There was evidently a degree of inexcusable wooziness operating in the higher mathematic community when they pushed New Maths for Schools hard in the 1960s. (They didn’t just ‘support’ it, they backed it to the nth degree.) Their conception of what would have meaning for ordinary children, parents and teachers, turned out to be miles awayfrom reality. So now, sixty years later, they should have long since seen the error of their ways and reformed their thinking…
This would have happened in an ideal world, but unfortunately the world isn’t ideal, and the mathematic establishment reflect this imperfection, by never making any definite commitments about anything, still less an admission that they got something wrong. They are the last embattled survivors —in the last redoubt— of ‘ancient notions’, because they have been assuming the role of secular high priests of thebrainiest, infallibly correct, logical fraternity since the time of Pythagoras.
But they have hit a bad patch. Bertrand Russell discovered a devastating contradiction at the heart of mathematics in 1901, and because no one could explain or resolve the problem, the high priests cravenly arranged in the 1920s to adopt new axioms for their subjectwhich made it impossible to state the contradiction. They made it look as if they had solved the problem, when they hadn’t. This became the higher mathematicians’ ‘Party Line’, and was rigorously enforced.
Since that time they have unquestionably conscientiously maintained their Line —accepting the role of an embattled elite. But it has been a bumpy ride, because they have tried to take the “timeless view” (=the unchanging view) during a period of unprecedented discovery and innovation… in knowledge, social solidarity, technology, attitudes to meaning, and attitudes to religion. They regard themselves as a secular priesthood, which must be a reliable guardian of their sacred,transparent, abstract knowledge, even when the ride is bumpy. They must, they think, look after this archive of slightly mystic timeless truthand pass it on to the mathematicians of the future. They consider that it must also be a timeless truth that there will be mathematicians in the future.
Unfortunately they have overlooked the mundane, obvious fact that what happens in schools is subject to all kinds of pressures, and some of these inevitably affect the supply of future mathematicians. The outcome of schooling has none of the characteristic qualities of timelessness.
But it is worse than this. After the Party Line was introduced, maths began to acquire a strained, slightly artificial air. The subject’s confidence had been shaken at a deep, subliminal level. The fiasco of New Maths for Schools was also quite deadly, and afterwards a new source of inspiration was clearly urgently needed. But the subject’s high priests stuck to their line of doing nothing, and this has remained the case for the past forty years. The school subject has been allowed to wither on the vine. It has lost its way hopelessly in schools, and the subject has become regarded by many teachers as a chore. The result: fewer and fewer highly intelligent young people are committing their careers (= their lives) to mathematics of the elite, artform, timeless, slightly mystic kind.
No, because today the subject ‘mathematics’ covers much more than hyper-abstract, arcane stuff.
There are actually plenty of jobs for young people with mathematical talent in today’s world. As a result of the IT revolution almost every area of human activity has been mathematicised. The UK Meteorological Office, it is said, employs about 2,000 mathematicians. The City’s Financial Sector employs thousands too.
The arrival of the computer has had an effect on maths rather like the arrival of photography had on painting: the new technology appears to have removed the main previous reason for studying and practising the subject —embellishing its glorious abstract artform mystique.
Meanwhile, according to the computer industry’s mantra, computing has insisted that it (computing) “has nothing to do with mathematics”…
The result of this insidious propaganda has been to open-up a gulf in the mind of the public between maths and computing: one which is entirely artificial, because computer software relies at almost every point on logic and mathematics. Those at the heart of the computer industry are fully aware of this. The industry has, in practice, of course ruthlessly exploited all those parts of mathematics which usefully relate to so-called “computer applications”. (Why wouldn’t it? They are just what computer programmers are looking for.) The first result has been that the computer is now widely credited by the public as possessing an “intelligence” superior to human intelligence. The second result is that the good name of ‘mathematics’ has shrunk to a tiny fraction of its previous stature, while the magic of the machines has burgeoned.
On a practical level, not much. Computers and gadgets of many kinds operate as black boxes and give you the correct answer.
But this omnipresent black-boxing has had an unobvious, invisible, subliminal effect on social reality. Maths used to be regarded by intelligent people as <<the heartland of truth>>. All the best truths were there in mathematics. They were, for a start, all-but certain. (This is a higher level of human certainty than empirical certainty —because it is not dependent on a large mass of empirical observations which might have been compromised by a slightly sloppy workforce. By contrast, the checks needed to establish mathematic truth are timeless, and are freely accessible to experts of the highest ability who are practised in discerning logical mistakes and only too pleased to expose lurking errors.) Mathematic truths also have an intrinsic aesthetic appeal —for those who take them seriously— resulting from their links with unusualforms and striking symmetries.
But the malaise in school maths, combined with the subjucation of maths to computing, has all-but destroyed this feeling.
So what we have lost is a strong public sense of the priceless value of objectivity, transparency and lucidity in ordinary reasoning.
Maths was formerly the impartial, culturally-independent agent of arbitration in many disputes. A common saying used to be <<You can’targue with the maths!>>. It served to ameliorate bruised feelings and preserve a sense of social stability. Maths was the final, widely respected heartland of truth. Now it is no longer that, and the mystique-obsessedleadership, which has let this lapse happen, needs to consider its position.
CHRISTOPHER ORMELL April 2021