MFRR POSTS
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 […]
01/12/2022
We know that the formerly superordinate power of rationality crashed, sadly, in June 1901 when Bertrand Russell discovered his deadly contradiction. It was not an ordinary, freestanding, optional contradiction like that which appears when someone remarks idly that <<the weather is fine, even though it is dark and teeming with […]
01/11/2022
Some readers will have registered that we are passing through a period of great strain, difficulty and hardship arising from factors like the Pandemic, the Crisis in Education, Turbulence in the Financial System, Scarce Energy, Climate Change and the War in Ukraine. The gloomiest congenital pessimists may read all this […]
01/10/2022
An Algebra of Knots The previous blog in this series (No. 28) introduced a construction protocol for knots which serves, in effect, as a way of classifying them mathematically. At first sight the construction diagrams arising from this protocol look much neater than typical knots. But the new protocol covers […]
01/09/2022
On Defining Knots The blogs in this series are being offered to stimulate reason… not by preaching or propaganda, but by example, by following reasoning in action —as it “works its magic”, as it “makes a difference” or as it “shines a light”… onto otherwise unexpected, unpromising mathematic dark corners. […]
31/07/2022
The higher maths establishment seem to insist, in effect, that no elementary version of Fermat’s lost theorem will, or could, ever be found. I think this is the best interpretation one can attach to their taboo against any notion that the problem needs to be re-opened. History appears to support […]
30/06/2022
Andrew Wiles solved the master problem whether Fermat’s conjecture was valid more than 25 years ago. He used highly-abstract modern concepts which were miles away from anything Fermat could have known. It was a triumph in a category (i.e. resolving notorious uncertainties) which has been conspicuously neglected for a long […]
01/10/2024
These blogs are intended to show the way in which reasoning-led maths can generate striking, even sometimes major, results. In an age of awesomely microscopic, awesomely fast, digital electronics, authentic, traditional maths cannot compete with the latest hardware —if the contest is simply about the efficiency of complex manipulative process. […]
12/09/2024
These blogs are intended and designed to show the way in which reasoning-led maths can generate striking, even sometimes major, results. In an age of awesomely microscopic, awesomely fast, digital electronics, authentic, traditional maths cannot compete with the latest hardware —if the contest is simply about the efficiency of manipulative […]
06/08/2024
The conjecture for which Christian Goldbach (1690-1764) is famous is that <<every even number can be represented as the sum of two prime numbers>>. Even after sixty years of exploration using incredibly powerful computers, no one has ever found an exception to this rule. So it has plenty of prima […]
03/07/2024
Before starting this blog there are two preliminary Notes. NOTE 1 The author’s bare hands (elementary) proof of Fermat has now been on-line for four years —and during these 48 months no hint of a counter-argument has emerged. No challenge has been posted. It is a scandal that no-one in […]