Mathematics today is still, broadly speaking, dominated by a relatively small group of higher purist mathematicians. Although the Met Office says it employs 2,000 mathematicians, they are not being paid to do ‘mathematics for mathematics’ sake’, but rather to try to improve immensely complex existing algorithms aimed at more accurately modelling the weather.  The era of big names in maths like Paul Erdos, Michael Atiyah and John Conway seems to have passed, and the subject’s sense of its own identity is faltering. The future looks rather bleak, because mathematics is no longer getting wave after wave of ambitious young researchers eager to carry-on the historic quest.  Some of the blame for this is the pathetic managerial stimulus-response (‘Cognitive Science’) way of running schools, which has now been operating for forty years.  It treats school maths as a bundle of ‘skills’, but clearly has no concept whatever of what these skills really are, or how to grow them. 

Today there is, if anything, a swing towards the perception that most of the mathematics of the future will be in modelling things like the weather and diseases. By contrast, in downtrodden areas school mathematics is now being impugned in public as a ‘cycle of despair’—something which would have been impossible a few years ago.

There are two main messages in this blog (1) a look back to what we have lost and (2) an outline of some radical changes which will be needed if mathematics is to be put back on a sound basis.

David Wells commented in 2015 on the Adrian Smith Report about School Maths:

<<…the message is, emphasise skills, and then skills again, but do not mention understanding, mention skills, but leave insight and understanding out of it, mention skills repeatedly, and if you must mention understanding, a single mention will do and then rush back to skills, skills, skills, skills, and more skills.>>  

This is a brilliant way to expose the absurdity of the managerialspeak which has dominated schooling now for four decades.  The gang of ‘cognitive scientists’ who manage the school system constantly witter on about the need for skills, but they show by their words and actions that they don’t begin to understand what they are wittering about. 

It is an extraordinary fact that the word ‘mathematics’ is gradually disappearing from the vocabulary of pundits, opinion leaders, critics and philosophers. It used to be regarded as the pinnacle of human knowledge, but now it is fading out. 

So what have we lost? Well, after Donald Trump entered the White House in 2017 there was an impassioned debate in the media about how to counter the danger of Trump’s post-truth attitude. On Newsnight Kirsty Wark interviewed the philosopher Simon Blackburn, who has written two books on the nature of truth. When Kirsty asked him where we can turn to rebut post-truth attitudes, he (Blackburn) could only think of two primary sources of truth —the BBC and The Times!  He made no mention of mathematics!

He seemed to have forgotten that there are millions of unobvious truths (theorems) in mathematics which can be checked, 2, 20 or 200 times to make absolutely sure that there is no mistake. Mathematics used to be regarded by virtually all educated people as the Heartland of Truth. Now few see it in this, or any other, light.

Why?  What has gone so badly wrong?

This issue was highlighted by Morris Kline in his last book Mathematics, the Uncertain Science (1980).  The truth is that the switch which happened in higher maths around 1900  —re-launching it as an ‘Intellectual Artform’— was a great mistake.  Such a change would inevitably take the nerve out of the subjects’ truth and rigour, something mathematics could ill-afford.

David Hilbert famously said in 1900 that nothing would induce him to give up <<the paradise which Cantor has opened to us>>. It was saying in so many words that <<you can believe what you want to believe in mathematics!>>.

Tell that to the 2,000 Met Office mathematicians struggling to get their predictions of the weather right!

CHRISTOPHER ORMELL November 1^st 2021.