The situation in advanced and higher maths in Academia is far from being satisfactory.  The Barons of Silicon Valley have been pouring scorn on the thinking and culture surrounding higher “Modern Mathematics” since 1960. They regard it as an artificial ego trip. They have been  claiming for more than 60 years —in brazen contradiction to all the facts—  that <<computers have nothing to do with maths!>>. (This “Big Lie”, they thought, was necessary if they were to sell their PCs to the ordinary public.) They have taken possession of all the subject’s spectacular “applications”, and thus stolen what was the mainstream subject’s previous well-earned thunder. At the same time they have brazenly credited computing as the source of all the magic which made their applications possible —rather than conceding that it is the background mathematising which is the hardest part of the deal.  They have introduced the new term ‘computer modelling’ as if it were the computer which does the modelling.  But the computer does not do any modelling (=thinking outside the box) at all.  What the computer does is to implement the modelling prospectus which was dreamt-up by the modeller… a previously unguessed agenda, the fruit of rare skills, realistic awareness, determination, imagination, synoptic reasoning, etc.. They have used their powerful machines to greatly enhance all kinds of easy applications of maths, especially the most lucrative ones, but they have not taken the trouble to insist on rigorous standards of epistemology in relation to the most challenging mathematical models of reality.  This has led to far too many disastrously inadequate fantasy models, especially in economics, which have led in turn to mathematical modelling getting a bad press… It indicates a sub-standard, nonsensical, negligent guardianship of the activity of modelling mathematics.

So what is needed to clean up this morass of muddle, lies, neglect and misplaced emphases? The first reform urgently needed is some recognition from the authorities that the meaning of mathematics is not (as was self-servingly imagined by the Platonist mathematicians for 2500 years) suis generis, (=“an end in itself”), but is direct a consequence of its uses (= the practical enlightenment arising from it). This was highlighted by C. S. Peirce in the 1890s when he pronounced perceptively that mathematics was the <<Science of Hypothesis>>.

For more than 2,000 years the principal body (elite) of the world’s acutest thinkers was a small community of (initially amateur) mathematicians.  They were Platonists who prioritised essentially aesthetic goals in their maths research, and who never bothered to ask themselves why they and their subject were lionised so much by the feudal thugs who bossed society.  By contrast, the mathematicians were principled, rigorous and consistent to the nth degree.  But they conceptualised “their” subject in a way which mirrored their own parochial, fascinating interest —exploring symbolic configurations. They treated maths as if it was an exceptionally prestigious game much appreciated by the powers that be… but an end-in-itself, not something with a use.  Around 1960 the first ultra-reliable computers arrived.

After 1960,  the mathematicians were unceremoniously deposed by a new, self-elected “elite” —-of programmers—- who were exploring the use of computers to solve practical problems.  This new “computer elite” however has not maintained the same level of rigour and accountability as that which they inherited from the Platonic mathematicians.  They have followed the trail of lucrative automated mathematic applications, but have given little attention to the synoptic epistemological conditions which must be met if such applications are to be reliable to the highest standards. Their IT managers have not appeared to be trying to be exemplars of their new subject’s internal discipline (as the maths gurus had previously been), but entrepreneurs determined to make as much money as they could.

This change-over has notoriously drained all the profuse, former moral support for maths from the intelligent public which used to exist. We have observed above that for more than 60 years the by-word put out by the computerists has been that <<Computers have nothing to do with maths!>> .  It is probably the most brazen example of a malicious lie in human history.  They must be congratulating themselves to no small degree, because they have got away with it.

This would not have mattered so much in “normal” times, but it has coincided with a seemingly bottomless crisis in science, maths and religion.  In such abnormal times we need every ounce of cognitive power and rigour to resolve the common quagmire.

Fortunately this mega-crisis could now now be seen-off —-in principle—- by the emergence of Anti-Maths, but —would you believe it— it is being actively brushed aside by the muddled, deflated, enfeebled former “elites” of computers, maths and physics. By failing abysmally to see the point of Anti-Maths, they are letting their already diminished reputations fall through the floor.

A PRIZE OFFER

To mark the 5-year anniversary of the so-far unchallenged on-line exposition of his “bare hands” proof of Fermat’s Last Theorem, the author has decided to offer a reward of £3,000 to the first person who can find a self-evidently exposition-derailing mistake in the on-line argument. He or she will have to recruit   two independent colleagues to check and confirm his or her claim —they will each receive £1000.

The exposition is on blogs 1 and 2 of this website.

The offer expires on July 1^st 2025 and if no disproof has been forthcoming, the author intends to adopt the default assumption that his reasoning <<must be correct>>.  Send your name, address, disproving reasoning, and confirming colleague names,  to:  per4group@gmail.com .

CHRISTOPHER ORMELL around May 1^st 2025.  chrisormell@aol.com