Quantum Physics World

Wednesday, March 29, 2006

Algebra and Richard Cohen

In a recent column in the Washington Post, Richard Cohen laments the demise of a high school student named Gabriella who couldn't pass algebra after 7 or so tries. Cohen tells poor Gabriella that he hates math and has never used algebra.

Cohen misses the point. Whether or not you use something later in life is not always the basis of what is important to take in school. It is important to have a broadly educated citizenry who have been exposed to the wide range of human knowledge. This includes among other things history, the arts, science, and yes mathematics.

Furthermore, it shouldn't be lost on people that we live in a highly technical society. The importance of science and technology is increasing, yet the populace as a whole is woefully ignorant in these topics. People are being asked to make decisions about nuclear power, global warming, biotechnology, stem cells, space travel and the like. These are all scientific issues and having a reasonable understanding of them is important. The population should have their own understanding of the issues to a certain degree rather than having to rely on experts for everything. This can only be done through the education system, and while these are conceptually based topics ultimately there is a mathematical underpinning. I am not suggesting that people should be going out and doing their own calculations of say uranium half-lives, but doing some calculations like that in school will allow someone to make more reasoned judgements on many issues-like storing nuclear wastes at Yucca Mountain.

Cohen says that algebra isn't a high or the highest form of human reasoning, and that writing is. Frankly Mr. Cohen I beg to differ. Mathematics is the highest form of human reasoning and is the basic underpinning of our modern society. It transcends the sciences, being at the root of the human genome project, the design of lasers, electric power, radio and cell phones and the internet. In short the entire modern world is fundamentally mathematically based. Writing was already highly developed long before calculus came into existence.

Cohen also claims that a computer or calculator can do math while they can't write. Cohen's understanding of how computers are used in mathematics is naive. In higher mathematics, doing a solution like the quadratic equation is trivial. Its the understanding of the solutions and properties of equations that require higher reasoning. The computer is used to churn out solutions to equations that are too hard for the human mind to solve directly (no analytic or closed form solution). In the end a human being has to analyze and interpret the results-something a computer can't do.

I am sorry that Gabriella couldn't pass the course, but that's too bad. We do need higher standards in this country. Otherwise China and India will come to dominate world affairs in the coming century.

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