It’s a mathematics curriculum: one does not expect much history or many references to other cultures. Typically there are a few Roman numerals, a quick hello to Pythagoras and Archimedes, and that’s about it. More would be good, but it is not to be expected.
Dozens of 20th century non-fiction titles deemed historically inaccurate or offensive have been removed from the Northcote High School library as part of a push to decolonise the school’s book collection.
This is a short one and, necessarily, is WitCH-like. It is an elaboration in the new Curriculum that smelled wrong to us. We checked enough to confirm there was sufficient wrongness for the elaboration to be added to the Awfulnesses list, but we haven’t sorted it out further. The comments may be interesting (or non-existent).
A few months ago, I asked blog readers for suggestions for what had gone wrong with mathematics education. Plenty of discussion ensued, and it was very enlightening.
The purpose of that blog post was to help with the writing of an article. Guy Rundle had suggested that I write something on mathematics education for the magazine Arena. The article has now appeared (and in print). The introduction to the article is below and the full article can be read at Arena. Thank you to Guy for the opportunity, thank you all for your suggestions, and thank you to my secret crack team of hypercritical editors. (I have no idea of the significance of Arena’s graphic, but that’s cool, and it’s cool.)
(19/10/22 In a comment below, Bernard has noted the proof should be properly attributed to Paul Erdős, not Thue. Thue’s counting argument is similar in spirit, but not as quick.)
This post has no deeper meaning.1 Its purpose is just to present a very nice argument, which we gave in our talk last week, and which we feel should be better known.
One of the beautiful theorems that every school student should see is the infinity of primes.2 The standard Euclid proof tends to be difficult for students to appreciate, however, since, although the arithmetic is trivial, the argument is typically clouded with the unsettling concepts of infinity and contradiction.3
Predictably, last week’s talk ran short of time, and we were forced to skip some slides. The most regrettable omission was a slide titled “How to Teach …”, the motivation for which was to talk about the man in the photograph above, and about the photograph.
Our approach to teaching is, shall we say, eccentric. We won’t comment on the effectiveness of our teaching but, if “method” is too strong a word, there is an underlying idea. This idea is best captured by Ralph Waldo Emerson, writing upon writing: “The way to write is to throw your body at the mark when your arrows are spent”. Even if it indicates one way to teach, however, Emerson’s quote is of course not a dictum on teaching. Teaching is communication, and every teacher has to determine for themselves how they can best communicate ideas to their students.
Which brings us, almost, to the man in the fuzzy photograph. For the twenty years we were involved in the popularisation of mathematics, including the giving of and arranging of presentations, we were privileged to witness a number of great teachers. The brilliant John Conway was a stand-out, of course, as was Art Benjamin. But there were also two Australian mathematicians that were truly and particularly memorable.
The first mathematician was Mike Deakin. We mentioned Mike in last week’s talk, as one of our go-to guys when we started LunchMaths at Monash, and he gave a number of beautiful talks. Before that, Mike was, for decades, an editor, proofreader, janitor and mega-contributor for Monash’s mathematics magazine, Function.
The other mathematician was, finally, the man in the fuzzy photograph above: that is E. R. Love, who was professor of mathematics at the University of Melbourne for about three hundred years. In 1992, when Professor Love was 80, Terry Mills encouraged us to invite Professor Love to give a talk to the mathematics department at LaTrobe, Bendigo. We did so and Professor Love accepted. Declining multiple offers to be driven, Professor Love took the train to Bendigo and gave an absolutely beautiful talk on Legendre functions. Afterwards, over lunch, Professor Love entertained all with stories of Cambridge in the 30s.
Why write about Mike Deakin and, especially, Professor Love? Well, why not, of course; Deakin and Love were great contributors to Australian mathematics and deserve to be remembered and honoured. There was a specific reason, however, why we thought they were relevant to our talk, and why we particularly regret not having included acknowledgment of Professor Love: they were great teachers in a manner ceasing to exist. They were great lecturers.
Mike Deakin, who was an undergraduate at the University of Melbourne and then a Masters student under Professor Love, reminisces here on Professor Love’s teaching:
Love, in particular, was a superb lecturer. It was said of him that he was a menace because he made his subject seem so straightforward and logical that one missed seeing its difficulties.
The point is not that Mike Deakin and Professor Love were popular lecturers; the point is that they lectured in a careful, scholarly manner that is being lost. Their lectures had no gimmicks, had none of the crazy showmanship of the Mathologer, or of the writer of this blog. They simply lectured, conveying carefully crafted ideas to an audience willing and keen to listen. And, the point is that almost no one now recognises this, or cares, or can even properly understand. Almost no one under the age of fifty can realise that what is being lost is an art form, and an extremely beautiful and valuable one.
The title of this blog post is a play on Neil Postman‘s book titled Building a Bridge to the Eighteenth Century, which was in turn a play on a Clintonism. Postman’s excellent, and final, book was written in 1999. It was concerned with society’s inability to understand and to cope with technology, and the consequent loss of tradition and authority, of wisdom and plain meaning. Subtitled How the Past can Improve our Future, Postman’s book argued that we should look back to the 18th century, to the Enlightenment, for guidance into the future.
And now, twenty years later? The idea of building a bridge to the eighteenth century seems utterly fantastic, and perhaps always was. Twenty years on, and there is scarcely a memory of the twentieth century. The photo above was the best, the only photo we could find of Professor Love.
Mike Deakin and E. R. Love are dead, and they are being forgotten. The scholarly tradition they represented, the gift they gave, is being lost. And no one cares.
Gareth Ainsworth has contacted us, noting that Scotch College had an obituary for E. R. Love, which included a short biography and a photograph.
In 1973, the BBC televised The Ascent of Man, the brilliant series by Jacob Bronowski on the development of science and society. In his final episode, The Long Childhood, Bronowski sums up what he regards as special to being human, and the essence of a healthy scientific society:
If we are anything, we must be a democracy of the intellect. We must not perish by the distance between people and government, people and power, by which Babylon, and Egypt, and Rome failed. And that distance can only be … conflated, can only be closed, if knowledge sits here, and not up there.
That seems a hard lesson. After all, this is a world run by specialists. Isn’t that what we mean by a scientific society? No, it isn’t. A scientific society is one in which specialists can indeed do the things like making the electric light work. But it’s you, it’s I, who have to know how nature works, how electricity is one of her expressions, in the light, and in my brain.
And we are really here on a wonderful threshold of knowledge. The ascent of man is always teetering in the balance. There’s always a sense of uncertainty as to whether, when man lifts his foot for the next step, it’s really going to come down ahead. And what is ahead of us? At last, the bringing together of all that we’ve learnt in physics and in biology, towards an understanding of where we have come, what man is.
Knowledge is not a loose-leaf notebook of facts. Above all, it is a responsibility for the integrity of what we are, above all, of what we are as ethical creatures. You can’t possibly maintain that if you let other people run the world for you, while you yourself continue to live … out of a ragbag of morals that come from past beliefs. That’s really crucial today. You see, it’s pointless to advise people to learn differential equations, “You must do a course in electronics or in computer programming.” Of course not. And yet, fifty years from now, if an understanding of man’s origins, his evolution, his history, his progress, is not the commonplace of the schoolbooks, we shall not exist.
Bronowski spoke those words forty-seven years ago. Three more years.