MFRR POSTS
01/02/2024
Some Reflections on the Four Colour Conjecture. A MISTAKE HAS BEEN FOUND IN THE ARGUMENT OF BLOG 44. This will be reviewed in Blog 46. The problem is that the removal of Q and R from the network is possible given the 4-colouring established by the initial P, Ax, Cx arguments, […]
02/01/2024
Some Reflections on the Four Colour Conjecture PART 3. A new proof of the Four Colour Conjecture. The four colour conjecture began as an observation about colouring maps with a palette of only four colours so that every boundary was represented by a change of colour. It soon turned into a […]
01/12/2023
There is a common tendency for computerists to over-estimate the applicability of mathematical modelling to mysterious entities like the universe and the human brain* We know that tally-bundling must have been the natural precursor to arithmetic, and that it (tally bundling) may have been in use for many millennia before […]
02/11/2023
Some Reflections on the Four Colour Conjecture Part 2 The four colour conjecture is a fascinating mathematical problem —because it is extremely easy to understand what it says. So it has a huge watcher-base. Also it is infuriatingly difficult to prove, which is puzzling (if it is a fact, which […]
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 […]
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 […]
03/12/2024
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 symbolic configurations will —of course— be mainly handed-over to computers. We can no longer expect to distinguish […]
01/11/2024
These blogs are offered to show the way in which conceptual, reasoning-led maths can generate striking, even sometimes major, results. In an age of awesomely microscopic, awesomely fast, massive digital electronics, authentic, traditional maths cannot compete with the latest hardware —if the contest is simply about the dexterity of manipulative […]