There is a largely unaddressed existential problem which currently faces the mathematical community, arising from the question: How does computer programming differ from mathematics?

This question first became a potential “Issue” around 1960, when the development of transistors resulted in computers becoming unbelievably reliable. Computers had arrived thanks to the insight, imagination and sustained attention of Babbage, Turing and von Neumann, three outstanding mathematicians. In the light of this, it was self-evident that computers were a new, mechanised way of doing mathematical operations. 

But the leading gurus of maths were totally unprepared for, even alarmed by,  this drastic re-appraisal of their subject.

They faced the same kind of dilemma as artists after the invention of cameras. Machines had muscled-in, and invaded an elite cultural arena previously navigable only by persons of unusual talent… talent honed and rooted in a venerable, historic culture of technical progress.

At the time it was abundantly clear that computers had automated some of the simpler processes of mathematics.  Later, after the emergence of Mathematica in 1988 this was extended in principle “to all mathematics”.  So the $64 question became whether this new computer-quasi-matematical activity, which was taking-over, should still be described as “a form of mathematics”?

A majority of leading mathematicians at the time said vehemently No!

Virtually all the computerists also said vehemently No!

It apparently suited both embattled communities to maintain a deep conceptual gulf between computing and maths.

So now the $64 question became whether this gulf was genuine, or merely a deliberate wall (= an artefact) which had been unconsciously created to maintain the comfort zone on both its sides.

If computers were essentially gadgets which automated maths, this implied that the new form of maths was going to be a thousand times more useful than the old maths had previously been.  This was a profoundly unwelcome thought for most of the gurus of higher maths. They had long since been totally committed to treating higher maths as an unique, privileged, “important” symbolic wonderland. They were full of scorn for maths treated as a “useful” discipline. They thought its so-called “uses” were uninteresting, over-hyped and trivial.

The computerists, on the other hand, were acutely aware that the concept of maths-for-maths-sake was anathema to the masses: the average person disliked it, dreaded it, and made it a butt of distaste.

So the computer industry’s salespersons started saying that <<Our computers have nothing to do with maths!>>.  This, they felt, was essential —if they were going to sell their PCs.  It was a mantra which <<said it as it wasn’t(=a lie)>> but it seemed to be the only simple way they could get round the profound animosity and negativity surrounding maths, treated as a privileged subject.

The gurus of higher maths welcomed this Historic Lie.  They knew perfectly well that computers had everything to do with mathematics… but they didn’t want to find their work drowned by a vast tsunami of trivial computerised maths.

The computerists also soon established the Truth that <<computerised maths is a thousand times more useful than uncomputerized maths>>.  The gurus of higher maths could now hardly dispute the fact that computers were becoming extremely useful gadgets… but they could dispute the fact that what they were doing was “really maths”.  For them “Real Maths” was “High Culture”… a unique, elevated, symbolic wonderland, miles away from anything utilitarian.

Unfortunately it has lost almost all its lustre.

They had the academic credentials to say, credibly, what counted as “real maths”.  But this has lost its lustre.

There is a solution. By adopting the Peircean insight that maths is the science of hypothesis (=plans for the future) we can change maths and turn it into the most attractive, interesting subject on the school curriculum.  

Maths is the main discipline on which today’s society rests, and it is needed in its role as the principal “pathfinder for the future”.  

CHRISTOPHER ORMELL around March 1^st 2025.  If you would like a free online copy of the P E R Narrative Maths Manifesto, send an email requesting this to per4group@gmail.com  Also comments on the reasoning in this or earlier blogs in this series can be submitted by email to the same address.  This includes any counter-argument submitted as a bid for the prize offered in blog 49.