Andrew Wiles solved the master problem whether Fermat’s conjecture was valid more than 25 years ago. He used highly-abstract modern concepts which were miles away from anything Fermat could have known. It was a triumph in a category (i.e. resolving notorious uncertainties) which has been conspicuously neglected for a long […]

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 […]