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 […]

In instalment 3 we looked at a serious social and educational crisis undermining the meaning of ‘truth’, and its inevitably deeply damaging effect on mathematics —which seeks, as it were, to copperbottom truth by raising it to the status of rigorous proof.  In instalment 4 we looked at a glaring, […]

In this instalment we look at the most howling mistake ever made in maths. But it went unnoticed.  It was then, unaccountably, accepted into the official body of mathematical thinking. This is a howler which has generated untold consequences. It was a very simple mistake,  but subsequent scholars evidently took […]

It will not have escaped the notice of most readers that we are passing through a period of crisis and general unease. The amount of rigour being applied in public affairs seems to have fallen to an all-time low. Lying seems to have become an accepted mode in parts of […]

The purpose of this website is to put a body of new thinking and analysis into the public domain. It is an emphasis which can bring reasoning back into mathematics, and not just as a minor item, but as the central core of the discipline. There was, during the 20th […]