We saw in the last blog that Kurt Godel’s ingenious 1930 proof that mathematics is incompleteable is actually really obvious. Today almost everyone is aware that arrangements can be changed, and hence that maths is full of potential starting points… which could be opened-up and developed, if someone took a fancy to do so. (The Japanese did this with their Temple Maths in the 19^th century.)

So the Immense Body of Maths, as we know it, is the product of a subset of the human race who prefer elegance to mess, and strict rule-following to chaos. They have very high standards, but they have failed to notice that it is their own very high standards which have created their illusion that maths is a sort of “Objective Reality”. If it were an “Objective Reality” it would be much more specifically completeable than we now realise it is. (We can’t expect “Abstract Reality” to be an open-ended creative playground.)

The High Priests of maths thought that they could establish the “truth”that maths was an Objective Reality by simply pulling rank and backing it with their unique authority.  So figures as talented as Roger Penrose went round asserting that maths was an “Abstract Reality”.

I’m afraid that they have forgotten that (a) they blew their own credibility when New Maths for Schools crashed in the 1960s (this revealing gross misjudgments about what children could appreciate and assimilate of a quite ludicrous kind), and (b) that Plato’s lemma that “Only the timeless is real” has been reduced to nonsense by modern sensibility. Almost no lay person nowadays thinks that this makes sense.

So the severe loss of authority suffered by the maths establishment means that their self-serving amateur philosophising has lost its lustre. Today’s typical worldview is much more down-to-earth than any special genre of “Abstract Reality” would require.

So there is a very permissive mindset behind “modern maths”. It has had the unexpected effect that it has led to a vast over-production of abstruse, way-out research inquiries which have effectively prevented the High Priests from understanding their own subject, i.e. what it “all means” in rounded terms. (Also why, in the past, lots of lay people used to believe-in maths, and hold it in high esteem.)

This is the crunch issue: where does the authority of today’s maths leadership come from? The educated public certainly don’t use maths to show-off —i.e. signal elegance-for-the-sake-of-elegance and rule-following for the sake of rule-following— but, much more importantly, they use it (or support it) seriously to pathfind the stages needed to bring big, promising, real-life projects to fruition.  Its’ role is primarily to build the confidence needed to convince the workforce that such projects can be achieved.

This kind of confidence is quite essential in today’s spaced-out, downbeat economic milieu.

Real-world opportunities (developments) need to be achieved, because the market requires the adrenaline of innovation —if it is to thrive.  The opinion of the High Priests seems to be that “using” maths is a kind of “dubious exploitation” motivated entirely by “greed”… or an attempt to please the hoi palloi. Again the High Priests’ world-picture has been found wanting. There is no automatic link between “applying maths” and “greed”. There are (contrary to their assumptions) many large real-world projects out there which prioritise urgently needed commongood aims, and even those commercial deals which make (justified) rewards for their initiators, are inevitably adding new accessible, public amenities and options to the lifestyle of millions.

NOTE: You can send your comments on the reasoning promoted on this website by sending your thoughts to: per4group@gmail.com
CHRISTOPHER ORMELL around December 1^st 2025. chrisormell@aol.com