Wikipedia:Articles for deletion/Felix A. Keller


 * The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review).  No further edits should be made to this page.  

The result was DELETE. Herostratus 16:11, 21 February 2007 (UTC)

Felix A. Keller

 * – (View AfD) (View log)

Subject is not notable and was placed here as self-promotion Dominus 16:36, 15 February 2007 (UTC)

Addendum: The subject's only claim to fame is having invented a simple expression whose value is e. He has repeatedly edited the e article to refer to himself. However, he is neither notable nor noted, and his contribution to mathematics is infinitesimally small.

The article Felix A. Keller was created by user Fak119, presumably Keller himself.

When he started adding his expression to the e page, I did some research to find out if the expression was actually known in the literature as "Keller's expression" or if Keller was known in the literature; my conclusion was that neither was. -- Dominus 16:43, 15 February 2007 (UTC)

I am also nominating the following related pages for the reasons above:


 * Delete. Per nom. --Bryson 17:41, 15 February 2007 (UTC)
 * Delete both unless anyone can dig up multiple reliable sources in the actual mathematical literature for the expression; in that case delete only the bio. Google scholar finds four hits for "Keller's expression" but none of the four are about the expression described in the article. No hits for that phrase in MathSciNet. —David Eppstein 18:43, 15 February 2007 (UTC)
 * Felix Keller also is not listed as an author of any article in MathSciNet (nor is he mentioned in any review). This also looks like the kinda formula that any number of people have stumbled on.  I'd vote delete for both, too. Steven Finch, on the other hand, has published a number of works.  I'm gonna take a quick look through the book mentioned in MR2003519 to see if it mentions Keller.  (And he does work at Mathsoft; see .)  Lunch 23:12, 15 February 2007 (UTC)
 * The formula is listed in Finch's book on page 15, but it isn't credited to Keller. Finch gives an a reference to Richardson's 1927 paper that discusses using differencing methods to accelerate convergence of sequences when an asymptotic expression is known for the error (this method is now known as Richardon's extrapolation).  Richardson doesn't mention that formula specifically, but with some tinkering one could infer it from the results there. As for Finch, the intro to the book says in part, "Steven R. Finch studied at Oberlin College and the University of Illinois at Urbana-Champaign, and held positions at TASC, Lincoln Laboratory, and MathSoft.  He is presently a freelance mathematician in the Boston area."  Lunch 00:03, 16 February 2007 (UTC)
 * Delete as not notable and self-promotion. DavidCBryant 19:03, 15 February 2007 (UTC)
 * Delete. The only claim to notability of the person is the mathematical formula.  The formula, however, has been well known to everyone at least since the 18th century and is found in all calculus textbooks.  To say that it was introduced in 1975, when everyone had already learned it from calculus textbooks, is to ignore all of history except the biography of this one person.  I anticipate that the author of this article will say that what the calculus textbooks actually say is
 * $$e = \lim_{n\to\infty} \left({n+1 \over n}\right)^n,$$
 * but the differences are trivial and every freshman (except those who ultimately never become mathematicians) makes many many similar "original discoveries". What if everyone who "discovered" this formula were to have a Wikipedia article?  How 'bout this: "John Smith in 1992 discovered this important formula: 12 +182 = 62 + 172 = 102 + 152, known as Smith's formula."  Etc. etc. etc. etc..... one article for everyone who's successfully completed a homework assignment. Michael Hardy 20:05, 15 February 2007 (UTC)
 * COMMENT: OK, a bit less hasty:  The formula is correct, as follows:
 * $$ \left({n \over n-1}\right)^{n-1}\cdot n - \left({n-1 \over n-2}\right)^{n-2}\cdot (n - 1),$$
 * so we have an expression approaching e MINUS another expression approaching e PLUS another expression approaching e. The last term comes from the cancellation of two minus signs, one of which is in the "(n &minus; 1)" at the end.  But still, it's a trivial consequence of a basic formula known at least since the 18th century. Michael Hardy 02:01, 17 February 2007 (UTC)


 * Comment. I see that two articles nominated for deletion both link to this same deletion-discussion page.  The other one is Keller's Expression.  I have already noted that "Keller's expression" has been found in all calculus textbooks since long before Keller's birth, but observe also:
 * The phrase "for |n| > 2" makes no sense. The variable n is bound.  Therefore, the value of the expression does not depend on anything called n.
 * It refers to "the natural logarithm e" when it presumable meant "the base of natural logarithms, e". Whoever wrote this is not particularly familiar with mathematical reasoning or conventions.  (Nor with Wikipedia's conventions.) Michael Hardy 20:14, 15 February 2007 (UTC)

$$ \left| e - \frac{n^n}{(n-1)^{(n-1)}} - \frac{(n-1)^{n-1}}{(n-2)^{(n-2)}} \right| < \epsilon $$. So the phrase "for |n| >2" is not correct. Jka02 21:49, 15 February 2007 (UTC)
 * Comment As noted above, the author of the article must not know much about mathematics as the equation has a limiting up to infinity involved, which means given an arbitrarily small number $$\epsilon >0 $$ there exists $$ m \in \mathbb{Z} $$ such that for all $$ n \geq m $$:
 * Delete both per nom, Hardy, wish we could speedy. --KSmrqT 01:18, 16 February 2007 (UTC)
 * Delete. Non-notable. linas 20:55, 17 February 2007 (UTC)
 * Delete both Quale 02:56, 19 February 2007 (UTC)
 * Delete both per Michael Hardy. This is a bit like making separate articles on $$e^{i\pi} = -1\,$$ and $$e^{i\pi} + 1 = 0\,$$, which we really don't need to do. The discoverer of a formula can be considered to have discovered all trivial consequences of the formula as well, so Mr. Keller didn't really discover his formula after all. --N Shar 20:35, 20 February 2007 (UTC)


 * The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.