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I am a mathematician and I am a math teacher. That does not mean that I am smarter or less sociable than the next fellow; math is just another profession. One thing I am certain of is that being a mathematician is the best profession in the world.
I am sometimes asked – by students, parents or strangers who see me wearing a geeky math T-shirt – what is the point of studying math? The question does not bother me. It is legitimate and non-trivial. What bothers me are the simplistic answers that are often given.
The most obvious rationale is to develop basic numeracy skills – from counting your change, to figuring out what your mortgage rate means, to interpreting some basic statistics in the news. Everybody agrees, but these only require math knowledge accumulated up to Grade 7. I teach high school. Is my work pointless?
Not if you think of math as a gym for the mind. Children develop strength, co-ordination and risk taking by climbing jungle gyms on the playground. Grown-ups stay healthy – both mentally and physically – by staying active. Math – when rightly and regularly done – keeps the mind active. It develops analytical thinking, creativity, pattern recognition, patience and focus.
Of course, the operative words here are "rightly" and "regularly." If we just load the students with a bag full of tools that they hardly use, there will be little benefit. It is like teaching your soccer team how to do correct throw-ins and how to recognize an offside position – but not spending much time playing games. The "right" way to do mathematics is not to learn many techniques, but to solve many problems using the learned techniques. The word "regularly" is also of essence. Some parents, who know how important thorough and focused practice is when it comes to developing piano or hockey skills, don't seem to realize that completing math work in the car when driven from the piano lesson to the hockey practice is not a formula for success.
It's not easy to see an obvious practical use for different branches of mathematics learned in school. To see the benefits, one needs to look beneath the surface.
Take Euclidean geometry, with its proofs of similarity and collinearity. Who cares if we prove beyond any doubt that three points are collinear?
But did you know that former U.S. president Abraham Lincoln was a lawyer by trade who carefully studied Euclid's Elements, a book that, through geometry, builds the fundamentals of clear and correct reasoning? In an ideal society, not just lawyers and mathematicians should be able to present a point of view in a convincing way: A follows from B, which is a consequence of C.
Algebra is also a target of smart alecs from respected authors (Stephen Leacock comes to mind) to stand-up comedians and even fellow teachers. Yes, I admit, factoring polynomials and completing squares – the stuff of teenage nightmares – hardly comes in handy in our daily lives. I also admit that we math teachers sometimes indulge in too much fancy technicality that may be more interesting to us than it is for our audiences. However, no matter what the sins of the math teachers, algebra is probably one of the most useful inventions of humankind. Airplanes fly because physics and engineering are written in algebraic terms. Computers are living, breathing algebra-based golems. Any science that does not use the language of algebra to some extent, well, is not quite science – it's opinion.
Paradoxically, one of the greatest practical advantages of learning mathematics is to develop abstract thinking. In a math problem, a bus travelling from A to B is stripped of other details – colour, size, age of driver – so we can apply the same formula when solving a problem about a motorcycle. Abstract thinking is one of the greatest assets of intelligent beings. From the paintings in the Lascaux caves to Salvador Dali's work, creativity stems from abstract thought. We cannot live our concrete lives without a feel for abstract concepts, from rhythm and comfort to the more complex: morals, beauty and love.
I've left the most difficult to understand benefit of studying math to the end: I think that math is beautiful. It is also a collection of some of the most amazing creations of human genius. Can I convince the uninitiated? It would be hard. One first needs to have the patience, respect and desire to learn the language of mathematics, then its idioms, then its quirks and subtleties. Then we can talk beauty.
In class, when we get tired of factoring polynomials, I tell my students that life is all about discovering the beauty that surrounds us – math, music, poetry, the structure of a living organism. You only need to have the patience to learn the proper language to see it.
Many, many years ago, I was graduating from high school and I was considering a career in mathematics. I asked a math professor for advice. "Why do you want to study math?" he asked me. "Because I think it is fun." He told me it wasn't, really, that there would be much tedious work and frustration. Then he paused, and added with a smile, "I guess it also has its fun and awesome moments." I spent my next 40 years doing math and never looked back.
Alexandru Pintilie teaches math in Toronto.