Sunil Singh writes:
What is mathematics? If I would have answered this question before I began my teaching career, I would have been provided some cliched, stock answer revolving around its importance to many disciplines like science, engineering, economics, etc. — basically it being some practical workhorse. Now? Well, since I wrote a book about it, it is simply about happiness. Finding sporadic moments of bliss learning something new and wonderful about mathematics. Just playing with numbers, puzzles, brain teasers, conundrums, algebraic ideas, etc — mucking around in the sandbox of math. The more I know, the less I know. The less I know, paradoxically, the better I feel about my ideas about mathematics.
There’s no doubt that mathematics involves happy moments. But does Andrew Wiles’ description of mathematics sound like happiness?
Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. You go into the first room and it’s dark, completely dark. You stumble around, bumping into the furniture. Gradually, you learn where each piece of furniture is. And finally, after six months or so, you find the light switch and turn it on. Suddenly, it’s all illuminated and you can see exactly where you were. Then you enter the next dark room…
Not that this is necessarily inconsistent with joy. Maybe you get your kicks wandering around anonymous dark mansions — there’s something for everybody. But you’ve got to admit, it sure doesn’t scream out FUN.
So which is it: is mathematics all about happiness or about stubborn frustration? Well, why not both? If, as Singh suggests, we’d best think of mathematics as an “art” then we get to ask, what other art is only about happiness?
I think educators sometimes emphasize feelings of joy and experiences of beauty in math at the expense of all the other things you can feel or see. For a while, I’ve been interested in visualizations of ugliness in math — is such a thing possible? And, as the Wiles quote shows, mathematics often involves far more than happiness.
“Of course math involves more than happiness,” you say, “but the point is that happiness is the goal, the purpose, the carrot that mathematicians are always chasing.”
Here’s an idea though: what if what we’re really in love with is the feeling of being lost in a dark mansion?