In instalment 3 we looked at a serious social and educational crisis undermining the meaning of ‘truth’, and its inevitably deeply damaging effect on mathematics —which seeks, as it were, to copperbottom truth by raising it to the status of rigorous proof.  In instalment 4 we looked at a glaring, unnoticed mistake made in the mid 19^th century when the subject’s Leaders and Guardians failed to distinguish pure set theory from applied set theory.

In this instalment we look at a related, even more serious, mistake made by the subject’s Leaders and Guardians when they tried to revolutionise maths in schools by turning it into a fast, direct introduction to a very formalistic version of so-called  ‘modern’ mathematics.

This happened in the early 1960s. It started with a culture shock.  The shock was Sputnik 1 which was successfully launched in 1957 by the USSR. It was essentially the brainchild of the rocket genius Sergei Korolev (1906-1966). It produced consternation in America, because the USA had always considered itself to be years ahead of the Russians in technology. Politicians and commentators started questioning the US school system.

So mathematics Departments in US universities were asked: <<What has gone wrong with American maths education, which has allowed the USSR, a cash-strapped totalitarian state, to overtake us in space?>>. 

The reply came back with surprising unanimity on the lines: <<Everything! The maths curriculum in in US High Schools still reflects the old-fashioned numerical maths we abandoned years ago! Modern maths is all about abstract sets, mappings, transformations, etc., not this pathetic obsession with numbers and space! Our High Schools are twenty years behind the times!>>.

So the US Government acted decisively. It backed a revolutionary agenda which meant that set-based maths (‘New Math’) would be rolled out, first in America, and later —by imitation— in most countries around the world. It was an Agenda which had the almost unanimous backing of the world’s top mathematicians, the US government, thousands of revolutionary Young Turks in schools, and the required millions of US dollars.

It was hyped as “the language of the future”, which was dubbed at the time as “the white hot technological future” by prime minister Harold Wilson. 

By turning the most conservative school subject (mathematics) upside down, it unleashed radical progressivism, the doctrine that children know better than adults what they need to learn in school in order to cope later with their adult lives. 

The alleged historic, necessary, nature of this revolution was endlessly plugged in messages to teachers and parents: <<This change in school maths is irreversible, because mathematics as a subject has moved on, and it is now a quite different subject from what it used to be!>>.

[This was a cruel con, because it flattered children and led them to think that “they knew it all” in a very competitive, unforgiving society.  It was also a negation of the essence of education, which means a leading of the mind of the child away from the naiveties of childhood, towards adult reality and the established moral and social order.] 

That this Revolution overtly and preposterously involved removing any hint of Newtonian Dynamics from the School Math Curriculum —the very maths needed to operate rockets in space— was brazenly downplayed. 

[How did education officials in Washington fail to notice this howling contradiction?] 

What happened, though, was less glorious than had been anticipated. It soon became clear that New Math was totally unsuitable to be taught in schools. René Thom, the world’s leading mathematician, commented that it was like trying to get children to run before they could walk. Warwick Sawyer said that teaching New Math was like expecting learners to understand the third act of a play when they had not seen the first two acts.

Looking back at this calamitous episode with the advantage of sixty years’ hindsight, it is quite evident that the advice leading US mathematical experts gave to the US government was jejune. The US experts made no attempt to decentre. To them, “modern mathematics” was simply what they did.  Their focus was entirely on deep abstractions involving formal concepts which were miles away from the common uses of mathematics, or indeed anything else in the real world. They were too self-absorbed. They could not see that the public word ‘mathematics’ referred to a vast, diversified enterprise most of which was much more essential to life than their specialist studies. Morris Kline  remarked later that it was when parents took their children to the stores and found to their astonishment that their children hadn’t the faintest idea how to “figure”, that the realisation began to dawn that the whole thing had been a mistake. 

The maths leaders in top US universities were in a bubble. They were living in splendid isolation from the rest of academia, not to mention the rest of the ordinary population. This had come about because of a combination of a consciously suppressed crisis in the subject (an abject failure to understand Russell’s Paradox), and the extraordinary anomaly of a lack of common culture in America, a condition later ruefully exposed by Neil Postman in his book The End of Education (1995). 

Today it is obvious that no one in the White House in 1957-60 had the slightest inkling that the world-famous higher mathematicians in their elite universities were living in this strange, academic, self-congratulatory enclave. Nor did they have the faintest idea that it was a bubble which had quietly downgraded reasoning, and embraced aesthetic formal appearance to the nth degree.  The Administration would never have committed millions of dollars of US taxpayers’ money to backing New Math, and turning the school system upside down —with all the damage and disruption this would cause— if they had realised that the architects of this chaotic revolution were, by ordinary, home-town standards, introducing a self-serving agenda, rather than one aimed at the common good. 

[Or if you prefer, that the experts who advocated New Math as the answer to Sputnik, were semantically blind to the different meanings of the word ‘mathematics’ in specialist academia and the public arena.]

There was too little intelligent conversation across subject boundaries. No one on Capitol Hill, it appears, had an informed over-view of the logical crisis which had happened earlier in the century in mathematics, or had registered the pathological formalistic ivory-tower state into which the pure academic subject had fallen.

At the end of the day the inevitable U-turn away from New Math for Schools was handled quietly and discretely. The higher mathematic leadership managed to disengage from a very embarrassing situation with remarkably little fuss and almost no public recrimination. They were no doubt, at the time, pleased with their completion of this “successful” correction. 

There was little public outrage.

So did the population register in any way that something had gone badly wrong?

Yes, they seem to have. But the blame was unfocused. It took the form of an unspecific, general loss of trust —in higher intellectuals of all kinds. It was put about that brainpower was no longer needed. Everything was easy! Computers would take the strain! One TV Ad showed a suited bank manager surfing the waves with his ledger, near a sunlit beach where pop music was ringing out and young people were having a hilarious time!  This was the historic start of the Post Modern Era, the society-as-headless-beast phase which has lasted for four decades.  It is hardly likely to survive for much longer, though.  An intense scrutiny is bearing down onto it, now that Post Truth Attitudes are being brazenly aired in the corridors of power, and the Pandemic is decimating the confidence, mental-health and employment prospects of millions of Americans.  

[That “Post Modern” attitudes won’t do, and that we must be much better prepared for Pandemics, are now becoming widely recognised, inescapable truths.] It is evident that society can no longer continue to operate under the umbrella tenet ANYTHING GOES!

CHRISTOPHER ORMELL OCTOBER 2020
Email: per4group@gmail.com