The Exceptionally Deep Dilemma which faces humankind today is that adulation about mathematic modes and values (a quest to establish a math-topia of regimentation) is becoming more and more oppressive, but the number of people qualified and minded to criticise this oppresive creeping Holy Grail is almost nil. So we seem to be destined to stay on this oppressive curve indefinitely.

 On the other side of the coin, those who have the genes to understand difficult maths painlessly are onto a bandwagon. They may be called the ‘Abstractifiers’. They mostly became Abstractifiers because they found the ordinary world messy, distasteful and tortured: they much preferred to focus their thoughts onto the elegance, symmetry and strict rules of maths. Maths was —and still is after some redactifications— the heartland of truth. Its conclusions can be checked twice, thrice… as often as you like. So they are, in effect, examples of absolute truth, something of great significance to any thoughtful person.  This is mentally quite perfect, and this kind of perfection is far stronger and more satisfying (for this tiny minority) than any of the supposed “perfections” credited in ordinary life.   So these Abstractifiers are able to feel mentally settled to the nth degree. They feel quite sure that they are right, and that their worldview is timeless.

They are bowled-over by the inner satisfaction they receive from this mental nirvana. Their first thought is to devise modes of mathematic education which will dangle this “rosy” future in front of as many young minds as possible. From their perspective, this is the great ideal which clever young people should be homing-onto.

They are, alas, totally unaware of the distaste this generates in ordinary children.  Ordinary children have no reason to glorify maths… Children of the kind who become Abstractifiers are usually thought to be as scarce as one in ten thousand. Some of this tiny, exceptionally talented body of children will of course naturally glorify the subject… as a generator (for them) of mental satisfaction.

Alan Turing and John  von Neumann conceptualised modern computers originally during WW2.  The early machines worked, after a fashion, but their valves kept burning out.  

Things changed completely after 1960. (1) Computers became reliable and they would do this perfect kind of abstract “work” (“called thinking”)  for you. The intense satisfaction of working it out for yourself had disappeared. The processes involved stopped being “thinking”, and the results became available to almost anyone. And once it stopped being a rare, personal thing, maths naturally lost much of its mystique.

(2) For this reason computers were initially brushed-off by most professional pure mathematicians, much as mountaineers would reject the idea that they should use helicopters to get to the top of difficult mountains.

(3) It gradually became obvious that automated maths was much more usable in business, administration, planning, medicine, genetic engineering, warfare, etc. than anyone had previously imagined. Ordinary intelligent people soon realised that you wouldn’t buy a computer to churn out thousands of absolutely true useless formulae. They were, effectively, now a kind of yawn.  You would buy it to deliver answers to practical questions. So the very raison d’etre of automated maths had switched-away from elegance and mental satisfaction… and had become, in effect…  pulling off predictions, feats of organisation, and finding optimal versions of known techniques.

This was a painful earthquake which the diehard professional pure mathematicians would never accept. It was saying that the best human brains had been misunderstanding the main point and purpose of maths for more than 2,500 years.

They had been.  The principal reason maths became idolised in Antiquity was that it created the foresight and confidence needed to build the pyramids.  This was what maths spectacularly did.  It wasn’t originally regarded as a rare, elegant, quasi-mysterious cult which generated absolutely useless formulae.

Now, gradually, the mathematicians of the 21^st century are switching their very conception of maths away from elegance-for-the-sake-of-elegance, and towards improving the arrangements of industry, development, technology, medicine and science.  There is plenty for them to do —things which will illuminate the projects of the future.    

You can send your comment on this website: email your thoughts to per4group@gmail.comCHRISTOPHER ORMELL around 1^st January 2026chrisormell@aol.com