Are some exotic mathematical claims counterproductive?

Mathematics is being increasingly impugned in public for its misuse of on-line algorithms, which are reducing sensitive human issues to banal computations. But this is only part of a broader trend which is quietly phasing-out the word ‘mathematics’ from common use…. a trend which began when the computer industry started treating mathematical models implemented on its computers as ‘computer models’. Thomas Kuhn’s attack on the rationality of science in the 1960s studiously avoided taking into account any role mathematics had in science. Since then the word ‘mathematics’ has almost disappeared from the discourse of opinion leaders, philosophers and critics. It has become, in effect, a no-go word. No one, it seems, wants to think about it. The average person tends to assume anyway that it has been thoroughly outmoded ---reduced to an anachronism--- by the computer. Meanwhile the mathematicians themselves have probably put themselves on the wrong side of history, by their refusal to be overawed by this now much-worshipped machine.

After Donald Trump entered the White House in 2017 there was an impassioned debate in the media about the dangers of the ‘post truth’ attitude associated with the new US President. When questioned on BBC Newsnight by Kirsty Wark, the philosopher Simon Blackburn could only suggest the Times and the BBC as reliable sources of truth. Whatever had happened to mathematics, which was for countless centuries, regarded by all serious opinion as the Heartland of Truth? In mathematics there are millions of unobvious truths which can be checked twice, a dozen times or a hundred times … thereby reducing the risk of error to zero.

During the early 20th century, though, a consensus of higher mathematicians decided that their subject should no longer regard itself as the ‘Queen of the Sciences’… but should settle instead for the more modest role of ‘Intellectual Artform’. Was there an implicit demotion of truth, and a valorisation of aesthetics, buried in this historic change?

We know the higher mathematicians had endorsed Cantor’s theory of super-infinity and supposed that they had produced the mathematical marvel to supersede all marvels ---the transfinite. That the cardinal number Aleph 2 is unimaginably larger than infinity is, perhaps, a striking, mysterious notion. But Aleph 2 is unimaginably smaller than Aleph 3, which can only diminish our sense of the marvel of Aleph 2. Each larger cardinal number throws the lower Alephs into shadow. Aleph M where M = 1,000,000 can only have a dreadfully ---unimaginably--- demolishing effect on our awe of ordinary Alephs. It seems that this reliance of mathematics on awesome aesthetic effects can be a double-edged sword.

The P E R Group has been brainstorming the personal and social concepts underlying education ---including maths education--- since 1993. You can read more on: philosophyforrenewingreason.com philosophyforeducation.moonfruit.com