Happy Birthday Évariste Galois
A ‘few’ years ago, I ‘explored’ a mathematics seminar on Galois theory at university. Though they spoke English, I knew I would mostly hear mathematical Greek. But for a few Greek words that filtered into the English language, I would’ve left there grasping nothing but the atmosphere of mathematicians having high fellowship with one another; it would’ve been only an anthropological experience.
I recall Vague pictures of a four year old hand trying to span an octave while playing a piece on a piano. That was on CNN, years ago; a little maestro in the making. He made the octave in two steps, and it was beautiful. That wasn’t the ideal, or the perfect, but he went around the task excellently like children know to do well. He must have had, at the very least, a good teacher, and some motivation.
(And we praise children for their efforts, above and over the results they yield. As they grow older do we come to focus on results far above effort?)
“I had given to Moscow high school children in 1963-1964 a (half year long) course of lectures, containing the topological proof of the Abel theorem.” That was a statement by V. I. Arnold. These students, I suppose, were teenagers like Évariste when he started writing fantastic mathematical statements about our reality. A good teacher with the right perspective and proper organisation can teach some ‘high-end’ university level courses to high school kids.
High school is currently designed as a preparation and ‘selector’ for tertiary education. As currently formatted in Nigeria and many other countries, it has relatively little merit by itself. Enough university courses could be ‘downgraded’ to high school level when we think about it. Why not skip the ‘preparatory’ period, for amenable programs, and send the children straight to the degree.
If we say that high school education need not be a prerequisite for some university courses or degree programs, we mean, for example, that one could go from primary school to an MBA in six years tops. (Teeneage years better spent?) This is more easily workable if we have truly knowledgeable teachers; who can actually help the young ones learn, and who see and assert that high school students can handle more than the current standard.
Topology doesn’t sound like something that currently features in the regular high school curriculum. You’d more than likely find it at university only. But they can learn it and a few other big things earlier. It now perhaps depends on whether thats in a (direct) route to were they want to be.
Abraham Lincoln is said to have said that we’re only as happy as we want to be; it is in the same spirit to say that we’re only as knowledgeable as we want to be. But the right guidance and motivation is helpful and serves to accelerate progress. Kids would be smarter if we trained them to be smarter. (There’s a saying that an husband and wife parent a child, but the whole community raises him.)
Galois’ work in his early years are one reminder that teenagers could be trained to handle ‘much’ more than the certified curriculum designed for them. While Évariste was an outlier, that he did what he did as a teenager is telling. And there are many other examples. V. I. Arnold’s teaching Topology to high school kids says that it’s more a matter of organisation and presentation than difficultly for the age-group or grade.
Born October 25, 1811, he died about 20 years later with a legacy that was said would fill only 60 pages. For the significance of his works, Évariste Galois’ sixty pages were worth a PhD and more.
To find out more about Galois’ interesting life, visit: