Simon: The Genius in my Basement

Alexander Masters began his writing career with a book called Stuart: A Life Backwards. It told the story of a young homeless man whom Masters had met and gotten to know. His second book, Simon, continues in a similar vein, telling the story of another unusual character that Masters got to know: the mathematician Simon P. Norton.

Both books take a similar approach to telling the story of a living person: Masters makes his subject part of the process, showing him drafts and discussing the book with him. The book includes emails and commentary from Simon, mostly telling Masters that he has gotten things wrong and objecting to various aspects of the narrative. There are photographs, newspaper clippings, and pages from old notebooks. Masters uses drawings to explain some of the story (and some of the mathematics) and keeps the text (relentlessly?) light. The result is somewhere between a biography and a blog, in which both “Alex” and “Simon” are main characters.

The main theme, in many ways, is that Alex is trying to figure Simon out, because Simon is a very strange man. He is Alex’s landlord, living in the basement of a house whose other floors he rents out. His basement is full of plastic bags and old paper, including many new and old bus and train schedules, which support what is now Simon’s biggest preoccupation: public transportation and its woes. Simon hates cars, thinks that the 1985 law that deregulated public transportation in England was a calamity, and campaigns ceaselessly on the subject.

Of course, Simon is also a mathematician, one of those who started out as a child prodigy. He seems to have been focused on mathematics from a very early age. At Eton, his talent in mathematics was supported by an imaginative private tutor. He then went to Trinity College, Cambridge, where he met John Horton Conway and got involved in the project of understanding finite simple groups. Norton is one of the authors of the famous Atlas of Finite Groups (now online); he and Conway wrote one of the most famous mathematics papers ever. It was called “Monstrous Moonshine” (Bull. London Math. Soc. 11 (1979), no. 3, 308–339). In it, Conway and Norton noted what seemed to be a series of amazing numerical coincidences relating the character table of a finite simple group known as “the Monster” and the Fourier coefficients of certain modular functions, the “Hauptmoduln” of genus 0 modular curves. They called the whole thing “moonshine” in the British sense of “foolish or unrealistic talk.” It was almost twenty years later that Richard Borcherds finally established that there was indeed a connection between the two subjects, with a tour-de-force paper that helped him win the Fields Medal in 1998.

So what happened? Well, perhaps nothing, really. Simon’s interest in public transportation goes back to 1966, and he continues to do mathematics and publish papers, as a MathSciNet search will confirm. But it is true that there was a big change around 1985. In his email to Alex, Simon says that this was the year in which two hugely important things happened: Conway moved to Princeton, and buses were deregulated. The latter is the reason for his current focus on public transport campaigning. Not having Conway nearby clearly made it much harder for Norton to do mathematics; furthermore, Conway quickly moved on to other subjects while Norton still seems mostly interested in group theory and “moonshine.”

Throughout the book, Simon tells Alex that his ideas about how and why Simon does mathematics are ludicrous, and he is right. Alex’s attempts to explain group theory are not wrong, but they are so elementary that they leave the reader wondering why this subject is of any interest. There is an amazing moment where Alex says something to the effect that simple groups are those that do not have subgroups, where an asterisk leads to the note

The word “normal” is essential, but too big a subject to discuss here.

A reader who actually believed Alex’s definition would definitely be puzzled that there is any theory of finite simple groups to talk about!

Alex admits that his account gives the reader very little to work with, but apparently has no idea how to fix it, arguing that the mathematics is far too difficult for normal people. There are far too many places where what he says is wrong (the Monster “is the largest simple group in the universe”), plays into math-phobic stereotypes (Hall’s Theory of Groups “looks terrifying”), or makes very little sense (the Atlas “is imbecilic with complexity”).

Masters presents Norton as fundamentally a happy man. (The subtitle of the British edition makes this explicit.) And certainly there are elements of happiness. Norton is blessed with sufficient money for all his wants, and is able to live as he wishes; people find him strange but he is certainly functional. He takes enormous pleasure from his many bus trips; towards the end of the book, he and Alex go on a long trip together, and he seems to have a great time. Nevertheless, when Simon speaks about himself, he often speaks about grief: losing Conway, bus deregulation, the death of his mother, feeling his age. Perhaps what strikes Alex as “happy” is simply the fact that Simon leads a simple life that suits him and has laid aside the anxious desire to be “successful.”

While there are some moments where the book becomes too cute for its own good, there is no doubt that Simon is entertaining. It will add to the already long list of stories about strange mathematicians and their funny ways. Still, I think Conway had a point when he told Masters that “You must be very careful not to jump to any easy answers with Simon” (epigraph to chapter 28). But Masters’ whole approach requires staying on the surface.

Fernando Q. Gouvêa is Carter Professor of Mathematics at Colby College in Waterville, ME.