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 the Maths Gazette as well as the Editor’s own over-view —on the preposterously, unsupported, supposition <<there must be a mistake somewhere!>> in 2020.

It took me twenty-nine years to get to this project to a state of closure —a result by “bare hands” methods which only use roughly A-level maths.  If it had been published in 2020 in the Maths Gazette, it might have tempted a few studious colleagues (here and abroad) to look at it sceptically, i.e. taking the trouble to understand the reasoning at each stage. But these timid referees and the even more timid Editor were evidently feeling very nervous about publishing it. They probably feared that someone would show them up by pin-pointing a hither-to unguessed, damning error.

They offered no evidence at all that this might happen: it was a kind of bias which had grown up after more than 350 years of failure.

I devoted approximately one hour a day for 29 years to this project, which amounts to over 10,000 hours. I’m afraid, however, these referees and several maths friends gave up their critique after 3-4 pages in Part 1. (Actually the reasoning they found too-puzzling-to-entertain in Part 1 had been already accepted by an earlier referee who actually found a palpable error in an erroneous, later, (abandoned), version of Part 2 … this was around 2011.

It is evident that the obstinate rigour-based culture needed to check heavy maths reasoning has now almost disappeared.

Fortunately the good news is that AI has —apparently— the innate stamina needed to undertake such checking. Though whether it is capable of pursuing such checking on a 20-page exposition isn’t clear.   (This is a positive aspect of AI… to set against the immense existential dangers it poses —if misused— to civilisation.).

There is now an actual, if small, chance that a proper assessment of this reasoning will emerge: we await the verdict AI is able to produce.

Anyone who has fully digested Part 1 of the proof will realise at once that Fermat’s conjecture would only stand a chance of being vindicated if the polynomial for v on page 15 is capable of collapsing —consolidation by consolidation— into a mere pth power of V, either exactly, or times p to the power p-1.  Without going into any details, the likelihood that this could happen is infinitesimal.

(So, as p increases, this overall conclusion becomes more and more convincing, because the polynomial for v has to imply an unlikely merger of term into term eventually resulting in V to the power p multiplied possibly by p to the power p-1 or 0.) The pages 15-21 simply “draw out” the inevitably impossible logic of this conclusion.

There might be a more direct way of establishing this obvious conclusion. There might be a professional mathematician who has a range of elementary results to draw-upon… ones capable of showing immediately that this cascade of simplifications cannot occur.

In retrospect the most likely counter-example should occur when p=3. (Because p=3 poses the reduction of this formidable polynomial to 1.) But this makes the case p=3 special, and this case  is sewn up by the reasoning set out on pages 20-21.

So now another year of absence of objections has almost passed, from five years to six. If left unaddressed, the de facto conclusion will eventually be that the reasoning must be valid.

To comment on the reasoning, email:  per4group@gmail.com  CHRISTOPHER ORMELL around June 1^st2026.