a list compiled by Alex Kasman (College of Charleston)

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 The Time Machine (1895) Herbert George Wells (click on names to see more mathematical fiction by the same author)
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This famous early science fiction novel opens with a clever (and, if you think ahead to the role of Minkowski Space in special relativity, prophetic) lecture on "the fourth dimension". Of course, discussions of the fourth dimension as time (and the place where "sprits" live) were all the rage in the late 19th Century, but I like Wells' approach especially Particular things to note are the mention of a lecture by Simon Newcomb to the New York Mathematical Society, and the clever analogy between our inability to go backwards in time and the inability of a person falling through the air to go up. Here's an excerpt (follow the links above and below for the entire text available from ebooks):

 (quoted from The Time Machine) `You must follow me carefully. I shall have to controvert one or two ideas that are almost universally accepted. The geometry, for instance, they taught you at school is founded on a misconception.' ... `It is simply this. That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. But some philosophical people have been asking why THREE dimensions particularly--why not another direction at right angles to the other three?--and have even tried to construct a Four-Dimension geometry. Professor Simon Newcomb was expounding this to the New York Mathematical Society only a month or so ago. You know how on a flat surface, which has only two dimensions, we can represent a figure of a three-dimensional solid, and similarly they think that by models of thee dimensions they could represent one of four--if they could master the perspective of the thing. See?' .... `But,' said the Medical Man, staring hard at a coal in the fire, `if Time is really only a fourth dimension of Space, why is it, and why has it always been, regarded as something different? And why cannot we move in Time as we move about in the other dimensions of Space?' The Time Traveller smiled. `Are you sure we can move freely in Space? Right and left we can go, backward and forward freely enough, and men always have done so. I admit we move freely in two dimensions. But how about up and down? Gravitation limits us there.' `Not exactly,' said the Medical Man. `There are balloons.' `But before the balloons, save for spasmodic jumping and the inequalities of the surface, man had no freedom of vertical movement.' `Still they could move a little up and down,' said the Medical Man. `Easier, far easier down than up.' `And you cannot move at all in Time, you cannot get away from the present moment.' `My dear sir, that is just where you are wrong. That is just where the whole world has gone wrong. We are always getting away from the present movement. Our mental existences, which are immaterial and have no dimensions, are passing along the Time-Dimension with a uniform velocity from the cradle to the grave. Just as we should travel DOWN if we began our existence fifty miles above the earth's surface.' `But the great difficulty is this,' interrupted the Psychologist. `You CAN move about in all directions of Space, but you cannot move about in Time.' `That is the germ of my great discovery....

 Contributed by "William E. Emba" I recently saw the first half of the 2002 film adaptation of THE TIME MACHINE (directed by Simon Wells, great-grandson of H. G.) The math consisted of two scenes with the main character writing lots of realistic equations on a blackboard. I have not seen the 1960 film or heard the 1999 radio broadcast.

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Works Similar to The Time Machine
According to my `secret formula', the following works of mathematical fiction are similar to this one:
1. The Time Ships by Stephen Baxter
2. The Accidental Time Machine by Joe Haldeman
3. The Plattner Story by Herbert George Wells
4. Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott
5. The Remarkable Case of Davidson's Eyes by Herbert George Wells
6. Round the Moon by Jules Verne
7. The Star by Herbert George Wells
8. The Planiverse: computer contact with a two-dimensional world by A.K. Dewdney
9. A Wrinkle in Time by Madeleine L'Engle
10. Star, Bright by Mark Clifton
Ratings for The Time Machine: