One of the difficulties of judging the ways of people is the fact that highly intelligent individuals can at the same time be in the grip of a totally cockeyed ideology.  One reads things like this:

Parents who dress their daughters in pink are holding back the economy, says minister

Now I am not including that government minister among the “highly intelligent individuals”.  But one very intelligent columnist for the Times (London), namely Libby Purves, is a proponent of the same ideology.  Nevertheless, she came out recently with a column

Learning facts helps us to recognise the truth

from which I extract this gem:

A famous broadcaster, seemingly equally at home with science and humanities once expressed to me his metaphor of mental “grids”. He said: “I have good history and literature grids, so whenever I learn something new in those areas it slots into its proper place and I remember it. But I don’t have a good science or maths grid, so, when I learn something about electrons or whatever, it drops out of my head in minutes.” [1] Young minds learn easily, so it is worth stocking up even on facts you are not interested in. I hated O-level biology, but it makes me less irritatingly stupid in conversations with my doctor, whereas my exclusion from physics classes and engineering basics makes me an easy dupe of any garagiste [2].

So when I read the following about an initiative from Finland concerning maths education:

21st Century Science: Legacy Math Education Isn't Going To Cut It

I think: you’re going to be up against our education minister, who wants to return to traditional methods.

The one thing, though, is — do not leave it to mathematical academicians to decide.  The illustrious French mathematician Jean Dieudonné (1906 – 1992), perhaps in a moment of pique, exclaimed at an education conference “Down with Euclid! Death to triangles!”

The effect of this was bad enough in Britain.  Traditional methods gave way to the “New Maths”.  But in France, the influence of the strange mathematical collective known as Bourbaki was to lead to the bizarre situation, described by the Russian mathematician V.I.Arnold (on teaching mathematics):

To the question “what is 2 + 3” a French primary school pupil replied: “3 + 2, since addition is commutative”. He did not know what the sum was equal to and could not even understand what he was asked about!

Another French pupil (quite rational, in my opinion) defined mathematics as follows: “there is a square, but that still has to be proved”.

(I wonder how fair it is, though, the blame Dieudonné himself.  France at the time was bogged down in legacy education.)  But here is another brilliant bit of Arnold:

Since scholastic mathematics that is cut off from physics is fit neither for teaching nor for application in any other science, the result was the universal hate towards mathematicians - both on the part of the poor schoolchildren (some of whom in the meantime became ministers) and of the users.

One of Robert’s theorems is that when someone comes along with a new method, those in power leap at it, because it appears to justify their own lack of progress in the subject under the old method.

 = = = = = = = = = = = = = =

[1] I really wonder, then, if that broadcaster is equally at home with science and humanities?

[2] I find the opposite problem.  I could not explain to the people at the garage, or even to those at the front of the manufacturer’s customer team, that what I wanted to know was simply how much current was leaking from the part that they had replaced at — possibly — outrageous expense.