a list compiled by Alex Kasman (College of Charleston)
|Note: This work of mathematical fiction is recommended by Alex for literati.|
|It is only after the death of her father that an Australian sculptor learns that her mother was one of five Hungarian Jews mathematicians who worked on math research together in a public park as Hitler rose to power. Her mother ended up moving to Australia and another member of her group of friends became a famous, prolific and itinerant mathematician.
That description will sound familiar to those who know of Paul ErdÅ‘s. Like the characters in this work of fiction, ErdÅ‘s and four friends met in a public park in Budapest to work on mathematics because anti-semitic laws prevented them from participating in normal academic life. ErdÅ‘s is famous for being a prolific, itinerant mathematician, while some of his friends moved to Australia.
In the book, the two female mathematicians in the group of friends begin investigating a question about random assortments of points being used to form the vertices of convex quadrilaterals and the generalization of that question to other polygons. Despite the fact that the book is vague on mathematical details, those familiar with combinatorics will recognize this as being as problem which Paul ErdÅ‘s named "The Happy Ending Problem" because its resolution led to the marriage of George Szekeres and Esther Klein. According to the book, this problem has grown into the more general "Upper Limit Problem", a supposedly famous open problem that serves as a MacGuffin for this story. Although I cannot find any reference to this name being used for a famous open problem in mathematics, this appears to be the book's version of the problem of finding the value of all Ramsey numbers. (See, for instance, this blog post by Evelyn Lamb which happens to quote ErdÅ‘s on the difficulty of that problem.)
Clearly the events described in this novel bear more than just a passing resemblance to the true story of Paul ErdÅ‘s and the group of mathematicians he worked with in Budapest before fleeing the Nazis, and the reason for that similarity is no mystery. In fact, one of those Hungarian mathematicians who eventually settled in Australia was Marta Sved, the Miriam Sved's grandmother who also wrote a work of mathematical fiction. It is fascinating to know that Miriam Sved met ErdÅ‘s when she was a little girl. She remembers playing a strange "game" with him that she has Pali Kalmar (the ErdÅ‘s-like character in the book) play with another child. However, "A Universe of Sufficient Size" is not a retelling of the true story of those Hungarian friends using pseudonyms. In many ways, both big and small, the plot of the novel deviates from reality, making it a work of literature rather than history. (If you want the true story, you can try to obtain Marta Sved's memoir, Two Lives and a Bonus.)
One of the small ways in which the story in this novel is different than the true stories that inspired it is that it shows Pali Kalmar speaking about mathematics in 2007 to an audience that includes one of his old friends and her grandson, whereas Paul ErdÅ‘s died in 1996. This small difference allows for a very nice subplot of the fictional version of the story: The sculptor's son (unaware that his grandmother worked on related math in her youth) is motivated to do math research in combinatorial geometry by questions about the spread of information on the internet and ends up collaborating with Pali Kalmar himself on the famous Upper Limit Problem.
There is also a very big difference between the true story and the one told in this novel, a major plot twist that is entirely the author's creation. I won't say any more about it so as to avoid spoiling the surprise for anyone who might read it.
I am a little bothered by the ways in which the importance of these mathematicians (and their mathematics) is exaggerated in this book. Pali Kalmar is not presented as simply eccentric and prolific (which I think are the words that best describe ErdÅ‘s as a mathematician), but instead seems to be the most important mathematician of the 20th century, which ErdÅ‘s certainly was not. When describing a mathematical result of Kalmar's that obviously is modeled on the deBruijn-ErdÅ‘s Theorem, the book claims that it showed that Gödel was wrong, as if to convince the reader that Kalmar is greater than Gödel. (BTW The deBruijn-ErdÅ‘s Theorem is a special case of a result by Gödel, so if anything the situation in reality seems to be the opposite.) The idea that the combinatorial problems which the Hungarian friends worked on together have application in the study of the internet does not seem very far-fetched to me, but the passage in which Kalmar explains its connection to mathematical physics (the passage from which the title of the book is taken) was a bit over the top, in my opinion. Perhaps the most extreme exaggeration occurs when a character is about to start working on a thesis project in "abstract geometry" and receives the following advice:
I understand that the author may have done this for either of two reasons: because of family pride and because it makes the story seem more important. But, I still would have preferred it without these embellishments.
It bothers me just a little bit to think that readers of this novel might be left with the misimpression that Paul ErdÅ‘s was that significant to mathematics. What bothers me more is merely that this reinforces the idea that there are a few people who are such mathematical "gods" that nobody else matters. The truth, as I see it, is quite different. Moreover, I believe the popular myth of mathematical superheroes probably does more harm than good by discouraging people from participating in mathematical research, which is much more of a cooperative activity than such stories would lead one to believe.
Despite this one niggling complaint [Miriam Sved apparently likes to use the word "niggling" and so I thought it would be appropriate to use it here. I hope I used it correctly! -ak], this really is a very nice piece of mathematical fiction. Along with doing reasonably good job of portraying mathematicians working on their research, there is plenty of drama, romance, angst, danger, and all of the things that make for a compelling story. Through the grandson's internet-related research, it implies that the math itself is important and applicable. The book also addresses the big questions of life and death, giving it some literary weight. It even tries to connect the math research and the big questions by suggesting that seeking convex polygons among random vertices is like trying to find meaning in a chaotic universe.
Note: As far as I know, the only other work of fiction to feature Paul ErdÅ‘s as a character is The Mathematician Repents, and I'm not absolutely sure that one is even fiction.
Thanks to my College of Charleston colleagues Renling Jin and Dinesh Sarvate for answering my questions about logic and combinatorics (respectively) on which I based some of the discussion above.
Note: I've written a joint review of this novel along with Machines Like Me that covers many details not mentioned in this post. It is to appear in the Notices of the American Mathematical Society.
|More information about this work can be found at .|
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(Maintained by Alex Kasman, College of Charleston)