# A Doubter's Almanac

Ethan Canin produces here a novel in the tradition of John Irving classics. There is however no humor in this one, but black tragedy is thoroughly present. The story is about Milo Andret who grows up in the 1950's in the Michigan countryside. He has a special gift for orientation and can find his way home from anywhere. Because of his gift for mathematics, he is accepted at the UC Berkeley, and meets there his lifelong love Cle Wells, who introduces him to drugs. She eventually leaves him and chooses for his best friend. Milo succeeds in solving the famous Malosz conjecture and therefore gets a position at Princeton. He however is rude, stubborn, neglects his teaching, has a serious alcohol and drug addiction and it all goes from bad to worse. Moreover he maintains an expensive lifestyle and has liberal sexual relationships, among others with the department secretary Helena, and even with the wife of a colleague Nobel prize winner. For his solution of the Malosz problem, he gets the Fields Medal, and he has embarked on a new mathematical target: the solution of the Abendroth problem. He however does not get anywhere near a solution, until a 14-year old writes a paper getting much closer using a computer approach. Milo jumps on the computer track like mad and is able to get some weak results, but the bomb explodes in his face when that same young guy submits a paper with the solution using a clever combination of his computer programs and appropriate mathematical analysis. Even though the department head tries to support him as long as possible, Milo finally has to leave the university.

The second half is told by Milo's son Hans. Meanwhile Milo was married to Helena and is teaching in the countryside. Helena is the grey mouse managing the household while Milo is still upholding his lavish Princeton lifestyle. At some point he takes his family to a shed he bought near a lake presumably to concentrate on mathematics. When the former department head comes to visit them it is Helena's hope that Milo will be offered again a job which will allow them to move back to the civilized world. But Milo tells his wife afterwards that he refused because it was only a job of assistant professor and moreover it was for algebraic topology which was not his specialized niche in topology. The discussion ends in a fight and at that point his wife decides to leave him and take the children with her.

The son Hans is a financial wiz and is applying rules from financial mathematics before the discipline was even invented. Hired by a firm he makes lots of money and becomes filthy rich himself. His two children Niels and Emmy have the same sense of orientation their grandfather had and they seem to have the math gene too, especially Emmy does. Hans is addicted to amphetamines and other drugs, but when his wife caught him red-handed in the house, he decides to rehab, he leaves the firm and becomes a teacher in a small town. When Milo is diagnosed with bone cancer, first Hans, and later other family members, and even Cle come to look after him and they look back on all the good and bad events of their lives. It comes to a Shakespearean dramatic ending when Milo dies shortly after he meets his grandchildren for the first time.

The reason why this novel is reviewed here is not only because the main characters are mathematicians pure or applied, but also because there is an abundance of references to mathematics and the world of mathematicians. The Malosz and the Abendroth problems are both fictitious, but many references are to true existing mathematics. As a young boy Milo carves a wooden chain from a beech tree and its links had the shape of a Möbius band. As a student he builds a copy of Tycho Brahe's quadrant. This instrument was used by Brahe to make very precise observations of the planets and these were later used by Kepler to derive his laws of planetary motion. So Milo does the observations too and rederives these laws all by himself. The formulas are actually given explicitly in the novel. In Berkeley, Milo discusses the Catalan-Mersene problem with his advisor, but the latter pushes him to engage in the subject of submanifolds of complex projective spaces. Milo solves the Malosz problem by lifting it to a higher dimension, but his competitors in the race followed the wrong approach based on the Hirzebruch-Riemann-Roch theorem (no further details given). There is also a long passage in which Milo explains what mathematical topology actually is (`this napkin ring and this coffee cup are topologically the same') but Canin elaborates the subject further including a discussion of Poincaré's *Analysis Situs* paper. Topologists manipulate undrawable shapes in their minds, a world derived from principles not bounded by empiricism, something that Milo is very good at and he can easily draw rotations of a Steiner surface on a napkin for a colleague. And there are many other examples. Even Zentralblatt and all the existing mathematical journals mentioned seem to be the proper ones.

Also the structure of the book, or at least the titles of the chapters, are somewhat like the way a mathematical paper is written: Introduction, Deduction, Contraposition, Restatement, Conjecture, Summation, Proof, Acknowledgments. But also many subtitles have a mathematical connotation. Some examples:

– *You can't comb the hair on a coconut* obviously refers to the hairy ball theorem.

– *Ant and rubber rope* may remind us of a well known drawing by Escher of an ant on a Möbius band.

– *Flatland* is the title of the book by E.A. Abbott.

– *The real are almost all irrational* could also refer to the approximation or real numbers by rationals.

– *Thomson's lamp* is a form of Zeno's paradox. A lamp is switched on and off at time intervals halving the previous one. Will it be on or off in the limit?

– *Drunkard's walk* is a synonym of a random walk.

– *A topologist's apology* is a parody on Hardy's book ``A Mathematician's Apology''.

– *The prisoner's dilemma* is the well known logical puzzle.

– *Witch of Agnesi* refers to the curve that is studied by Maria Gaetana Agnesi in the 18th century. She called it `versiera' (from the Latin `vertere' meaning turn) but the Italian `avversiera' means female devil. The translation was wrong but the name stuck.

– *4656534* is a curious title and may refer to an abundant number that is the product of 5 primes: 4656534 = 2 × 3 × 23 × 41 × 823. There are indeed 5 mathematicians in the novel that do not communicate well with each other (The solitude of prime numbers). However Wikipedia also refers to the first 4-6-5-6-5-3-4 triple play in a baseball game in the Major League history played by the Yankees on April 12, 2013, and the chapter has indeed many references to baseball. So I am not sure about the proper meaning here.

And then there are the names of the main characters. The full name of Milo's son is Hans Euler Andret. Hans refers to Milo's advisor in Berkeley, and Euler is obvious of course. If you add to this his father's name Andret, then he is named after three mathematicians. Hans also has a sister Paulette who is named after Paul Erdős. Emmy's full name is Emma Lovelace Andret named after two female mathematicians Emma Noether and Ada Lovelace, and Niels obviously refers to Niels Abel. A non-mathematical reader may not be aware of these references, so Canin makes this clear in the text.

Including higher mathematics in a fiction novel is not a trivial thing to do, but Canin is obviously a good craftsman and comes away with it very well. Not a pleasant feel-good scenario, but rather a dark family story spanning three generations with a maudlin ending in full Hollywood style. How much of the mathematics should be taken seriously? Canin was certainly helped by his friend Jon Simon, who is a topologist and professor emeritus from the University of Iowa. I consider it somewhat negative for mathematics that Milo, the archetype of a mathematician has these stereotype features of being somewhat autistic and socially inapt to function properly. But of course, in this novel it is basic. If he would not have this dark side, there would not be a novel, or not the one we have now. That Milo constructs his replica of the Brahe quadrant and rederives the Kepler laws clearly says something about Milo's mind but I am not sure what function it has in the overall story since Canin puts relatively much emphasis on it. I have the same problem with the woorden chain Milo carved as a youngster but that canin takes along in the story. It seems also somewhat unrealistic to me that a winner of a Fields Medal would just run out of ideas on what to work on or not be mathematically productive anymore. It is true that a Fields medalist has a strong negotiation position to define his future working conditions, being exempt of teaching obligations and the likes, but running dry on ideas seems unlikely. If this Abendroth problem was indeed a long standing open problem, then it is hard to believe that a 14-year old will find its solution. That might have been true in Gauss' or Euler's time, but not anymore at the end of the 20th century. It is also strange that the preprint of the Abendroth solution was given to Milo by the department head. If Milo is indeed deeply involved in the problem, then he would be aware of all what has been or will be published in his domain of expertise, so why would the department head have a copy before Milo. Nevertheless, this book is a page turner that submerges the reader in a world of addiction (to drugs and mathematics), stubbornness, servitude, isolation, incommunicado, and yet after all also love (in addictive and altruistic form). A marvelous novel.

**Submitted by Adhemar Bultheel |

**9 / Sep / 2016