Charles Peirce originated the revolutionary interpretation of maths as the <<Science of Hypotheses>>  in the late 19thcentury, and it was kept under wraps until 1956. But, although it has captured a little attention in the last 70 years, it has yet to gain anything like the credibility it deserves. This […]

The opinion leaders in maths tried, around 1900, to rethink maths’ public footprint as a much admired discipline. They tried to turn it into an artform, which was so heavily admired by the educated public that it could be a credible “end in itself”. The opinion leaders felt at the […]

It is a scandal of the greatest magnitude that the maths establishment have flatly ignored the insights of Charles Peirce and Ludwig Wittgenstein… into the nature of meaning, and particularly into the meaning of maths.  It is also an insult to their colleagues in Academia, because the gurus of maths […]

We are living in an era in which respect for truth has, alas, been widely rubbished.  If we need anything to save us from chaos, dereliction and confusion, it is a renewal of respect for truth.  In the past it was regarded as self-evident that truth was the most important […]

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 […]

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 […]

Kurt Godel was famous for his ingenious 1930 proof that mathematics is incompleteable.  However, he himself felt rather disappointed that his landmark result was highly praised by his colleagues… but then, in effect, forgotten. (Towards the end of his life he became chronically pessimistic, and in the end he effectively […]

Probably the development which has had the most damaging effect on the morale of school maths, is the early decision of the computerists that <<Maths has nothing to do with computers!>>. It was a much-circulated mantra which was aired when new PCs were being sold.  We know why the computer […]

Can the flame of mathematics, the historic logos which was recognised as the Queen of the Sciences —and as the most authoritative category of human knowledge— for more than two millennia, survive in today’s fevered, over-hyped promotion of AI, based on neural networks? Mathematics has been, in effect, by-passed by […]

That the advanced democratic world is stuck in a quagmire of muddled, unresolved thinking… hardly needs to be said.    We are in a parlous state, which is potentially dangerous, and which could —all too easily— lead to a second “Dark Age”.We might even be heading for extinction. So what are […]