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 starved himself to death.) The 1930 proof was evidently laden with implications —for how we think about higher maths. But few seemed to want to know. Almost nobody took the trouble to think its implications through.   For example, higher maths can hardly be portrayed as an area of “timeless truth”, if new truths are liable to manifest themselves at any moment. (These “new truths” might throw a distinctly new slant onto the old truths.)  

For example: the totality of real numbers cannot be a set, because it is a totality which is incompleteable.  (Cantor’s Diagonal Argument proves this.) A “set”, however, is “all the Xs”: and we are never going to be in a situation where we have properly conceptualised “all the real numbers”. 

This points to the unwanted, unpopular, in-house conclusion that higher maths is essentially a creative activity —created by extremely talented, unworldly, higher mathematicians. 

Hardly any professional mathematicians are happy with this interpretation of their subject. It seems to imply that the higher subject is merely a playground for very clever creative minds to extend and enjoy.  The former orthodox suggestion that higher maths <<held the keys to understanding physical reality>> had originated from the dramatic success of pioneers who had discovered things like time lapses of the Sun, Moon, and planets, elliptical orbits and thousands of patterns in physical observations which could be studied mathematically. But today the body of known maths is much larger than the bits which apply in an outline way to physical reality. And mathematics is too timeless to be able to be the principal logos of a “theory of everything”.  (This “theory of everything” would have to field ultimate nouns representing the “stuff” involved. So the “stuff” would have to be timeless. The universe we see in our telescopes is much too ferociously changing and violent to fit this frame.)  This —left unexplained— is a severe subliminal body-blow to the morale of the maths profession.

Descartes, we know, got maths models to represent change, but there was a cost. It involved human envisaging what the model portrays at different values of t, the time variable.  This presupposes that human consciousness exists, a mystery to the nth degree.

We are now getting close to the hundred years anniversary of Godel’s neglected proof.  We need to take a deep breath, and, in effect, face the music: because the stature of higher maths in the eyes of the public has taken a nose-dive.  The main body of public opinion seems to have finally accepted that pure higher maths is indeed an abstruse in-house creative activity, with little, if any, implications affecting one’s view of reality. 

It is the subsequent loss of authority (of the higher mathematicians) which has taken the bite out of various feeble, amateur explanations of Platonic maths. Before the crisis the authority of the higher mathematicians was white hot, so they were able to get-away with these amateur rationalisations. 

By contrast, the computerists of Silicon Valley seem to have taken-on the white-hot authority. They still seem to think that <<physical reality is mathematical>>… 

But look at what a mess they have made since they took-over the high moral ground!  They have shamefully hyped the authority of AI. So much so, that it now has the fragility of a potential bubble. They have also, in-effect, rubbished the significance of the school subject, elementary maths.  (They have stolen all the thunder of elementary maths’ inspiring contributions to technical progress… by crediting it all to their superb micro-electronics and, in effect, airbrushing maths out. Result: school maths looks purposeless to the average student… which is another way of saying meaningless-in-the-ordinary-sense.)

I’m afraid that the long false era of Platonic maths has ended. Maths is an abstract created playground, bits of which have an outline application to science. (Japanese Temple Geometry was a creative extension of Euclid, but they realised in the end that it was just that… a mere in-house creation.) The main future of science now lies with anti-maths, a much more suitable, authentic, credible, abstract playground.

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CHRISTOPHER ORMELL around November 1^st 2025.