FERMAT REVISITED An initial look at <<What the sum of two seventh powers of natural numbers can’t be>> Oh dear: this instalment was intended to be a routine exposition of the special case when p=7 of the reasoning contained in the second part of Blog 2 (2022) which introduced the […]

What the sum of two quintic powers of natural numbers can’t be.  INTRODUCTION In 2020 the author of this blog posted an elementary proof of a result Pierre de Fermat claimed to have found more than 350 years ago.  It had taken the current author twenty-nine years of “bare hands” […]

How a Peircean interpretation of mathematics leaves room for a second, dazzling 100% abstract logos Charles Peirce said, probably in the 1890s, that mathematics was “the” science of hypothesis.  We learnt about this insight many years later when it appeared in an essay in The World of Mathematics which was […]

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 […]