October 6, 1995
I'm very well acquainted too with matters mathematical,
I understand equations, both the simple and quadratical,
About binomial theorem I'm teeming with a lot o'news-
With many cheerful facts about the square of the hypotenuse.
William S. Gilbert, 1880
In Gilbert and Sullivan's Pirates of Penzance, Major general Stanley knows just about everything that was taught in British schools. The only things things that he doesn't know have to do with military matters. He sings "When I have learned what progress has been made in modern gunnery, When I know more of tactics than a novice in a nunnery: In short, when I've a smattering of elemental strategy, You'll say a better Major-General has never..."
In those days, no one could get to a university without passing exams in classic Latin and Greek. The assumption was that if you knew those two languages, you are highly intelligent and would automatically acquire whatever knowledge you needed in whatever occupation you chose -or were assigned to.
Latin and Greek have pretty well gone by the boards. Nowadays, it's mathematics. Calculus is required for admission to many medical schools, and three years of high school math are required for admission to many colleges and universities. In the California state universities, if you can't pass an exam in math, you are required to take "remedial math." I saw a couple of questions on that exam. They were Greek to me, and I am not illiterate in mathematics.
Mathematics is extremely valuable. It is a cornerstone of science. As a consequence, the priests of mathematicians have a large say in what is taught. Unfortunately, what is extremely valuable to a professional mathematician may be of no use whatever to people in other fields. When my kids were going to school, there was a thing called the "new math." In junior high (now called middle school), children were taught set theory; an exquisite way of looking at numbers. For those who would become mathematicians, it was a head start. For the rest, it had no more relevance than learning how to play chess or, if you wish, Latin and Greek.
Calculus is vital to much of engineering and physics. Does it have any value to someone going into medicine? I doubt it. So why is it required?
Geometry is essential to anyone designing just about anything, and for carpentry. Is it necessary, or even desirable, to know the theorems of Euclid? That was what I was taught and tested on in high school. It is a fact of life that the vast majority of people forget what they don't use. I had to re-learn geometry when I built my house.I re-learned algebra when I studied genetics and statistics. Had I remembered my high school experience? I doubt it.
Logarithms are wonderful things, but hardly anyone uses them any more, thanks to the calculator and computer, which can perform difficult and time consuming calculations in an instant.
An education during the dark ages consisted of memorizing The Bible, and learning to converse in Latin.In some quarters, that still applies. Now mathematics has become the substitute for classical Latin and Greek as the means of weeding out those people who lack the ability or motivation to absorb, and regurgitate on exams, massive amounts of useless information. Isn't that what we consider the mark of the educated man? Whether or not he needs, and can make any use of that information, seems to be completely irrelevant.