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 […]