Today the case for embarking on a radical reform programme for mainstream school mathematics teaching is overwhelming.  The existing status quo is palpably in trouble, and in a significant subset of secondary schools the subject has sunk to the point where it is regarded, both by teachers and students, as […]

We know that the formerly superordinate power of rationality crashed, sadly, in June 1901 when Bertrand Russell discovered his deadly contradiction.  It was not an ordinary,  freestanding, optional contradiction like that which appears when someone remarks idly that <<the weather is fine, even though it is dark and teeming with […]

Some readers will have registered that we are passing through a period of great strain, difficulty and hardship arising from factors like the Pandemic, the Crisis in Education, Turbulence in the Financial System, Scarce Energy, Climate Change and the War in Ukraine. The gloomiest congenital pessimists may read all this […]

An Algebra of Knots The previous blog in this series (No. 28) introduced a construction protocol for knots which serves, in effect, as a way of classifying them mathematically.  At first sight the construction diagrams arising from this protocol look much neater than typical knots.  But the new protocol covers […]