|Although there is only a short discussion of mathematics, I had to include it because it is just too interesting that this is not only one of the oldest science-fiction stories but moreover the fact that it was written in 1666 by a woman!
I can see why she is such a topic of conversation these days; the way she signed her name to this work is an indication of how interesting a person she must have been: The Description of a New World, Called The Blazing World. Written by the thrice noble, illustrious and excellent princess, the Duchess of Newcastle.
Anyway, down to the specifics. In this story, a woman is kidnapped and taken to the North Pole, where her kidnappers freeze to death and she accidentally slips into another world which is attached to ours at the pole. (That world has its own sun, which we usually don't notice because ours is so much closer to us than its sun is.)
On this other world, she meets a variety of creatures that looks like animals from our world but behave like humans: bear-men, fish-men, parrot-men, etc.
You can tell that Cavendish does not like mathematics from the start, because she says that "each followed such a profession as was most proper for the nature of their species." The bear-men were experimental philosophers, the bird-men astronomers, the fly, worm and fish-men were natural philosophers and the spider and lice-men were the mathematicians.
We get a long, interesting discussion from most of these species about the state of their area of expertise. There is lots of interesting science/science-fiction here. For instance, we learn about the composition of the sun (which is a giant reflective stone, not a burning substance as some would believe) and that the plague is transmitted when one person's healthy cells begin to imitate the sick cells in another person. These are all interesting ideas and show that she was somewhat knowledgeable and interested in a variety of scientific subjects even if she was not correct by our modern viewpoint. However, her description of mathematics is rather different:
|(quoted from Description of a New World, Called The Blazing World)|
The Empress having hitherto spent her time in the examination of the bird-, fish-, worm- and ape-men, etc. and received several intelligences from their several employments; at last had a mind to divert herself after her serious discourses and therefore she sent for the spider-men, which were her mathematicians, the lice-men, which were her geometricians and the magpie-, parrot- and jackdaw-men, which were her orators and logicians. The spider-men came first, and presented her Majesty with a table full of mathematical points, lines and figures of all sorts of squares, circles, triangles, and the like; which the Empress, notwithstanding that she had a very ready wit, and quick apprehension, could not understand; but the more she endeavoured to learn, the more was she confounded: whether they did ever square the circle, I cannot exactly tell, nor whether they could make imaginary points and lines; but this I dare say, that their points and lines were so slender, small and thing, that they seemed next to imaginary. The mathematicians were in great esteem with the Empress, as being not only the chief tutors and instructors in many arts, but some of them excellent magicians and informers of spirits, which was the reason their characters were so abstruse and intricate, that the Empress knew not what to make of them. There is so much to learn in your art, said she, that I can neither spare time from other affairs to busy myself in your profession; nor, if I could, do I think I should ever be able to understand your imaginary points, lines and figures, because they are non-beings.
There is even less said about the lice-men, and the logicians just stumble over each other with contradictory syllogisms like "Every politician is wise: Every knave is a politician, Therefore every knave is wise." and "No politician is wise: Every knave is a politician, Therefore no knave is wise."