(Back to my main blog.)
(Notice to newcomers: This page is ordered in inverse cronological order. To read it in a way that makes sense, start with the last headline and read what is underneath it, then move back to the next-to-last headline, and so on.)
Today I was made aware of a document posted by Stein Johansen on the web site kunne.no. The document has been there since late January / early February. The document, like most others at that web site, is in Norwegian. Its title translates somewhat like Rebuttal of an attempted critique of Erik Trell's proof(s) of Fermat's last theorem (available as PDF). (Note the word «attempted»!) Since he wrote it in Norwegian, my response will be in Norwegian too. It is available as PDF as well. A short summary: Johansen tries to explain Trell's proof. I point out two fatal flaws in the reasoning. The most serious one: Johansen believes that a third degree equation cannot have more than one rational solution. This is patently false, of course. At this point, I am not sure if the flawed reasoning is representative of Trell's work or if it is Johansen's own misunderstanding: Johansen's work is much more clearly written than Trell's, so it is easier to point out mistakes without resorting to desperate attempts at interpreting what the writer wrote.
A side note on kunne.no: The site appears slightly dysfunctional to me, with many of the buttons producing no response when pressed. This is using Opera under FreeBSD. I tried Internet Explorer with Windows NT, and then the site works OK. Most likely a case of programming for that specific browser rather than for the standard.
Debating gives most of us much more psychological satisfaction than thinking does: but it deprives us of whatever chance there is of getting closer to the truth.
The previous response from Trell and Johansen ends with these words:
And since intelligible words failed HHO altogether at the third-line, probably most akin to Fermat, reproof stage but yet brought defamation into it, we will have reason to come back to that also, for which the present channel has been officially designated by HHO.s extraordinary inauguration; the more the poorer his conduct regrettably is.
I never quite figured out what this «third-line» refers to, but never mind that. It is true that I have attacked a paper by Trell, and I did not mince words in so doing; but I have worked hard to avoid getting personal: My attacks were directed at words on paper, not at people.
Oh well. The other thing that is clear from the above quote is that more might be expected from their hands, and now it has arrived. After some thought, I decided to make it available, as they want it, on the same conditions as chapter one. You can download it here in the original Word format and converted to PDF.
The new chapter starts with some statements that demand a response, and perhaps some clarification:
It has now been a month without disapproval of our Fermat's Last Theorem (FLT) proof replication on this site [...]. However, there has also been no retraction of the rather devastating denouncement offered by Harald Hanche-Olsen (HHO) on the deliberately somewhat idiomatic paper (Trell ) under attack:
To which I must respond: Firstly, it has hardly been a month, but let us not split calendrical hairs. Secondly, the main reason I have not offered a «disapproval» of the two gentlemen's FLT proof is that I did not think it necessary. Entertaining as watching a heated debate might be, I would rather adopt C.P. Snow's wise words as my own and recommend that the readers of this site think for themselves. All the information they need to do so is available here. Thirdly, the reason I have not retracted anything I said is that I have not been convinced that any retraction is necessary. Rest assured that if I ever find reason to retract something posted here, this is where such a retraction will be found. And finally, I am not sure that I will wish to say more at all. Perhaps later, as the dust settles some more and I have the time to study chapter 2, I will come back with a further response. But for the time being, I have too much else to do, and besides I am still suffering the after-effects of a particularly nasty cold, which limit my working capacity and force me to prioritize my time mercilessly.
A response to my writings on Trell's paper on FLT has reached me via the NTNU webmasters. As promised yesterday, I hereby make it available, both in the original Word format and converted to PDF. I think it is fair and reasonable that I make the response available without further comment from my side. In a way, I am glad for this response, for it is somewhat uncomfortable to criticize a paper that most people will have a hard time getting hold of. It does leave one open to charges of misrepresentation. (My paper, which the authors are responding to, is available via a link at the bottom of the current page.)
It has come to my attention that Erik Trell has threatened legal action against NTNU because of this page. In particular, he is upset because he has no way to respond to my claims. But he has never contacted me about it. If he had, I would have offered him room for a response. Or, if he prefers to use a web site which he himself controls, I will provide a link to it, right here in this page. I have no interest in suppressing his side of the story.
O happy day! The great Trell has deigned to notice my miserable existence! (See the clipping on the right, if you read Norwegian. If not, I'll try to translate below.)
Three more articles have appeared in Adresseavisen since my last update:
«Thus his [Baas'] initial outburst was as primitive as feared, wonder if he now reads the paper the way a certain other potentate reads the Bible. He is trying to defend his compromised shield of armor, and for that purpose he has sent out one of his minions [yours truly] with an awful message in an apocryphal website from Ultima Thule, as if the servile polishing of the lead male's theses was anything other than the pitiful falsification it constitutes in reality.»(Text in [brackets] is mine.) From a man of Trell's caliber, this is high praise indeed. I notice with interest that he does consider my little note a falsification of his work, even though he calls it «pitiful». Yes, professor Trell, I know it is pitiful. Your paper simply does not contain enough substance to warrant a more clever critique from my hand. But now you'll just have to excuse me as I must go and polish my master's boots.
This is a strange tale indeed. Erik Trell is a professor of medicine at the University of Linköping. But his interests extend well beyond his chosen profession: He likes to work with mathematics and physics as well. So far so good. I heartily approve of people with broad interests. However, if you dabble in disciplines outside your own specialty, you need to learn the language and methods of that discipline, so you can build on what is known and avoid the pitfalls and traps that are so ubiquitous in any human endeavour.
In December 2002, Trell visited NTNU. I am not sure what prompted his visit, but he did visit Stein Johansen, who is on the faculty of the department of social anthropology. As part of this visit, he also spent a couple hours trying to convince three professors at the Department of Mathematical Sciences of the correctness of his proof of Fermat's Last Theorem. The three professors were not convinced, however.
The rest of the action so far takes place in the pages of Adresseavisen, a local Trondheim paper and one of the major Norwegian papers outside Oslo. Unfortunately, the first articles are no longer online, and the debate column is never online. So the interested reader is referred to the flat dead tree version of the paper.
My purpose with this rather lengthy sketch of the story is to introduce my own modest contribution. After all the above articles appeared in the paper, we have finally got hold of Trell's paper. It was not very surprising to discover that there is no proof of FLT in this paper. Still, I found the whole story sufficiently interesting to produce a short exposition of the core elements of the paper, explaining why it does not prove anything. Since HTML is far from an ideal medium for mathematics, I wrote it in TeX instead, and make it available as a PDF file.
Harald Hanche-Olsen (blog) 2003-04-18 13:41 UTC