i*i=-1 which is not imaginary.) But, more importantly, it is naive to consider the real numbers and the complex numbers to be the only possible mathematical expressions. Why not also quaternions and infinite dimensional Lie groups and C^* algebras and.....

Another complaint I have about this story is its presentation of mathematics as a completely dry field of study. Consider the opening paragraph:

 (quoted from The Brink of Infinity) One would hardly choose the life of an assistant professor of mathematics at an Eastern University as an adventurous one. Professors in general are reputed to drone out a quiet, scholarly existence, and an instructor of mathematics might seem the driest and least lievely of men since his subjet is perhaps the most dessicated. And yet -- even the lifeless science of figures has had its dreamers -- Clerk-Masxwell, Lobachewski, Einstein and the rest. The latter, the great Albert Einstein himself who is forging the only chain that ever tied a philosopher's dream to experimental science, is poinding his links of tenuous mathematical symbols, shadowy as thought, but unbreakable.

The "lifeless science of figures" indeed! All of the mathematicians I know are "dreamers", and none are the "driest and least lively of men". This is a stereotype I could easily disprove by inviting any believers to a math conference or seminar. Math is an active field of research, and those involved in it are as enthusiastic about it as those involved in biology research or physics research or psychology research. It is not just a few dreamers, but the vast majority of mathematics professors whose dreams keep pushing the field forward, little by little. And, the suggestion that Einstein was the first person to find application for abstract mathematics is absurd.

So, this story is insulting to mathematicians and not entirely mathematically accurate. Still, I cannot help but like the story. It is fun to read. It is well written. And, given the context, one cannot take it too seriously anyway. (Context? Well, I have a photocopy from Fred Galvin. It shows the cover listing other stories that appeared in the same issue: "Brain Stealers of Mars" and "Mutiny on Europa". The illustration for the story shows sea monsters brandishing mathematical expressions like weapons with the caption "Fantastic figures, in a myriad swarm, connive with the haunting specter of death".)

 Contributed by Vijay Fafat I recall reading somewhere that this particular story by Weinbaum was not meant for publication but was sent for printing after his death by his wife. The story is a direct take-off from George England's "The Tenth Question"

 Contributed by david joyner Interesting math fiction short story written with a good pace. I enjoyed it very much and recommend it.

Author Andrew Breslin wrote in January 2017 to notify me that this story is now available on YouTube in the form of a radio show. Personally, I think I would rather read it than hear it. But, if you want to listen to it as you drive to work, then letting the announcer read you the story aloud as part of the "Mind Web" dramatization series might be a good alternative.

 More information about this work can be found at gutenberg.net.au. (Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)

Works Similar to The Brink of Infinity
According to my `secret formula', the following works of mathematical fiction are similar to this one:
1. Fermat's Room (La Habitacion de Fermat) by Luis Piedrahita / Rodrigo SopeĆ±a
2. Aleph Sub One by Margaret St. Clair
3. The Imaginary by Isaac Asimov
4. The Math Code by Alex Kasman
5. The Sinister Researches of C.P. Ransom by Homer C. Nearing Jr.
6. Mad Destroyer by Fletcher Pratt
7. Twisted Seduction by Dominique Adams (writer and director)
8. Prime by Steve Erickson
9. A Slight Miscalculation by Ben Bova
10. The Integral: A Horror Story by Colin Adams
Ratings for The Brink of Infinity: