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The Brothers Karamazov (1880)
Fyodor Dostoevsky
(click on names to see more mathematical fiction by the same author)

In this classic final masterwork by Dostoevsky, the existence of non-Euclidean geometry is mentioned at one point. Although the theme is not explicitly carried throughout the rest of the novel, it plays an important role by bringing into doubt the idea of objective morality which the `truth' of Euclid was meant to support. For more detailed information, I turn to David Reid who first wrote to suggest that this work be added to my list:

Contributed by David Reid

Dostoevsky was an avid newspaper reader, and one of the things that made the headlines in the Russian press (for the small percentage of literate Russians at the time) was the consequences of Lobachevsky's non-Euclidean Geometry. Lobachevsky himself did not understand the import of his work when he came out with it, but others quickly pointed out that the results (along with those of Bolyai) showed that the main example upon which Immanuel Kant had based his main thesis in his masterwork "Critique of Pure Reason" (thesis: that there were a priori synthetic truths; example: the sum of the angles of a triangle adding up to a half-circle) was false, hence the thesis was false. The importance to the literate Russians was not the philosophical points, but that a Russian had toppled this great German, since the general assumption in European philosophy were that the Germans were the greats and the Russians mere provincials, mere peasants of the philosophical world. So, Dostoevsky wanted to put this in. Although he does not use the word "Lobachevsky", the reference was clear for his readers at that time, as Ivan says, roughly:"Did God create man or did man create God? The axioms of the usual Russian is the former, but I respect both hypotheses. Now, if God created man, the question is whether he created him according to Euclidean geometry, with an understanding of only three dimensions. But if he did, then there is a problem, as there are geometers and philosophers today, including some remarkable ones, who put into doubt this Euclidean geometry, who can come up with systems that do not appear on the earth, and are not understandable to most of us. Hence, Alyosha, I would advise you to not even think about whether God exists. All these questions are posed in our three fact, let parallel lines meet, let me even see that they meet, but even then I will not understand it."

The discussion is longer than this short loose translation, and the interested reader can easily find these passages in Chapter III, "The Brothers get to know each other."

Here is the relevant passage copied from

(quoted from The Brothers Karamazov)

"Joking? I was told at the elder's yesterday that I was joking. You know, dear boy, there was an old sinner in the eighteenth century who declared that, if there were no God, he would have to be invented. S'il n'existait pas Dieu, il faudrait l'inventer. And man has actually invented God. And what's strange, what would be marvellous, is not that God should really exist; the marvel is that such an idea, the idea of the necessity of God, could enter the head of such a savage, vicious beast as man. So holy it is, so touching, so wise and so great a credit it does to man. As for me, I've long resolved not to think whether man created God or God man. And I won't go through all the axioms laid down by Russian boys on that subject, all derived from European hypotheses; for what's a hypothesis there is an axiom with the Russian boy, and not only with the boys but with their teachers too, for our Russian professors are often just the same boys themselves. And so I omit all the hypotheses. For what are we aiming at now? I am trying to explain as quickly as possible my essential nature, that is what manner of man I am, what I believe in, and for what I hope, that's it, isn't it? And therefore I tell you that I accept God simply. But you must note this: if God exists and if He really did create the world, then, as we all know, He created it according to the geometry of Euclid and the human mind with the conception of only three dimensions in space. Yet there have been and still are geometricians and philosophers, and even some of the most distinguished, who doubt whether the whole universe, or to speak more widely, the whole of being, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidian earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with an idea of only three dimensions. And so I accept God and am glad to, and what's more, I accept His wisdom, His purpose which are utterly beyond our ken; I believe in the underlying order and the meaning of life; I believe in the eternal harmony in which they say we shall one day be blended. I believe in the Word to Which the universe is striving, and Which Itself was 'with God,' and Which Itself is God and so on, and so on, to infinity. There are all sorts of phrases for it. I seem to be on the right path, don't I'? Yet would you believe it, in the final result I don't accept this world of God's, and, although I know it exists, I don't accept it at all. It's not that I don't accept God, you must understand, it's the world created by Him I don't and cannot accept. Let me make it plain. I believe like a child that suffering will be healed and made up for, that all the humiliating absurdity of human contradictions will vanish like a pitiful mirage, like the despicable fabrication of the impotent and infinitely small Euclidian mind of man, that in the world's finale, at the moment of eternal harmony, something so precious will come to pass that it will suffice for all hearts, for the comforting of all resentments, for the atonement of all the crimes of humanity, of all the blood they've shed; that it will make it not only possible to forgive but to justify all that has happened with men- but thought all that may come to pass, I don't accept it. I won't accept it. Even if parallel lines do meet and I see it myself, I shall see it and say that they've met, but still I won't accept it. That's what's at the root of me, Alyosha; that's my creed. I am in earnest in what I say. I began our talk as stupidly as I could on purpose, but I've led up to my confession, for that's all you want. You didn't want to hear about God, but only to know what the brother you love lives by. And so I've told you."

In his article Mathematics as Science Fiction, David Fowler wrote:

Contributed by David Fowler

Ivan Karamazov sees his inability to grasp non-Euclidean geometry as evidence that he can't understand God. Although Euclid may no longer be the ultimate source of geometric truth, Ivan still accepts the work of the modern non-Euclidean thinkers as a standard of truth. Albert Einstein's supposed claim to have “learned more from Dostoevsky than from any scientific thinker” may be apocryphal; but in any case, Dostoevsky's reflections on time and space can certainly be viewed as compatible, in qualitative fashion, with the framework of special relativity.

Contributed by T. Tilley

Most would find the math unimportant. However, having taught The Brothers Karamazov a number of times and read some, at least, of the major secondary literature in English on it, I have come to see that a main claim of the interpreters, that Dostoevsky is arguing for faith and against reason, is wrong. Rather, Dostoevsky, in the section cited and in some other places, is arguing that the Euclidean mind of Ivan cannot envision a non-Euclidean universe. Ivan's rationalism is as much a faith as is Alyosha's Orthodoxy. What counts are the outcomes of living in and living out these different faiths, which is the subject of the rest of the novel. So even if math is not central to the work, noticing the math is important to understanding the work.

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Works Similar to The Brothers Karamazov
According to my `secret formula', the following works of mathematical fiction are similar to this one:
  1. War and Peace by Lev Tolstoy
  2. Petersburg by Andrei Bely
  3. Diary of a Bad Year by John Maxwell Coetzee
  4. Notes from the Underground by Fyodor Dostoevsky
  5. Young Archimedes by Aldous Huxley
  6. Flatland: A Romance of Many Dimensions by Edwin Abbott Abbott
  7. Brave New World by Aldous Huxley
  8. The Odd Women by George Gissing
  9. Royal Highness (K├Ânigliche Hoheit) by Thomas Mann
  10. All the Light We Cannot See by Anthony Doerr
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Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.

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