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 […]

Advanced and higher maths in Academia is far from being in a satisfactory state.  The Barons of Silicon Valley have been pouring scorn onto the thinking and culture surrounding higher “Modern Maths” since 1960. They regard it as an artificial ego trip. They have been claiming for more than 60 […]

The situation in advanced and higher maths in Academia is far from being satisfactory.  The Barons of Silicon Valley have been pouring scorn on the thinking and culture surrounding higher “Modern Mathematics” since 1960. They regard it as an artificial ego trip. They have been  claiming for more than 60 […]

We are approaching the fifth anniversary on-line of the author’s extraordinary “bare hands” proof that the sum of two natural numbers raised to the power n can never itself be an nth power of a natural number (when n>2). When it was sent to the Mathematical Gazette in 2019 no […]