MFRR POSTS
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 […]
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 […]
03/06/2024
Fermat, the last frontier The 20-page bare hands proof of Fermat’s conjecture which I posted on-line in 2020 in the first two of these blogs has now survived intact for almost four years —with no sign whatever of a demolishing counter-argument. I have since that time posted essays in the […]
01/05/2024
Further Reflections on the exciting new proof of the Four Colour Conjecture using induction The new proof (See Blog 46) begins by posing the provisional hypothesis that all fully triangulated, fully weeded, networks of up to n nodes can be four coloured AND ALSO that this colouring can contain 3-coloured […]
02/04/2024
Some Reflections on the new proof of the Four Colour Conjecture using induction The new proof (See Blog 46) begins by posing the provisional hypothesis that all fully triangulated, fully weeded, networks of up to n nodes can be four coloured AND ALSO that this colouring can contain 3-coloured circuits […]
04/03/2024
Some Reflections on the Four Colour Conjecture A NEW INDUCTION ARGUMENT WITH 4-COLOURATION PLUS The motif of this Blog is to pick up the pieces after the mistake in Blog 44, for which, further, profuse apologies. The heart of the problem is that this conjecture seems to cry out […]
02/06/2025
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 […]
01/05/2025
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 […]
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 […]