There appears to be a peculiar mood today in professional higher maths which is subliminally —and quite effectively— re-aligning to the ‘modelling’ or ‘Peircean’ interpretation of maths, whilst still paying lip service to the extravagancies of late Platonist (“Inward  Modern”) maths.

Common opinion in society has changed profoundly, and is now far away from the absurdity involved in the Platonist notion that <<Only the timeless is real>>. The specific absurdities of this notion include the illusion that all sets are mathematical objects, that transfinite sets exist, that ZF theory offers a valid description of sets, and that fractional dimensions make sense. The most deadly aberration  is that “time is a dimension”, because a ‘dimension’ means an absolutely autonomous category of freedom, and we have no freedom at all to change our position in time. We are stuck, inexorably, in “The Now”.  We know that “The Now” keeps moving on, and that we are powerless to affect this flow.  

The notion that its timelessness was the principal characteristic of maths, was probably a spin favoured by the overall dominance of religion in the golden age of Greece.  There was a religious narrative already firmly established in Antiquity that the mysterious heart of maths was the “sense of infinity”. Plato took it further, in a way which appealed greatly to the mathematic gurus: towards the quest for personal satisfactions to be enjoyed as a result of  discoveries made in difficult “pure” maths.  This was essentially an introspective quest.  

The main social hold of maths on the minds of the ancient world, though, was exemplified by the existence of the Pyramids of Giza. The pyramids could never have been built without the co-existence of 100% dominant simple maths. It was the maths which generated the over-powering confidence needed to build these immense tetrahedral stone edificies. Once built, they conferred a huge credibility onto the afterlife, or at least onto the notion that consciousness somehow continues to “eternity”.

Later the Romans used simple maths to build aqueducts, an amazing road system, temples and ceremonial arches, not to mention the logistics they developed to add stamina to the legions.

So maths has always had two sides, (a) its capacity to pathfind major projects and (b) the personal virtuosity to be had from finding solutions to very difficult formal problems.

For most of 2,500 years the virtuosity interpretation (b) dominated, and the potential usefulness was understated. Now the pendulum is swinging back.   

NOTE You can send your comments on the reasoning promoted on this website by sending your thoughts to: per4group@gmail.com
CHRISTOPHER ORMELL around January 1^st 2026. chrisormell@aol.com