mfrrchris1984
02/10/2023
Some Reflections on the Four Colour Conjecture Part 1 The four colour conjecture has been allegedly resolved by Appel and Haken and others using “computer proofs” which, however, leave a sense of slight doubt in the mind of cautious critics. After the original computer proof was published in 1976 its […]
01/09/2023
The way to a massive, much needed, renewal of morale in teaching maths can be via a new approach —‘Narrative Maths’ based on the methods of Mathematics Applicable, an idea-before-its-time (a ten-year project) which the present author led from 1969 to 1978 at Reading University. Narrative Maths is a radical […]
01/08/2023
Maths, we know, is today in a sorry condition, and on all levels, from uninspiring school teaching, to mathematical logic which still can’t solve Russell’s Paradox or the Continuum Hypothesis. Maths used to be the central motif which was responsible for Western Culture and the Modern World. Now Western Culture […]
06/07/2023
That there is a crisis in school mathematics is hardly news. It has been around for so long that it has long since become part of the given status quo. The last significant attempt at introducing a “new brush” into the teaching of maths in schools was the so-called ‘Practical […]
01/06/2023
It is now exactly three years since the conclusion of my project to explain the validity of Fermat’s Conjecture by elementary methods was put online and also published by Ingleside Ashby in a small cottage edition. Fermat had claimed in a marginal note in a book found after his death […]
28/04/2023
The importance of getting a radical Narrative Mathematics Course established in schools is underlined by the recent financial verdict that interest rates are likely to go down again… back towards zero. This, it is thought, will happen sooner rather than later. These rates reflect the intrinsic demand for business investment […]
03/04/2023
It is impossible to over-state the seriousness of the fiasco surrounding ‘New Maths for Schools’ which imploded disastrously in the 1970s. It was, from the beginning, a fantasy based on an ideological single-mindedness, a specialised (‘modern mathematics’) mindset which turned its back on a panorama of ordinary human pursuits and […]
01/03/2023
There has been a chronic crisis situation in school mathematics since the 1980s when an alternative (i.e. a remedy) to ‘New Maths for Schools’ was urgently needed. The broad outlines of a replacement were suggested by the much hyped Cockcroft Report Mathematics Counts (HMSO 1982). It threw attention onto the […]
01/02/2023
Thought experiments putting us in the shoes of our prehistoric ancestors are the best way to get a secure, grounded view of how maths began. If we do this the “essential nature” of maths becomes plain. It is a kind of kit of written symbols which can be used to […]
02/01/2023
Today the case for embarking on a radical reform programme for mainstream school mathematics teaching is overwhelming. The existing status quo is palpably in trouble, and in a significant subset of secondary schools the subject has sunk to the point where it is regarded, both by teachers and students, as […]
01/04/2025
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 […]
02/03/2025
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 […]
01/02/2025
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 […]
03/01/2025
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 […]