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 […]