Please don't forget Jan Potocki 's brilliant "Manuscript Found in Saragossa", also known as "The Saragossa Manuscript"! The chapters devoted to the geometer's adventures contain some real mathematical problems (usually associated with Pascal). Though the manner of proving is sometimes ...khm ... not quite rigorous.

Frederic, among the German writers Hans Magnus Enzensberger (I read only a few poems by him, so don't know his work as a novelist) is known for his interest and 'informedness' on mathematics. So one might find something of this kind in his work if one is willing to dig.

Well of course there is Raymond Queneau...same group as Georges Perec.

Flatland by Edwin Abbott

Chlebnikov (Хле́бников), russian futurist and mathematician, tried to develop an artificial language based on numbers which he called "Zaum"/"Sternensprache" (language of stars):

http://books.google.de/books?id=-so3pkzwaQUC&dq

Mathematische Konzeptionen in der russischen Moderne : Florenskij - Chlebnikov - Charms München : Sagner 2006 (is written in german and i'm not sure if there's a translation...)

Famous Godel theorem can be seen as one of the underlying inspirations for Stanisłw Lem's novel "Golem XIV" http://en.wikipedia.org/wiki/Golem_XIV

Very right, Joaquim, to mention the wonderful essay by Hofstadter ! Since it was inspired, at least in part by the self-referential feedback addressed in Gödel's incompleteness theorem, I should also draw attention to a brilliant, recent novel that plunges the reader in the Vienna of the 1930s and then the Princeton of the 1950s, under the pretext of a quest to retrieve the personal archives ('Nachlass') of this immense logician from the hands of his widow Adèle ... who turns out to be a formidable, greater than life character. The inventive narrative mixes real and 'probable' facts, and is rich in imagined, funny and profound dialogues between Kurt Gödel, Albert Einstein, Robert Oppenheimer and the likes. A pure delight. The author is Yannick Grannec and her book is entitled "La Déesse des petites victoires" . Its publication (in 2012) met with critical acclaim and I would expect to see it translated into English rather soon.

@Joachim: As far as I understand, you misunderstood Hofstadter's TNT. It is a treatment of natural numbers in the framework of first-order logic, whereas Peano's axioms are second order. Admittedly not a relevant difference in the present context.

Obviously some Lewis Carroll "minor" works:

A Tangled Tale

What the Tortoise Said to Achilles

Borges work "El Aleph" as well as "El jardín de senderos que se bifurcan"

Eco's Foucault Pendulum

You said literary works and not only novels, so The Raven by EA Poe shall get a place there

Lope de Vega's Violante

Le città invisibili by Italo Calvino

And I have once read on the statistical significance and interpretation of Don Quixote and Sancho in the Cervantes masterpiece

Stendhal "The Life of Henry Brulard"

Dostoyevski "The Brothers Karamazov"

Some poems by Valle-Inclan

A la divina proporción by Rafael Alberti

Almost every work by Jardiel Poncela

"Geografías" by Julio Cortázar, as well as "Instrucciones para subir una escalera" or "Preambulo a las instrucciones para dar cuerda al reloj"

and so many others... actually I think you cannot separate them, and you can find mathematics in almost any book (literary masterpiece or reader's digest)

Thank you Samuel for this rich, thought-provoking input. Among the works in your list, one can sense indeed mathematical thinking or linkages behind Calvino’s “Invisible Cities”, some of Umberto Ecco’s novels, or Lewis Carroll production. But I find your references to “Don Quixote”, “The Karamazov Brothers” or “The Life of Henry Brulard” less convincing. Could you substantiate your hypothesis that they rely (even in part) on clear mathematical foundations?

Further, the lack of affinity between most writers and mathematics makes me question your conclusion that one “can find mathematics in almost any book”. But thanks anyway: all this is definitely stimulating.

p.s. You are correct to place poetry squarely within the frame of this question: the connections between mathematics and poetry are many. But I would not confuse mathematical “inspiration” with the inventive but “mechanistic” combinatorial techniques, for instance the S + 7 technique used by the Oulipo group (whereby each noun in a text is replaced by the seventh noun following it in a given dictionary).

Thank you Frederic,

Concerning “Don Quixote”, it is not my finding, but I once read that both characters Don Quixote and Sancho can be seen from a normal distribution standpoint as the closest points that are out-of-normality (say outside the 3 to 97 percentile) in each of their attributes:

http://cvc.cervantes.es/el_rinconete/anteriores/marzo_03/26032003_01.htm

Don Quixote is tall (very tall for that time), very skinny, and with an abnormal sense of justice

Sancho is short, very fat, and with an abnormal "passive" acceptance of the world as it is presented to him

Well you can argue, Cervantes did not know the notion of the normal distribution and Gauss was born long time after Don Quixote was published. But if we consider that mathematics are "extemporaneous" and they do exist independent of our understanding, you may agree an intendedly statistical (out-of-normal) opposition of both characters. since both characters are actually the essence of this work, you may conclude that Don Quixote uses a clear "mathematical structure leading to great, enduring literary work".

Re-reading your post (mathematical structure), I must agree that Karamazov and Brulard are not the best examples, I was broadening too much the mathematical concept, sorry.

Brulard being partly an autobiography has sufficient links with mathematics but not a clear mathematical structure behind it.

In Karamazov you find references to mathematics and euclidean and non euclidean geomtery, but again no mathematical structure for the whole work.

Another work, I would definitely include here is Monsieur by Jean-Philippe Toussaint. It seems (whether intendedly or not) that Monsieur only provides the descriptions (as Mathematics) but never interacts (this would be Physics).

Thank you for your understanding and sorry for my mistake,

sam

I recommend Lawrence Sterne's "The Life and Opinions of Tristram Shandy". This book is written well before the invention of fractals, but to storytelling and the numerous digressions in the text point to a fractal-like structure. The author experiments with the text and the narrative advances on different levels and directions at the same time. Each object/character mentioned in the text becomes in itself the object of a new story which then leads to other stories. Thus, the book starts to build a complex universe around the main character but never finishes it, as there is always an infinite amount of details related to each character that need to be described.

One good item in the list should also be "The Divine Comedy" by Dante Alighieri although most of his mathematical theories are no more trusted nowadays.

George Perec (mentioned above as an example) belonged to a group of writers "OULIPO=Ouvroir de littérature potentielle", who used different combinatorical or statistical devices and 'restrictions' for the creation of texts/poetry. To my opinion it is important to consider these devices not as a substitute for content but as a way to liberate the writer from certain conventions or idées recus and to foster creativity. A procedure to select words from a dictionary in itself is funny and can lead to strange nonsense texts, but when the new connections of ideas arising from the procedure serve as a basis for further writing it may lead to great works, especially if the original device is no longer visible. More membres of OULIPO: Raymond Queneau (e.g. 'Cent mille milliards de poémes', which is a poem-generator; in fact the poems are the orbit of a group action that replace certain parts of the poem), Jacques Roubaud (who was in fact a mathematician, too), Oscar Pastior (who somehow combined these methods with a surrealist approach to poetry.)

One type of 'restriction' I like, arguably not very mathematical, is to write books that do not contain certain letters. It leads, according to the abilities and ideas of the author, to strange texts, where nothing is expressed in ordinary ways, though the uninstructed reader may wonder quite a while before discovering the reason. This has not only been used by OULIPO (Georges Perec, La Disparition), but actually already in ancient greece, and more extensively in the baroque. I own a small romantic novel by Leopold Kolbe (1813) "Keine Liebe ohne Qualen", which, if I remember correctly, does not contain the letter "R". Georges Perec, however, somehow managed not to use the letter "E", which would seem almost impossible if it hadn't been done.

I think both a-void-ing A or E while keeping literary quality are nice exercises, but I think they are a bit outside the original topic of a mathematical structure.

Anyway in this new sense, there is a very entertaining book: "La tienda de palabras" by Jesus Marchamalo (not a masterwork but a very enjoyable piece). In this book several of those literary experiments are cited.

Do not forget as well the "pameos y meopas" by Cortázar.

Cabrera Infante, Augusto Monterroso, Alfonso Reyes, Mariano Brull, Torrente Ballester are other authors with similar (probably a couple of levels below) exploratory language.

Mary Everest

Boole "Philosophy and fun of algebra"

Umberto Ecco, "The Island of the Day Before"

Please don't forget Jan Potocki 's brilliant "Manuscript Found in Saragossa", also known as "The Saragossa Manuscript"! The chapters devoted to the geometer's adventures contain some real mathematical problems (usually associated with Pascal). Though the manner of proving is sometimes ...khm ... not quite rigorous.

The Danish author Inger Christensen (1935-2009) used to structure her poems in mathematical series, as in Summerfugledalen (Valley of Butterfies, 1996) and Alfabet (2000). See Stougaard-Nielsen, J and Lock, C (2009) Obituary: Inger Christensen. Eminent Danish poetwhose work followed mathematical models, The Guardian, 2009. Also http://ndbooks.com/author/inger-christensen and http://circumferencemag.org/?p=1012. Another math-experimenting author is the Frenchman Raymond Queneau (1903-1976), founder of the avant-garde group Oulipo. See http://www.themodernword.com/scriptorium/queneau.html.

We are starting to build a nice-looking anthology here. Let's just try to resist the temptation to cite didactic works on mathematics; ok ?

John Reese, "The Symbolic Logic of Murder". Using Boolean algebra to solve a murder.

the formula 2+2=5 lead to a reflection about the truth by George Orwell in his work 1984

I have just published a literary work, a 13,000 line epic in iambic tetrameter, nested with mathematical game structures and composed in sonata form.

THE WATER MAGE'S DAUGHTER: A NOVEL OF LOVE, MAGIC AND WAR IN VERSE is divided into three long Canticles and numerous shorter Cantos within each Canticle. For instance, Canticle I contains 30 Cantos, Canticle II contains 31 Cantos and Canticle III contains 33 Cantos for a total of 94 Cantos, yielding the sequence 30, 31, 33. In this sequence, the absent number is 32. The poem also includes 3 introductions, one for each Canticle, for a total of 97 discrete sections of verse. Working with these two numbers, 94 and 97, if we divide each by 3 (the number of Canticles) we obtain two results: 94/3=31.333333... and 97/3=32.333333... If we dispense with the irrational tails, we find two numbers: 31 and 32, the second of which is the absent number in the sequence 30, 31, 33.

The poem also features couplets, quatrains, whorls and free verse, including a symphonic modulation in Canticle III from free verse gradually back to couplets, the way a symphonic work returns to the tonic. The modulation is subtle and well-hidden, with numerous recapitulations.

Just published, THE WATER MAGE'S DAUGHTER is available in ebook form at Amazon. Quick introductions as video trailers can be found at:

•The Water Mage’s Daughter Official Story Trailer (2) : http://youtu.be/OoPkk9VTTCA

•The Water Mage’s Daughter Official Text Sample Trailer (2):

http://youtu.be/Mv-cU6ALUBA

•The Water Mage’s Daughter, Canto I, read by the author:

http://youtu.be/WoUNwTvaAlY

Enjoy!

Calvino and the Oulipo groupe. They are related to Perec

I just have learned about prime spiral also called Ulam's spiral:

http://mathworld.wolfram.com/PrimeSpiral.html

As stated in the page referenced above a concept of prime spiral appeared first in Arthur C. Clarke's novel "The City and the Stars" just seven years before the prime spiral was discovered and formally analyzed by Ulam. I know this example of connection between mathematics and literature is somehow in opposite direction to the one indicated in the question but I find it quite funny.

Thanks Roman. It is a good idea to bring Arthur C Clarke into this loop. Like Jules Verne and H.G. Wells (whom he deeply admired), Clarke accomplished a rare tour de force: to produce stories that anticipated a number of important inventions (e.g. the application of geostationary satellites to communications) and still stand as literary masterpieces. Quite a feat.

I've been reading GAIA IN TURMOIL: CLIMATE CHANGE, BIODEPLETION, AND EARTH ETHICS IN AN AGE OF CRISIS, a series of essays, one of which is written by a friend and colleague, Martin Ogle. Luminaries like Lynn Margulis and Stephen Harding also contributed to these 19 essays. Although Martin's essay is science-based (as are those of all the writers), he considers it critical––and mentions this in his essay––that new myths be created to bring Gaia Theory (based principally on an appreciation of feedback loops in climate modeling) awareness to humanity at large. Oddly enough, my new publication, THE WATER MAGE'S DAUGHTER: A NOVEL OF LOVE, MAGIC AND WAR IN VERSE (http://ow.ly/h8Bsr), is just such a myth.

In an earlier post I outlined one of the nested mathematical structures in the poem. Next up is one of the "prosodic games" one can find in the text. Here, in Canticle III, Canto IX (this Canto features 95 rhymes all told), is where the challenge is set:

First, through free verse our tale will wend,

Then back to couplets t’ward the end,

Yet each end-word shall kiss a mate

Somewhere––that’s if you take the bait

And feed on fancy, that old stuff

We love. So what if it’s just fluff?

Just filaments so nacreous

And thin that any sudden whim

Unspins awkward fugues to scherzos?

As the modulation from free verse to couplets begins here in Canto IX, the reader learns that within any modulating Canto, some of which are many hundreds of lines long, every end-word is rhymed somewhere, some quite far apart. Half the fun, in this gaming sense, is finding those distant or more proximate mates. "scherzos" for instance, is paired with "prose" which appears earlier in the Canto.

For its geometrical pattern, I should advise Palliser's Quincunx. popular at one time, it seems to have disappeared from the front page. The book is good read though. I went through the 1000 pages in 3 days. I will not give you more details on the pattern because the whole mystery is built on it.

My recomendation is the work of Fernando Zalame Traba

I don't know whether you have read the book Godel, Eschar, Bach: An Eternal Golden Braid by Douglas Hofstadter. It is probably the best book I have read so far on the Mathematics, Art and Music, if you have not yet, I would strongly recommend you to read it.

Jacques Roubaud, member of the Oulipo group: The "Hortense” cycle (Combinatorics), “La Princesse Hoppy” (Group Theory), for example.

Cube - a canadian sci-fi, where the identification of the primes and prime powers makes the difference between life and death.

Atlantisz es a kezirat titka (Atlantis and the secret of the manuscript) by Györfi András - a scientific adventure story where Fermat's Last Theorem, the ideas of Cardano (Tartaglia), Hamilton, Graves (Cayley) are parts of the introduction to the extra dimensions of string theory. The main characters later take a tour in these 26 dimensions of bosonic string theory to examine what would be this world around us:

- creation of God?

- a computer-simulation?

- a biotic experiment on this planet, initiated by an alien life form?

- The result of evolution and competitive adaptation to the environment, based on the laws of physics?

The Soviet mathematician Elena Venttsel wrote under the pseudonym "I. Grekova"--some of her works her have been translated into English, German, French, etc. Evgeny Zamyatin, trained as an engineer, wrote the astounding 1920s dystopia _We_, which influenced Huxley and Orwell. Zamyatin was influenced by Taylor sequences.

Shame on me - I did not know that Grekova's books have been translated from Russian! I should have mentioned her without hesitation.

OK, then let me add Arkady and Boris Strugatsky. They have been mentioned here already, but in a very general way. And I'd like to specify: the episode from the very beginning of the "Milliard Years before the Doomsday", where Malyanov (an astronomer) thinks over a certain mathematical model of stellar clusters and then describes it to Vecherovsky (a high class pure mathematician).

I've created an entertaining 3-minute video that describes the prosodic structure of THE WATER MAGE'S DAUGHTER epic with some music I've composed. Enjoy!

http://youtu.be/Y_dD4CJMJSQ

Life of Pi!

"If all things are but quick displays

––Scintillant blurs of yeas and nays

Competing in creation's fold––

Then nothing can be new or old.

Instead, a combination thrives

As conformation then contrives

To order things so that they'll stand,

Before to chaos they remand."

-- CANTO XXII in CANTICLE I

Here are a few more lines from THE WATER MAGE'S DAUGHTER epic that speak poetically to the physics of sensible reality. I've always wondered whether our narrow bandwidth of senses––a limited range of sound (ULF sound whales can hear that we cannot, for instance); a bodily survival range that hovers very close to the temperature of liquid water; and a narrow set of light frequencies we perceive (we can't see UV light as bees routinely do)––and our concomitant physics are fundamentally boxed in by this limited sample of phenomena, or whether, thanks to modern science's sensitive instruments and mathematics, we have truly overcome our narrow human bandwidth and plumbed all reality that exists around us. In other words, whether we can be confident that the electromagnetic spectrum is the only spectrum.

One cannot help but wonder, though, whether phenomena that operate in completely different theaters of reality might exist around us which we have no clear way to investigate, or even form questions about, at this point of our evolution.

The poem is here: http://ow.ly/h8Bsr

@McKenzie Bodkin. Sound and light one spectrum? Not for physicists! Gravitational waves (not yet detected directly but having a very strong theoretical basis) make up a third spectrum.

Many thanks, Harlan, this is a real find.

Stimulating!

Thank you, Ulrich, for the clarification. Didn't mean to suggest that sound waves in air and the electromagnetic spectrum are the same. Simply illustrations of my speculation about human bandwidth in general and what we can and as yet cannot know. As a layman and poet, I would appreciate your thoughts (as a physicist) about gravitational waves as a potential third spectrum not yet detected but theoretically suggested. If such a spectrum is detected and measured some day, do you think it will eventually be unified with the electromagnetic spectrum at some deep level, or will the two operate without any relation to or influence on each other? Or does the mathematics suggest that they will? Thanks!

Physics for poets, for McKenzie Bodkin in particular: Electromagnetic waves and gravitational waves are very similar in nature: violent motion of electric charges causes the first kind and violent motion of masses the second kind of waves. Quantitatively, much more violence is needed to make noticible intensities of gravitational waves than to make electromagnetic waves. How these waves influence us reflects their mode of generation: electromagnetic waves move the electric charges in our body (thus may induce a happy idea) and gravitational waves let our masses vibrate (to be exploited by the wellness industry).

For Ulrich and others, on gravitation generally:

“Cold comradeship do stars provide.

They light the closer, inner side

Of night's vast weight, which, chill and clear,

Pulls 'pon us like some puppeteer.

Its unseen threads to heads and hearts

Attached, it acts us through our parts,

From birth's first cry to bent old age,

Upon our distant, tiny stage.”

Canticle I, Canto X,

THE WATER MAGE'S DAUGHTER

http://ow.ly/koe43

To add to the original response: not sure if intentional, but Voyeur by Robbe-Grillet with its repetitions and permutations has clearly (for me) a mathematical structure, and so do certain Beckett works.

I think Andrzej is absolutely right, unforgettable piece (whether or not enduring literary work) mixture of fractal structure (repeated pieces with subtle differences).

Great contribution I think!

Thank you, Samuel. That reminds me of "Last year in Marienbad", which was based on R-G screenplay as well. Beckett is full of short repetitions and permutations (sort of like a DNA sequence or perhaps a chant) in "How it is" and also in "Rockaby".

The funny thing, I just realized, these repetitions make the pieces seem abstract or at least ambiguous, while in visual arts, in post-Malevich abstraction, abstract is often synonymous with random...

Lewis Carroll. Alice's Adventures in Wonderland Through the Looking-Glass and What Alice Found There.

My English is not good but i can understand.

I answer you in Spanish.

Básicamente, el discurso poético responde a directrices matemáticas. El ritmo, la rima, la métrica son estructuras matemáticas. Al igual que la música y sus movimientos, la poesía se construye con movimientos marcados por el ritmo.

Las formas del poema tradicional (soneto, romance y otros) marcados por rima consonante o asonante, poema en verso libre o poema en prosa, tienen estructuras matemáticas.

La estructura mental que exige las matemáticas es la misma que utiliza el crítico literario. El análisis literario hace un desmontaje, trabaja con ecuaciones, resuelve incógnitas.

La literatura y las matemáticas están hermanadas, eso lo sabían los antiguos matemáticos.

Greetings

Maria Antonieta, gracias. As you point out, there are correspondances, bridges between rhymes and metrics in poetry and mathematical harmonic structures.

Regarding the "father" of Alice, Charles Dodgson, it is clear that he was "fluent" in mathematics. At the same time he was critical of the latest developments in that domain (e.g., imaginary numbers, or non- Euclidean projective geometry). How ironic that it was this resistance to modernity which prompted him to write (brilliant) satires of modern mathematics into "Alice" (1) !

(1) Details will be found in Melanie Bailey's solid paper (New Scientist 2009) http://www.newscientist.com/article/mg20427391.600-alices-adventures-in-algebra-wonderland-solved.html?full=true

Please take a look at the following link for some examples.

http://math.unipa.it/~grim/SiLipsey.PDF

Thanks, Frederic, for your answer. H.E. and Frederic thanks for the links.

Thank you much H.E. for this paper (exact ref ??) by Sally I. Lipsey and Bernard Pasternack on 'Mathematics in Literature'. Definitely worth reading. While some of the works mentioned have been cited here before, others are new to this thread.

Maria, Frederic, you are welcome.

Frederic, unfortunately, there is no exact ref that I know of and I do not know if there is any. It seems that this paper is available in various places but only in e-format.

Has the Holy Bible been mentioned yet?

Cj. If you have solid, science-based arguments backing up the hypothesis that the Bible was much inspired by mathematical theory or structure, please go ahead and develop them here. We are open.

Frederic. To answer your secondary question, "solid, science-based arguments" are well-developed in the branch of knowledge (from Latin, sciencia) known as Theology, no better well-developed arguments than in any of the other sciences.

I see ...

Comes to mind "The Name of the Rose", by Umberto Eco, for the topological structure hinted by its labyrinthine library.

Maybe somehow off topic: if we are to consider the 'ontological'/'cognicitive' consequences of some of the postulates by Galileo, Descartes, Laplace, and others concerning math's universality for the representation or cognition of reality, it is possible that Goethe's "Faust" may be of some interest. And Kierkegaard's "In Vino Veritas", too. They come to mind because at times discussions concerning math may be predisposed to the kind of opposition shown, for exemple, in the essentialist/instrumentalist antinomy.

I would like to mention the work done by the italian writer Italo Calvino, in particular the "Cosmicomics" and the "Ti zero". Mathematical theories or, in general, scientific facts are taken as the starting point to create a complete world of characters that are "entities" which interact following the law of the universe.

A link to a description of the author can be found here

http://en.wikipedia.org/wiki/Italo_Calvino

Hope it helps ;)

In «La Disparition» Georges Perec write a complete novel without using letter «e». The result is awesome and extremely original. This can be seen as a kind of combinatoric writing style.

indeed - Georges Perec and the Oulipo group make recurrent, well deserved apparitions in this thread. Interestingly Gilbert Adair produced a noted English translation of "La Disparition" entitled "A Void" which won a literary prize in 1995. Further translations in Spanish"'El sequestro" (without this time the letter 'a'), Russian, Turkish, Swedish, etc, were published as well. But are we dealing here with a truly mathematical underlying structure, as in Perec's "La Vie mode d'emploi" for instance?

Another option which comes to my mind is the "Divina Commedia" (The divine Comedy) from Dante Alighieri. In this work (of course, is not a novel) the author puts a lot of the mathematical/theological ideas of that time to build a "divine" world which is run by rules and that has a precise (i would say) "geometrical" structure.

Dear Leonardo,Frederic and company,

Especially in Dante's concentric design for Hell in "Inferno," where he sketches circles within circles filled with souls guilty of an increasingly dense gradient of evil. And, interestingly, Dante placed a location just outside Hell itself for the "uncommitted"––those who never really commit to anything in life. I've not been back to ResearchGate recently in that I've been committed to something very Dante-esque, which feels synchronistic to me, since I returned just today. Some of you might recall my postings of excerpts from my new epic poem, "The Water Mage's Daughter," as well as a few of the mathematical mysteries contained within it. Well, over the last 20 days I've been managing a Kickstarter campaign to fund a chimera of a project. Firstly, to record the epic (15 hours) in my storyteller's voices, secondly, to compose original symphonic music to score it, thirdly, to create an enhanced ebook where reader/listeners can hear the poet's voice (synched to the ebook's pages) and lastly––which speaks most pertinently to this conversation––to employ a simple game engine for puzzle-solvers that both suggests and offers tools to solve the mathematical and prosodic games built into the text.

I know that's a mouthful, but it's all true. I invite you to take a look. It would be wonderful to find backers from the scientific community. Best to all!

http://www.kickstarter.com/projects/331860368/a-modern-day-epic-brought-to-life

"Alice in Wonderland". Written by a mathematician, too.

I should probably add a few plays by Tom Stoppard. Definitely, "Arcadia", which is a beautiful work. There is also some math in Act I of "Rosencrantz and Guildenstern Are Dead" (the coin keeps landing on the same side over and over and over).

This is not the first time that "Arcadia" is mentioned (see useful links on the subject given here ca. one month ago), but this is the first time that Stoppard's (much earlier) play "Rosencrantz and Rosencrantz and Guildenstern Are Dead" is suggested. Thank you.

Vladimir Nabokov uses the cyclic structure in his story called "The Circle". Its first sentence begins with "In the second place..." and its last sentence begins with "In the first place...", so the arc of the story seamlessly closes into a circle.

I should also add Stanislaw Lem, especially his "Cyberiad". It's mostly philosophy, I guess, but there is definitely some math there, too, and not just math logic. One of the short stories there even contains a math poem.

I also recall a short story call "The Poet" by Karel Čapek (the first user of the word "robot" -- he said his brother invented the word). It probably has more to do with psychology and art, as the math there is very basic and mostly has to do with the shape of the digits 2, 3, and 5, but the story is so funny that I would still count it in.

OK, maybe one more. Nikolay Rubtsov, a 20th century Russian poet with a tragic fate and very lyrical body of works, has a poem called "Morning Before the Exam". The exam in question is one in mathematics, and all the imagery (of nature and people) is mathematically inspired. Here is the original: http://stroki.net/content/view/16821/110/ . I could not find a translation. An automatic translation of course won't do it justice, but at least it may give you some idea as to what it is about.

Bruno Schultz, The street of crocodiles (strange mistranslation from Polish, should be Cinamone stores), not sure why, but I find it mathematical...

Not sure if this counts but both Robert Musil and Alain Robbe-Grillet were trained as engineers.

Albrecht von Haller (18 c., German poet). I'll try to translate it into English:

I put together a lot of numbers,

I sum up millions in the form of a mountain,

bulk times into the bunch,

spaces of innumerable worlds.

When I look at you from the wild high-

You are above all the numbers and measures.

They are the only part of You!

Zeiten worlds of unzuhli ge Bereiche

Ralph Waldo Emerson wrote an essay entitled "Circles" in 1841. "The life of man is a self-evolving circle, which, from a ring imperceptibly small, rushes on all sides outwards to new and larger circles, and that without end." Men and women grow, in concentric circles, in ability and interests as they encounter and assimilate new environments, at first with some confusion and distress because they do not yet possess and are in the midst of constructing their internal guidebook for these environments. Emerson also published a poem, "No Number Tallies Nature Up," later set to music as a Unitarian hymn. The text for the essay, "Circles," can be found in http://www.bartleby.com/5/109.html .

Shakuntala Devi of India, who died earlier this year,known for her mathematical wizardry, wrote a few mystery thrillers based on some mathematical formulae.

Excluded chapter possibly from Robinson Crusoe at http://plus.maths.org/content/mathematical-man-friday

And the works of Plato.

A most original, truly inspired work is the 1884 novel "Flatland - A Romance of Many Dimensions" by an English schoolmaster, Edwin Abbott, who invites us to a world populated by two-dimensional geometric figures such as polygons and circles -starting with the narrator itself called 'the Square'.

This society is based on a rigid system of castes where social status is linked to regularity and number of sides of polygons : lines and irregular polygons form the 'lower class', while squares and pentagons make up the 'gentlemen class', and 'nobility' starts with hexagons all the way up to 'the Circle' ... viewed as the perfect shape. The cruel rulers of Flatland ban innovation and colour but cannot prevent the rare visit- once every millennium- of 'the Sphere' who attempts to convince flatlanders, at the risk of imprisonment and even death, of the existence of a third dimension.

Happy New Year everyone !

P.S. This book perhaps inspired the great classic 1941 short story by Robert Heinlein "And He Built a Crooked House" about an architect designing a multi-dimensional eight-room home which collapses- and all the people trapped inside it- into a folded two-dimensional structure. As a result, all eight rooms appear to be contained within just one; like in a Escher drawing, the stairs appear to form a closed loop, and there seems to be no way of leaving.

If not mentioned yet, of course the script and storyboard of the film cube ant its sequel...

While Die Vermessung der Welt is a nice book, and related to science and maths, I do not know whether it can be considered:

a) having a mathematical structure ("Certain important writers did resort to hidden or explicit mathematical structures to construct novels...")

b) even a great, enduring literary work ("...novels that are now widely regarded as literary masterpieces) (but this is only my humble opinion")

As the quesiton posted, I think this novel fits more to "books (many of them, excellent) that focus on mathematics or on the life/works of mathematicians."

In a broader sense, I may add Of Mice and Men by John Steinbeck.

Finally being more and more interested by the thread, some google searches led me to those pages with more information (although also here the term "masterpiece" must be taken with caution).

In order to preserve the honour to the authors of the reviews (since I have not read all thos new books), I will just add the links for future discussions:

http://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf667

http://en.wikipedia.org/wiki/Anathem

http://dimpost.wordpress.com/2013/10/17/on-what-the-luminaries-is-actually-like/

http://mathforum.org/t2t/faq/brandenburg.new7.html

Sorry for the lack of originality of my post.

'The Da Vinci Code' by Dan Brown’ uses numbers and geometry quite a bit.

Sure ... and it has been mentioned (more than once) on this thread.

@Frederic, I have just read a "new book" by Cortázar based on his lectures in Berkeley 1980, and as I could understand, he would actually not have wished having Rayuela in the same group as Perec...

I undersaood that he said Rayuela is an existencialist game, whereas Perec was entertainment...

Would you agree to that? In the sense that Perec's works while nice they have no other value than the text itself, whereas other works cited here (and not only Rayuela) do have a deeper meaning?

Samuel, I've just found a reference to a 2013 edition of CLASSES DE LITERATURA (Alfaguara), in Spanish.Seems like an interesting book indeed. Is that the edition you've read? thx for mentioning it.

Rayuela (Hopscotch) by Julio Cortazar and La Vie, Mode d'emploi (Life, a User's Manual) by Georges Perec are two literary monuments of the 20th century. While both writers master the art of experimental literature, their sources of inspiration are rather different. Cortazar often borrows from a complex world of dreams, surrealism, puzzles to take and lose his reader through a narrative maze. Perec, for his part, takes literary creativity to rare levels thru a unique mixture of self-imposed aesthetic and mathematical constraints that will remain hidden to the vast majority of readers. In Life a User's Manual for example, a complex set of mathematical rules alone drive his sequence of chapters (and repeated visits to the many tenants of the building), but also impose the choice and spatial distribution of words, all lifted from 99 distinct lists of items (one per chapter). All this without affecting the literary quality of his novel. This has been thoroughly studied in a number of doctoral theses (see for example the pioneering 1991 thesis of Sonja Schak "Mathematik und Literatur/ Georges Perec" at the Univ. of Klagenfurt; or the remarkable 'Cahier des charges de La Vie mode d'emploi, by Hartje, Magné and Neefs published in 1993 by CNRS Editions, Paris (304 p.)

True, on both counts, as mentioned by earlier contributors on this thread.

@Diogenes: exactly!

that one is the book

There is a huge production of mathematical literature,

Pythagoras' Revenge: A Mathematical Mystery

By Arturo Sangalli http://press.princeton.edu/titles/8862.html

and many more in:

https://www.goodreads.com/shelf/show/math-literature

Am much grateful to you for adding the universe of Homer Simpson to our large family of enduring works directly - or indirectly - influenced by mathematics. Few books will ever match the lasting, jubilant impact of The Simpsons worldwide and I was amazed indeed to find that renowned mathematicians often joined the series' writing team.

Ernest Hemingway in The Old Man and the Sea employes number symbolism.