Please review my work, which I have been working on for 34 years

[Greg71]

Dear Colleagues,

Please review my work, which I have been working on for 34 years.
This is the final, completed version No. 25.
https://www.researchgate.net/publicatio ... Retrospect
Sincerely,
Ph.D, Grigoriy Dedenko

[wtf]

Dear Colleagues,

Please review my work, which I have been working on for 34 years.
This is the final, completed version No. 25.
https://www.researchgate.net/publicatio ... Retrospect
Sincerely,
Ph.D, Grigoriy Dedenko

Congratulations on completing this 34 year project.

I'm not qualified to judge the mathematical and historical details of your interesting paper. I hope my comments are not a disappointment to you, but I can not offer any feedback on the math or the history.

I did give it a cursory read and I have some comments.

It would have helped me immensely to have you say up front in the abstract, "This is a historical speculation of what Fermat might have been doing." Two keywords: History and Speculation.

You sort of said it, but it wasn't clear enough to focus my attention. I thought you were trying to prove FLT with what seemed to be nothing more than elementary algebra. That appoach is futile, as it's been proven that no elementary algebra proof could ever prove FLT. That's because the p-adic integers satisfy the same commutative ring axioms as the integers, and these axioms characterize elementary algebra. The p-adics contain counterexamples to FLT. Therefore no proof that depends only on elementary algebra can work.

I had all this in mind as I was skimming over the calculations. Elementary FLT "proofs" always make my eyes glaze, first because I don't want to wade through the calculations; and mostly because I already know that any such proof must be flawed.

For readers like me, who are just trying to gain an overall impression rather than a detailed understanding of your paper; it would be helpful to hit me over the head with History and Speculation descriptions. Also, if you did or didn't figure out what Fermat did, you should tell us that, so we have a roadmap.

After I went over it again, I realized what you were doing. But I'm still not sure what you concluded.

Again, I apologize that these are not substantive criticisms, but rather reflect the wishes of a casual reader like myself, someone just trying to get an overview.

With that said, I have a couple of questions.

1) Did you determine that your idea of Fermat's method did or did not work?

2) I've read that Fermat may not have written the annotation at all, and that it was added by his son after Fermat's death. Fermat never wrote about the subject again as I understand it. Do you know anything about this?

Congratulations again on your accomplishment.

[alan1000]

I admire the objectivity of wtf's reply and, Greg71, after 34 years of work, is this really the best forum you could find to review a lifetiime of work? Does that tell you something?

[alfalfaye]

I was impressed with your insight into the overwhelming nature of basic algebraic proofs. For authors looking to connect with diverse audiences, what strategies do you think might be effective in bridging the gap between complex mathematical concepts and general reading comprehension?