Two valuable, but neglected, sides of mathematics Mathematics, insofar as it is an asset to the human race, has two distinct sides.  It serves both as the Heartland of Truth (“pure” mathematics) and as the main Pathfinder for Progress (“applicable” mathematics). It would be more accurate, though, to say that […]

The question about mathematics which has baffled most commentators for a long time is the question of the meaning of mathematical statements.  Wittgenstein introduced the idea that the meaning of a statement was to be seen in its use and usage, but pure mathematics appears to have no obvious use […]

The overall theme of these articles on the Renewal of Mathematics is that the subject has been grossly over-mystified and its most important manifestation —mathematical modelling— has been grossly under-valued. Pythagoras —the first significant polymathematician*— founded  a Brotherhood of colleagues which has, in a sense, survived for more than 2,500 […]

Mathematics today is still, broadly speaking, dominated by a relatively small group of higher purist mathematicians. Although the Met Office says it employs 2,000 mathematicians, they are not being paid to do ‘mathematics for mathematics’ sake’, but rather to try to improve immensely complex existing algorithms aimed at more accurately […]

The fanciful notion that mathematics is, broadly speaking, an inquiry into a world of ‘Real Abstract Objects’ quite independent of humanity —and just as real as physical things— has often been cited by mathematicians of the highest calibre as the main justification for their lifelong commitment to it.  These Abstract […]

Mathematics is, broadly speaking, a highly disciplined, rational, rigorous, carefully-led human activity.  In spite of this general reputation, however, there were four moments in history when the leadership of the subject lapsed into uncharacteristic, palpable, mind-boggling, inexcusable irrationality. This blog asks the question <<How could such huge lapses of judgment […]

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.  […]