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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 […]

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 […]

01/10/2021

The fanciful notion that mathematics is, broadly speaking, an inquiry into a world of ‘Real Abstract Objects’ quite independent of humanity —and just as real as physical things— has often been cited by mathematicians of the highest calibre as the main justification for their lifelong commitment to it. These Abstract […]