If you've never heard the term “Mathematical Fiction” before, Edwin Abbott Abbott's 1884 novella, Flatland can certainly enlighten you!
Flatland: A Romance of Many Dimensions was published in 1884 and since then, it has been discovered and re-discovered by succeeding generations who have been delighted by its unique view of society and people.
The plot opens with a description of the fictional Flatland. The narrator calls himself “Square” and asks readers to “Imagine a vast sheet of paper on which straight Lines, Squares, Triangles, Pentagons, Hexagons and other figures, instead of remaining fixed in their places, move freely about... but without the power of rising above the surface or sinking below it, very much like shadows...” This is a country where the “solid” or the three dimensional do not exist. The women are Straight Lines, while the men, depending on their status, are figures with three or more sides. The lowest class are the Triangles, while the highest class of all are the Circles.
One night the Square has a dream about a world with two dimensions, but it turns out to be a nightmare, and Square is glad to return to the “reality” of Flatland. He has another strange experience, when he has a visitation. A strange presence enters his room. It is a Sphere. Square and his wife are shocked to see such a weird creature. But it begins talking to them and informs them that it belongs to a world called Spaceland. Square visits Spaceland with his new friend and once he realizes that more dimensions are possible, he undergoes a huge spiritual metamorphosis. However the rulers of Flatland are not about to accept such subversive views...
Flatland is essentially a novel that uses satire to portray the rigid, unfair and oppressive social class system that pervaded Victorian England. Birth and status determined everything in a person's life and it was almost impossible for people to move into the upper echelons of society. Flatland is also a virulent attack on the prevailing ideas about women, their role and status. Abbott portrays the unrelenting hierarchies that prevented people from achieving their personal goals.
Readers may be reminded of other allegories and satires, notably Plato's Cave and Swift's Gulliver's Travels. For modern day readers, Flatland is indeed an eye opener into concepts that seemed fixed and certain a century ago, but have been proven otherwise through scientific research. Knowledge is seen as a continuum and not a fixed goal; this is what books like Flatland teach us.