Most intelligent people consider that a set with an infinity of elements (e.g. the natural numbers) is the largest a set can be. But Cantor persuaded the maths establishment that infinity was tiny in comparison with Aleph 1.  Not only that.  Aleph 1 itself was uniimaginally tiny in comparison with […]

To continue to comment on the apparent complacency of the maths hierarchy’s failure to reconstruct the elementary proof which Fermat claimed he had achieved four centuries ago…  is like a red rag to a bull.  But it is essential. It can only be acutely embarrassing to accept that no one […]

It is now time to ponder on the significance of my still unchallenged putative elementary proof of Fermat’s last theorem. It has now been under nominal scrutiny online for six years… and so far no flaw has been found. It was brazenly turned down by two pairs of referees at […]

Charles Peirce originated the revolutionary interpretation of maths as the <<Science of Hypotheses>>  in the late 19thcentury, and it was kept under wraps until 1956. But, although it has captured a little attention in the last 70 years, it has yet to gain anything like the credibility it deserves. This […]

The opinion leaders in maths tried, around 1900, to rethink maths’ public footprint as a much admired discipline. They tried to turn it into an artform, which was so heavily admired by the educated public that it could be a credible “end in itself”. The opinion leaders felt at the […]

It is a scandal of the greatest magnitude that the maths establishment have flatly ignored the insights of Charles Peirce and Ludwig Wittgenstein… into the nature of meaning, and particularly into the meaning of maths.  It is also an insult to their colleagues in Academia, because the gurus of maths […]

We are living in an era in which respect for truth has, alas, been widely rubbished.  If we need anything to save us from chaos, dereliction and confusion, it is a renewal of respect for truth.  In the past it was regarded as self-evident that truth was the most important […]

There appears to be a peculiar mood today in professional higher maths which is subliminally —and quite effectively— re-aligning to the ‘modelling’ or ‘Peircean’ interpretation of maths, whilst still paying lip service to the extravagancies of late Platonist (“Inward  Modern”) maths. Common opinion in society has changed profoundly, and is […]

We saw in the last blog that Kurt Godel’s ingenious 1930 proof that mathematics is incompleteable is actually really obvious. Today almost everyone is aware that arrangements can be changed, and hence that maths is full of potential starting points… which could be opened-up and developed, if someone took a […]

Kurt Godel was famous for his ingenious 1930 proof that mathematics is incompleteable.  However, he himself felt rather disappointed that his landmark result was highly praised by his colleagues… but then, in effect, forgotten. (Towards the end of his life he became chronically pessimistic, and in the end he effectively […]