Letters to a Young Mathematician -- 23 October

I picked up Ian Stewart's Letters to a Young Mathematician mostly on a lark the other day at the library, attracted by the jacket blurb that suggested it as a charming read that even non-mathematicians (of which I most certainly am one) can enjoy. It is so, it is so, but it's having some surprising side-effects, this little book.

I've long had a sort of sick fascination with mathematics and mathematicians and what they can do, but always from a distance (which is why I describe it as sick). I have always taken my math at one remove, usually via fiction. Neal Stephenson is a constant favorite, and Alastair Reynolds (whose Diamond Dogs gets a mention in Letters but not entirely a favorable one*), and I still dive in occasionally to see how far I can go in Douglas Hofstadter's Godel ,Escher ,Bach: An Eternal Golden Braid (about halfway, generally, though I have finished the book once, back in my Bard College days with the help of a cute computer science professor). I am, therefore, not entirely one of the "non-mathematcians" whom Stewart describes as automatically equating mathematics with arithmetic and thus finding it all so horribly dull and tiresome and limiting. Sure, I still have that basic gut reaction when I look something up and get a page full of parentheses, operands, italic type and Greek letters, and most of the time I am too lazy to even try to see if I can follow the operations, but still my imagination is captured; I feel awe that we have made as a species so much progress in finding ways to describe and imagine what is going on beyond the brute evidence of our senses, when creamer swirls into coffee, when a semi slides across an icy road at tremendous speeds and smashes into another, when we find the urgent need to encrypt streams of data that represent the fincancial doings of millions of individuals using the internet or ATMs or the international banking system.

Stewart's book has re-awakened all of this curiosity and more, and along with it a tenuous kind of hope. He points out, in blunt and critical terms, that much of what is taught under the name of mathematics in primary schools (i.e. elementary, middle and high schools) is really just dull old arithmetic, and that the algebra, trig and calculus that eventually confronts students is also very limited and unimaginative, gives not even the slightest hint of how creative math really is when it only presents problems that have solutions, and not just that have solutions "in the back of the book" but only have one solution each, which the student who still finds himself drawn, usually alas on his or her own, to go beyond high school requirements quickly finds are not necessarily the norm. Many problems have many solutions, or no solutions. And then there are things like number theory and non-Euclidian geometry (just that phrase has always kind of thrilled me)... and as Neal Stephenson taught me the history of math itself is fascinating and sometimes (Newton vs. Leibniz anyone?) very dramatic. You don't get a hint of that in school, though, as you stand up in front of the blackboard solving a crappy quadratic equation in front of the rest of the class, your teacher standing beside you mocking your slowness and tendency to make fluff-headed mistakes under pressure ("3+3 is not 5, you dumb broad" -- but that's a tale for another day).

Like everyone I know who took math at my particular high school, like pretty much everyone I know except for a few funky math majors at Bard, the odd professor, and a math graduate student I met about a month ago at Starbucks, I let that unpleasant experience give me a poor attitude towards my own prospects for and prowess at math for a long time. My one attempt to see beyond was more or less deliberately (unconsciously?) sabotaged by my choice to take college calculus the same semester I also piled on four other heavy duty courses (Philosophy of Language, some deconstructionist American history course, a computer programming class the title of which I forget but had us working a lot in Modula 2, and Joseph Conrad -- I was, after all, a literature major) and so I tanked badly (kicked ass in everything else, though).

But now as I read and enjoy Stewart's book, and look up what other of his stuff my local library has or can ILL for me, I'm brought around again to wanting to take the time to settle a question that has plagued me since college: is my mathematical ignorance a result of actual incapacity, or of laziness?

*Stewart is critical of Reynolds' underlying notion that our mathematics is somehow universal, that concepts like number and so on would necessarily be a part of the math of any alien intelligence we might encounter. Reynolds story centers on a series of puzzles posed by an alien intelligence, which the human explorers of a structure must solve to progress (or die!). An amusing quotation: "It includes topology and an area of mathematical physics known as Kaluza-Klein theory. You are as likely to arrive on the fifth planet of Proxima Centauri and find a Wal Mart."