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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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 […]

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.  […]

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 […]

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 […]