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 […]

There is a largely unaddressed existential problem which currently faces the mathematical community, arising from the question: How does computer programming differ from mathematics? This question first became a potential “Issue” around 1960, when the development of transistors resulted in computers becoming unbelievably reliable. Computers had arrived thanks to the […]

These blogs are offered to show the way in which conceptual, reasoning-led maths can generate interesting, sometimes important, results. In an age of awesomely microscopic, awesomely fast digital electronics, the manipulation of chosen symbolic configurations will —of course— be mainly performed by computers. We can no longer expect to distinguish […]

These blogs are offered to show the way in which conceptual, reasoning-led maths can generate interesting, sometimes pivotal, results. In an age of awesomely microscopic, awesomely fast, massive, digital electronics, the manipulation of chosen symbolic configurations will —of course— be mainly handed-over to computers. We can no longer expect to […]