We are still in a Covid-19 pandemic, which is a health crisis of very serious proportions. We are also still stuck in Ulam’s Dilemma, a mathematic credibility crisis of very serious proportions.  There is not much we can do to ameliorate the Covid Crisis, but there is a great deal […]

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 […]

The time has come to blow away some cobwebs from the increasingly dusty body of supposedly established mathematical truth. There are a few fully accepted false results, which are there, embarrassingly, because in recent times mathematics has too often been handled in a slightly uncritical way. Consolidation has been neglected […]

This is the twelth essay offered in the cause of this series: increasing the use of reasoning in maths, and also increasing the perceived relevance of thinking in maths to social progress. The original idea was to assist in raising our faith in reasoning to the level of 20-20 vision.  […]

This instalment is a Case Study concerning an unresolved elementary geometric problem which has recently come to light. It is another example of neglect of reasoning in maths. The problem was printed on the cover of the July 2020 issue of the Mathematical Gazette. It showed a triangle /\ ABC […]

In this instalment we continue the line of thinking of No. 9 in relation to the current phase of epidemiological mathematical modelling.  One small positive by-product of the current tragic pandemic has been that it has shown mathematical modelling in a surprisingly  favourable light. Before the pandemic there was a […]

In this instalment we look at the fundamental question <<Where did mathematics start to diverge from its proper destiny?>>. Part of the answer is the Artform Turn which occurred around 1900, because it has led to a tendency to valorise strange, counter-intuitive concepts in mathematical research. In this way it […]

This is the last instalment this year of the blog which looks at the role mathematics could play in helping to renew reason —something we urgently need if education and civilisation itself are not to become extinct. The soundbite this year has been that we need to achieve 20-20 vision […]

The theme of last month’s blog was a review of disappointments: a list of six mistakes made by the leadership of mathematics, plus reflections on their consequences, and a suggestion for remedying the demoralising effect of Ulam’s Dilemma.  These historic ill-judged decisions of the leadership resulted in maths losing big […]

Let’s take stock of some unfortunate glitches which have occurred in the record of Maths and which have been chewed over with some reluctance in this series.  Having surveyed the seriousness of the glitches, the next stage is to consider what can be done to put the record straight.  Maths […]