[John O]

I want people to read the book for the specifics of his arguments, but I want to discuss one important point that he makes. Many people in math education claim that in order to make math more understandable and interesting to students, we need to show how practical it is and how it is used in everyday life. I've always felt like this idea was wrong, or at least limited in its usefulness in that regard. Well, Lockhart demolishes the idea, essentially claiming that practical uses are simply by-products of math, and that the real excitement and beauty of mathematics is in the abstract, imaginary, and creative world of mathematical ideas that have no specific connection to the everyday. By-products and applications can make math seem boring and secondary to the uses it serves. I agree with him--and much more now after having read his argument.

(A quote form the first comment on the book.) Without applications almost any body of knowledge is next to useless.

Calculus was a total mystery to me for the first two semesters. The one question I had that none of my profs could or would answer was "Why do I need to know this?" The answer was always "Because your degree requires it, or because you'll need it for the next class".

Finally I had Dr Earl W Swokowski for the third semester of Calculus (He also was the author of the textbook we were using). So I asked my question "Why do I need to know this?"

We spent the next 2 sessions exploring where calculus is usefull using real world (but somewhat fanciful) examples. The one that sticks to me is if you were swimming and knew the topography of the bottom of the lake a second order deriviative of that topography would tell you which direction to swim to get to shallower water fastest.

Finally! an application for this stuff. The rest of the class just clicked. Everything suddenly made sense.

So sometimes, for some people, the application is all important while the "abstract, imiaginary and creative" is just useless noise.

BTW, to get back on topic. I loved high school algebra, geometry, trig and pre-calculus. I guess geometry was my favorite though. I'm one of those twisted, thoroughly damaged people that loves doing proofs.

[kosciusko51]

I admit that I haven't read the book yet; it came to me earlier this week as a recommendation from Amazon because I bought some Dover math classics recently for my library. I did see this comment, though.

In response to the comment to the book, I do think that some of the elegance of math is lost when ONLY applying it to practical situations. From the title of the book, there is an artistic element to math, especially some of the abstract math (group theory, topology, etc.) For instance, some abstract math had no "practical" value until recently.

Creative thinking in math creates tools that may later be used for practical applications, but some of this creative thinking leads to the math equivalent of a painting: there is no value in what was done, save for the elegance of the final product.

That being said, I am an engineer, and use math for practical purposes. I also like the show "Numb3rs", which showed some of the "practical" uses of math (a side note is that the technical consultant to that show was my prob & stat prof in college).