More Thoughts on Mathematician’s Lament

At some point in 1993 before the movie was released in theaters, I read Michael Crichton’s Jurassic Park. At the time, it inspired me so much that I used it as the basis of a college entrance essay; I also signed up to meet the Mathematician at my school’s career day (yes, I was and am a total nerd). I really think Jurassic Park is one of the most profound works of science fiction. Reading A Mathematician’s Lament by Paul Lockhart brought the book to my mind once again.

My favorite character in the book was mathematician Ian Malcolm (even though he wasn’t quite as sexy as Jeff Goldblum). Malcolm knew that Jurassic Park would fail because he studied the predictable unpredictability of mathematics (chaos theory). He knew that mathematics is not something set in stone as we are taught to believe; it is a living thing which, like the bio-engineered dinosaurs, can not always be kept in neat little boxes. And throughout the book Malcolm can tell just by looking at the numbers and graphs that the park is going awry. No one will believe him, though, until all hell starts breaking loose. (Perhaps, I always liked Malcolm because Cassandra has always been my favorite character in Greek mythology.)

I always thought it kind of odd that it was the mathematician who understood the human ignorance and arrogance that would make Jurassic Park such a disaster. As Lockhart laments, I was raised to think of mathematics as cold and logical formulas to be used as tools, not intuitive and innovative ways of looking at life. And as I read the Lockhart’s essay, I thought about my initial introduction to fractals through Michael Crichton’s book. For those of you who are unfamiliar with fractals, I strongly recommend looking them up on Wikipedia. And if you needed any further proof of the connection between mathematics and art, fractal patterns have even been found in the seemingly random paint flinging of Jackson Pollock.

Now what will I do with this revelation about mathematics, besides use them as a focal point for two blog entries that very few people will probably ever read? I think this might have quite an influence on the way I homeschool my children in the area of mathematics, especially when we get to things like formal Algebra and Geometry. I have never had any intention of teaching my kids Calculus unless they asked for it, because most people have no need to learn Calculus and I believe that attempting to learn calculus in school ruined my basic math skills. Lockhart makes me now question how much of the normal Algebra and Geometry curriculum is really necessary.

Now I can kind of envision us mixing a little bit of basic Algebra and Geometry definition with reading books by mathematicians and throwing in some trial-and-error problem solving. It makes me wish that Lockhart would put together a book with examples of the mathematic puzzles that he gives his students to solve. I’ve also thought about teaching Algebra and Geometry based on an SAT prep book. Because even though Lockhart offers a vision of a utopian world in which mathematics is seen as the art that it is, my kids will still have to pass their college entrance exams that test on the same old empty definitions and theorems that Lockhart deplores.

On one last note, I tried looking up Paul Lockhart’s essay on Wickipedia and came across A Mathematician’s Apology by mathematician G.H. Hardy. After reading a synopsis of Hardy’s essay, you can tell that Lockhart has obviously read and been influenced by Hardy. Since Hardy died in 1947, I would not be surprised if Lockhart holds him in great esteem as a pioneer of number theory. And I may have to add G.H. Hardy to my own reading list, if I have any brain cells left after I deliver this baby.

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