User talk:Klaus Barner
Klaus Barner, you are invited to the Teahouse
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Hi Klaus Barner! Thanks for contributing to Wikipedia. |
Adequality
[edit]The discussion at Talk:Adequality#Dubious_Scholarly_controversy_content may be of interest to you. Tkuvho (talk) 16:18, 10 February 2013 (UTC)
Mahoney
[edit]You may be interested in working also on the recently created article Michael S. Mahoney. Tkuvho (talk) 17:47, 20 February 2013 (UTC)
As an experienced mathematician, I want to provide you some comments on the content of your edits in this article. The talk of the article should be devoted to the discussion on about improving the article. My comments being WP:original research, there would be misplaced there. The opinions that follow have nothing to do with the revert of your edits, except that it took some time to clearly separate my opinion on your edits from the reasons to revert them.
If you want to answer to this post, please do it here. I'll watch this page.
Terminology
[edit]As I have noted in the article, adaequalitas has cognates in French and English. Thus the literal translation of adaequentur in English should be adequating. This is a neologism, but equating would be an acceptable translation. Note that this word is yet used frequently by mathematicians and physicists, in a sense that is very close to that of Fermat, as you can see by typing "equating the two" (with quotes) in Google Scholar.
In French (Fermat's language),
This remark is so evident that I can not understand the controversy on the meaning of the word.
Thinking again to that, I believe to remember that the locution "Par adéquation" were not rare in French mathematical texts of 19th and beginning of 20th century (this has to be checked). In any case, a research by Google Scholar shows that it is yet used in non-mathematical texts. Thus your sentence "Next Fermat puts the two terms equal:" may accurately be translated in French as "Par adéquation de ces deux expressions, Fermat obtient l'égalité:". This is correct French language (without neologism), which may be understood by a mathematician without further explanation.
References to Bourbaki
[edit]Your main mathematical reference is Bourbaki. On this question about mathematical logic and semantics, this is probably the worse reference, which has always been considered as not really serious by the logicians.
A bit of epistemology
[edit]I do not know any place where the following remarks are written. It may be because that mathematicians do not write much about the epistemology of their field. But I am convinced that almost every mathematician would agree with what follows.
Normally a mathematical discourse has three components:
- An informal explanation giving the intuition and the content of the formal results. In geometry, this role is played by the figure. Another example is the pseudo-definition of a line given in the beginning of Euclid's elements: The line is the first species of quantity, which has only one dimension, namely length, without any width nor depth, and is nothing else than the flow or run of the point which [...] will leave from its imaginary moving some vestige in length, exempt of any width. This explanation is never used in any proof.
- Formal statements (theorems) and proofs
- Some computations
The two latter components may be mixed and difficult to distinguish. Moreover, a proof is, in some sense, a logical computation. This is clear if one consider the computer proofs of four color theorem and Feit-Thompson theorem.
This distinction was already clear at Fermat's time: He wrote that he had a proof of its last theorem, but had never claiming of a proof in our case. Looking on what is written in Adequality it is clear that what is called "his method" is simply the presentation and the explanation of a method of computation. In fact, this is the description of what is now called an algorithm. For a modern mathematician every algorithm should been proven. In Fermat's case, I guess that he was aware of the need of a proof, but he was unable to provide it (the needed technology was not yet invented). Nevertheless he was certainly proud of providing by computation the desired result.
Looking on Fermat's method form this point of view, shows that the exact meaning of adaequentur for Fermat is not important: it belongs to the informal part of his discourse and, whichever meaning is chosen, this does not change anything to the method of computation.
What is e?
[edit]In my opinion, the only thing whose analysis is relevant is the nature and the significance of e. In fact, Fermat computed with it as it were a number, but it is not a number because, at some point it was supposed to be zero, and just after, it is put to zero. I am convinced that Fermat considered it as some kind of "imaginary number" (the modern meaning was not yet invented). The question "what is e?" is double. The first question is "what intuition of e had Fermat?". The second is "what modern meaning may be given to e to make his algorithm provable?"
"What intuition of e had Fermat?"
[edit]From your section "How did Fermat hit upon his method?", it seems clear that Fermat had the intuition of what has been expressed later as "a tangent is a line that cuts the curve at two infinitely close points". It is impossible and of small interest to know what mental representation Fermat had of e. It could be static (e is as small as one want, but non-zero) or dynamic (e is a quantity that becomes smaller and smaller and tends to zero), or a mixture of the two. This has absolutely no impact of the method of computation.
"What modern meaning may be given to e to make his algorithm provable?"
[edit]Contrarily to what you and some other historian wrote, there are several meanings that may be given to e to makes Fermat's computation provable.
- It may be an infinitesimal in Leibniz's sense, denoted dx in modern mathematics. This formalize the small increment of the physicists.
- It may be an indeterminate. In this case, the expression that appear in Fermat's computation should be considered as polynomials or rational fractions.
- It may be infinitesimal in non-standard analysis sense.
These three choices are equally correct. Thus selecting one of them and asserting that it is the right mathematical interpretation (as done by cited authors) is a blatant mathematical mistake.
Conclusion
[edit]I have been a little lengthy. I hope that I have convinced you that your theses are, for a mathematician, highly controversial.
March 2013
[edit]Dear Klaus Barner,
In the future, do not post an editor's personal information, such as his real name, or what you think may be his real name, onto Wikipedia. This is a violation of the outing policy, and repeated attempts will result in your being blocked from editing. Someguy1221 (talk) 02:05, 14 March 2013 (UTC)
Blocked
[edit]Since you ignored my previous warning not to post what you think is the real life identity of an anonymous editor, you have been blocked indefinitely from editing. If and when you understand that we have zero tolerance for this behavior, you may appeal this block by adding the text {{Unblock|Your reason here}} to this page. Someguy1221 (talk) 09:34, 24 March 2013 (UTC)
suspected banned user edits
[edit]You are being discussed here. Tkuvho (talk) 08:38, 3 October 2014 (UTC)