An Algebra of Knots The previous blog in this series (No. 28) introduced a construction protocol for knots which serves, in effect, as a way of classifying them mathematically.  At first sight the construction diagrams arising from this protocol look much neater than typical knots.  But the new protocol covers […]

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 […]