As a Novel

Some would say that, in a work of fiction, all that matters is the story, the emotion, the humanity, and the beauty that the book conveys. Even though this book does contain at least some of each of those things, I think they are too sparse in this work to please such readers. Others, myself included, can be satisfied with ideas in the book, both facts and philosophical musing. However, there are too many misleading statements and too little of a coherent philosophical thesis for me to strongly recommend it to this category of reader either. Consequently, I am not sure whether there is a type of reader who would really appreciate Wilson's The Ishango Bone. (Being a mathematician, I would be happy to have this question resolved through a "constructive existence proof". That is, if you are someone who really liked this book, please write and tell me why and I'd be happy to post the information here.)

The Riemann Hypothesis and Amiele's Proof

Let me try to offer my own description of the Riemann Hypothesis and what we would gain by knowing that it is true:

On the other hand, the method of proof (whether it is proved or disproved) may end up revealing some useful information beyond simply the answer to the question of whether all of the zeta zeroes are on the critical line. Some attempts at a proof stray into areas well outside of number theory, and it is one of these that Amiele seems to implement in the book. In fact, mathematicians and physicists such as Hugh Montgomery, Andrew Odlyzko and Michael Berry have worked on the idea that the zeta function zeroes seem to be distributed something like energy states in quantum physics (or, equivalently, like the eigenvalues of a linear operator). In the book, none of their names is mentioned and instead this idea is attributed to Amiele, who apparently is later able to turn it into a proof that RH is false. I say "apparently", because I'm not sure I understand the description of the proof which appears in the book, and cannot even tell if it is indeed a proof. (It sounds as if it is either probabilistic argument, or as if it merely turns the RH into an equivalent but similarly unresolved question about particle dynamics in quantum theory. Either of those would be of interest, of course, but would not be a proof that the RH is false, which is clearly what the book implies she has.)

Like another work of fiction, Life After Genius, this one had me LOL by suggesting that the Mathematical Intelligencer would be an appropriate venue for publishing a proof of an important theorem. No offense intended to that fine publication, but it is a magazine about math, not a math journal! (Annals of Mathematics would seem more appropriate.) Of course, this is a harmless mistake...I just thought it was funny.

A more worrying misrepresentation is the implication that Amiele is denied the Fields Medal for illegitimate reasons. Almost immediately after she announces the proof, colleagues suggest her for the prize, and the selection committee apparently denies it to her either because (a) the proof involves probability (b) they don't want RH to be false (c) she is a woman or (d) they do not like her personally. Of course, prize selection committees are subject to personal bias, but this suggestion seems almost slanderous to me. (Moreover, it is silly to think that because she did not get it immediately that she never would. The Fields Medal is not for a paper that came out in the months preceding the award but rather for a body of work of an individual mathematician before the age of 40. Since she was only supposed to be 26 when she published her disproof of RH, there would be plenty of time for her to still win the prize!)

Gödel and Ramanujan and other doppelgangers

However, Wilson apparently wanted to include interactions between Amelie and the mathematician Srinivasa Ramanujan. Consequently, he includes a character very similar to Ramanujan, named Rabindranath Shree, a former student of G.H. Hardy who serves as an early mentor for Amelie.

I am more perplexed by his similar inclusion of a character based on Kurt Gödel named Magnus Behman. It is not just certain characteristics, but Gödel's actual work that Wilson attributes to the fictional Behman. This seems likely to confuse a reader who is not already well familiar with Gödel, and seems somewhat unnecessary since his death in 1978 would seem to allow for him to possibly have met Amelie even without creating a dopplelganger as in Ramanujan's case.

So, there are at least some seemingly unnecessary name changes. Am I to suppose then that other factual (or spelling) errors, such as the reference to American President "Reagen" or the attribution of a proof of Fermat's Last Theorem to André Weil rather than Andrew Wiles, are also intentional? And why is Shree said to have had a Buddhist wedding rather than a Hindu one?

Turing and his work are also mentioned, but for some reason he gets to keep his name.

The Ishango Bone and other musings

Since this will probably be my only opportunity to voice my opinion about this intriguing discovery, let me add that while these things are interesting to speculate about, I am among those who remain unconvinced that it has any mathematical significance at all and is not merely a bone that has been notched to make it easier to grip. Moreover, although there seems to be much discussion about what the numbers on it mean, there seems to be too little discussion about what numbers they actually are. For instance, although the first column is often said to "list the prime numbers between 10 and 20", when I look at it (as in this picture stolen from Wikipedia):

Anyway, I have to admit that there is something emotionally potent about having this character examine this ancient object and speculate about its mathematical meaning. This is a case in which emotion, rather than logic or reason, makes this an interesting part of the novel, probably enough so that it deserves to be the title of the book.

As for the other speculations in the same "Coda", their significance to either the plot or message of the book eluded me. In my opinion, like the Ishango Bone speculation, they do not present strong arguments. The analysis of the anthropic principle seems entirely out of place, and misses the point besides. And the discussion of the role of intuition in math, while certainly an interesting topic and one that Gödel certainly thought his discoveries would address, is muddled here by the author's implication that any conjecture or hypothesis as well as any proof involving geometry or probability necessarily is "intuitive" rather than rigorous. Moreover, I did not see how they were tied to the overall story...unless we are to think that Amiele did not have a rigorous proof.

In the end, I'm afraid I have trouble strongly recommending this book. It has too much technical detail to interest someone seeking literature on a human scale, and too many of those technical details are misleadingly presented for someone interested in those details for their own sake. Moreover, I never grasped an overall philosophy or message that the book was attempting to convey. Still, I wonder if maybe I missed it. If you think you can explain it to me, I would be very grateful to hear your thoughts on it.