Taylor’s theorem gives quantitative estimates on the error in this approximation. Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial. The Taylor series of a function is the limit of that function’s Taylor polynomials, provided that the limit exists.
—Taylor Series, Wikipedia
I keep encountering people who want to learn more about mathematics. Not only those who enjoyed it in school and have had no opportunity to pursue it once they began their careers, but also many who performed poorly in school and view it as a lingering challenge. As the Stanford mathematician Keith Devlin argues in his book “The Math Gene,” human beings are wired for mathematics. At some level, perhaps we all crave it.
—Manil Suri, How to Fall in Love With Math, the New York Times, Sept. 15, 2013
I was not “wired” for Taylor Series.
Somewhere in the vicinity of just-18 (and you know what I mean) I crashed into Taylor polynomials and the limit of my ability to grasp math. This limit was further described as I pondered the partial mystery of Schrödinger equations at 19 and the total mystery of homogeneous first-order linear and constant-coefficient ordinary differential equations at 20.
I did not get to 21.
Professor Suri, of the University of Maryland, pens a wonderful note from the vista of those-that-got-it at age 9. Most of us did not and do not and will not get it.
It goes without saying that America has unlinked from the global brains war on math education. It is our “lingering challenge.”
The singular way to Love of Math is for parents to place front-and-center its foundational importance, to provide support in its joy—and critically, to be there when math gets hard.
I was fortunate. I grew up in math nirvana and didn’t run into “hard” until Brook Taylor darkened my eighteenth year.
Others are not so fortunate. We need a massive and urgent understanding that math is not mystical. We need to confront that math matters to a society … that the clouds do not part.
What is needed is parental and community support to all children at all moments, particularly the fragile I-don’t-get-it moments. And they are early and often. Celebrities must climb on board the math-as-cool train. (See Phil and Amy Mickelson for hole-in-one leadership, here.)
Read Manil Suri. Better yet, bone up on our abysmal and collective American failure. Get to work. Get over it. Math is hard. Discuss.