July

THOUGHT: The World has recently descended into a fragile state.  ‘The World’ here means the human world, the procedures, institutions, methods, customs, civilities etc. which allow seven billion of us to “get along together”, after a fashion, on this planet...


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01/02/2025

Maths for Renewing Reason – 57

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

Maths for Renewing Reason – 56

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

Maths for Renewing Reason – 55

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

Maths for Renewing Reason – 54

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

Maths for Renewing Reason – 53

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

Maths for Renewing Reason – 52

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

Maths for Renewing Reason – 51

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

Maths for Renewing Reason – 50

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

Maths for Renewing Reason – 49

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

Maths for Renewing Reason – 48

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 […]
02/07/2021

Maths for Renewing Reason – 14

The nine questions of the 13th part of this blog are, of course, unanswerable. The notion that something described as a ‘transfinite set’ can exist is quite clearly a chimera. Cantor’s Diagonal Argument and its generalised corollary indicate that these totalities necessarily have the potential to grow unpredictably, and therefore […]