On Defining Knots The blogs in this series are being offered to stimulate reason… not by preaching or propaganda, but by example, by following reasoning in action  —as it “works its magic”, as it “makes a difference” or as it “shines a light”…  onto otherwise unexpected, unpromising mathematic dark corners. […]

The higher maths establishment seem to insist, in effect, that no elementary version of Fermat’s lost theorem will, or could, ever be found. I think this is the best interpretation one can attach to their taboo against any notion that the problem needs to be re-opened. History appears to support […]

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 […]