Talk:e (mathematical constant)

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The reference to April 1 1994 is simply wrong...[edit]

When one actually reads the reference to the 1,000,000 record of April, 1994, it says that the computation was done to 10,000,000 NOT the claimed record of just 1,000,000!!!! Correct this error please!!!! — Preceding unsigned comment added by (talk) 21:50, 6 April 2015‎

Only the first million were checked, so the reference is correct. -- [[User:Edokter]] {{talk}} 22:15, 6 April 2015 (UTC)
I independently verified Nemiroff & Bonnell's 1994 5,000,000 digits and sent an email to Nemiroff 2015-03-15 telling him that he could remove "(currently unchecked)" from that page. He just hasn't done so. Is there any reason I shouldn't change their 1994 April 1 record from 1,000,000 to 5,000,000? I also asked Nemiroff for their 10,000,000 digit 1994 results (mentioned on the page linked to, but not provided). He replied that he couldn't find those files. Rick314 (talk) 21:25, 28 June 2015 (UTC)
The reason is that everything on Wikipedia needs to be verifiable through third party sources. We cannot accept self-published assertions. -- [[User:Edokter]] {{talk}} 21:35, 28 June 2015 (UTC)
I don't understand -- I am saying I provided 3rd-party verification for Nemiroff, to Nemiroff, 3 months ago. Are you saying the 1994 results can now be updated by Nemiroff but not me, or what? Rick314 (talk) 21:51, 28 June 2015 (UTC)
Erwin (Edokter) please reply. I see you are a Wikipedia administrator and so can provide clarification regarding Wikipedia processes. I provided a link above to Nemiroff & Bonnell's 1994-05-01 5,000,000 digits. I verified their results by comparing all 5,000,000 digits against the output of my own program, and they agree. I told them so in an email 3 months ago. What more has to be done before extending their 1994 milestone from 1,000,000 to 5,000,000 digits? Rick314 (talk) 16:59, 29 June 2015 (UTC)

circular definition[edit]

The article says "The number e is an important mathematical constant that is the base of the natural logarithm", and the article on natural logarithm says "The natural logarithm of a number is its logarithm to the base e". This is a circular definition. any ideas on how to fix it? (talk) 05:00, 23 April 2015 (UTC)

The "definition" in the first sentence of the article is not a definition in a mathematical sense. It's just a way for a reader to look at an article and find out quickly what the article is about.
So really I don't see anything that needs to be fixed here. I'm not saying the lead sentences of the two articles are perfect, or necessarily what I would have written, but it's not a problem per se that taken together they give a circular definition, not if you can get genuine mathematical definitions from the articles themselves. Which, I believe, you can. --Trovatore (talk) 05:56, 23 April 2015 (UTC)
The natural logarithm is formally defined as the integral \ln x = \int_1^x dt/t. This is not circular. Sławomir Biały (talk)
talk, Trovatore, and Sławomir Biały, something still needs to be fixed: a math article should have a mathematical tone and mathematical jargon. And Sławomir Biały, where did you get that "formal" definition of e? Dandtiks69 (talk) 23:49, 25 May 2015 (UTC)

────────────────────────────────────────────────────────────────────────────────────────────────────Dandtiks69 you need to be more specific about what you think the problem or problems with the article are, and how they can be addressed. I agree with Trovatore, and do not see anything seriously wrong that needs fixing with the lead or definition.--JohnBlackburnewordsdeeds 00:36, 26 May 2015 (UTC)

From the lead:

The natural logarithm of a positive number k can also be defined directly as the area under the curve y = 1/x between x = 1 and x = k, in which case, e is the number whose natural logarithm is 1.

From the article natural logarithm, the first line of the "Definition" section reads:

Formally, ln(a) may be defined as the integral,
\ln(a)=\int_1^a \frac{1}{x}\,dx.

-Sławomir Biały (talk) 11:26, 26 May 2015 (UTC)

I was confusing the formal definition of e instead of ln (x), sorry. The one for e is the limit, as x approaches infinity, is (1+1/x)^x. — Preceding unsigned comment added by Dandtiks69 (talkcontribs) 21:10, 26 May 2015 (UTC)

Exponential-like functions[edit]

I just undid this change to the Exponential-like functions section. Although it made mathematical sense, in that there were no errors that I could see, as a whole it turned a concise and clear section into a mess, which seemed to be trying to do far too much and draw on too many things to be easily understood, touching on an covering material already covered elsewhere, in the main theory sections of the article. As such it was excessive and out of place in this article.--JohnBlackburnewordsdeeds 02:22, 5 June 2015 (UTC)

I accept much of your criticism and have re-edited my change to be much shorter and more streamlined. Now using only one example, what the change adds to the article is a connection between an exponential function property and a main theoretical representation of e as a limit. True, the change does reference a main theoretical point covered elsewhere, but only as much as is needed to illustrate the connection. I hope you find the re-edited change satisfactory for the article. Bwisialo — Preceding undated comment added 07:31, 5 June 2015 (UTC)
I also did not find this an improvement. We don't need to illustrate a "connection" of the extrema of functions like x^{1/x} to the mathematical constant e, much less to commit original research in doing so. The global maximum already is at x = e. That's the connection, without any need for embellishment. This is a famous mathematical problem. What's written is already quite standard and clear, without the need to inject our own interpretations. Sławomir Biały (talk) 11:28, 5 June 2015 (UTC)
Let f(x) = (1+x)(1/x); g(x) = x(1/x); and h(x) = (n+x)(1/x)
On the level of explanation and illustration, there is a clear difference between the two following statements that relate a limit property to an extrema property:
1) \lim_{x\to 0} f(x) = e and the global maximum of g(x) occurs at x = e. = e is the connection or shared functional property between these two expressions, and as such does not need to be stated.
2) f(x) and g(x) are instances of h(x), and the extrema of h(x) for 0n < 1 form a continuous curve from the global maximum of g(x) until they approach the limit coordinates (0, e) where h(x) = f(x).
(1) treats f(x) and g(x) as two discrete / isolated functions, with the exception of = e. (2) illustrates a continuity of functional properties between the limit property of f(x) and the extrema property of g(x).
On the issue of original research: (2) is is not a synthesis that states a new thesis but is an explanation of sourced statements in a different way. "SYNTH is when two or more reliably-sourced statements are combined to produce a new thesis that isn't verifiable from the sources. If you're just explaining the same material in a different way, there's no new thesis." The statement that f(x) and g(x) are instances of h(x) is a simple and verifiable one. The remainder of the explanation in (2) derives from routine calculations of plugging in values for n, and "Routine calculations do not count as original research."
As such, I argue that my proposed change or something equivalent be added to the section.Bwisialo
I disagree. This does not actually explain anything in the article. One is still left the task of verifying through some method that the maximum of x^{1/x} occurs at x=e. Sławomir Biały (talk) 08:28, 17 June 2015 (UTC)
That the maximum of x^{1/x} occurs at x=e is already stated and verified in the article, prior to my proposed change. Any additional verification of this maximum seems unnecessary and, second, would be a change other than the one I am proposing.Bwisialo
So why is the section enhanced by your proposed revision? It seems like we agree that it's a red herring. Sławomir Biały (talk) 17:24, 17 June 2015 (UTC)
My comments here are admittedly long, but I am trying to address potential misunderstandings, clarify potential confusions, and answer your question.
I feel that you are not extending the principle of charity when interpreting my comments. Obviously, I do not agree that it is a red herring. If I did, I would not propose the change. For my part, if I understand your comments correctly, the stated reasons behind your objection seem to change in an inconsistent way. Your first comment suggests that the change suggests that the change introduces into the article a new thesis and personal interpretation based on original research. As a response to my most recent comment, your last comment seems to suggest that the change is redundant to the verified statements limx→0 (1+x)(1/x) = e and f(x)max {{x(1/x) = e. Perhaps there is mutual misunderstanding on these topics.
Your comments do consistently pose the question: what does the proposed change add to the section? I have stated an answer to this, and rather than restate those comments, I will provisionally phrase the answer somewhat differently.
The change neither advances a new thesis nor is it redundant. As I suggest in my previous comments, it explains the expressions limx→0 (1+x)(1/x) = e and f(x)max {{x(1/x) = e in a different way than what is presently in the article -– specifically, in a way that illustrates a connection between these two expressions.
Illustrating a connection is different than the statement that both of the these expressions = e. In effect, such a statement merely lists the two as discrete expressions that both fall under a category of expressions that = e.
Exponential-like functions –- including (1+x)(1/x) –- express central functional properties of e, and the relationships / connections between these functional properties are worth indicating or stating briefly. The relationship / connection between limx→0 (1+x)(1/x) = e and limx→∞ (1+1/x)(x) = e is obvious and is indicated in the article by the use of the word “similarly.” The same applies to the relationship / connection between f(x)max x(1/x) = e andf(x)min xx = 1/e.
What is less obvious and merits a brief illustration is the relationship / connection between, for example, limx→0 (1+x)(1/x) = e and f(x)max x(1/x) = e -- a limit property and an extrema property. The change I am proposing, and what it adds to and enhances in the section / article, is a brief illustration of the relationship / connection between the relevant functional properties of (1+x)(1/x) and x(1/x) as they relate to e. I am not suggesting that it is necessary to illustrate every relationship / connection between extrema properties and limit properties of exponential-like functions: the example serves the purpose of illustrating that the connections are there and illustrating one example of such connections. Again, illustrating such relationships / connections consists of something other and more than listing the functions as discrete expressions under a category of expressions of e. Bwisialo

I think I have been charitable in even responding, trying to get you to see the mathematical error involved in trying to say that the existence of this one-parameter family of functions somehow links up the value of a limit with a critical point, to see for yourself thst the entire point is pure mysticism. I see now that further discusdion is a waste of time, since it's clear you plan to continue this pointless discussion regardless. So I'l just be gery clear. The material in question does not belong on Wikipedia. It is WP:OR. If you cannot find a reliable source that clearly and explicitly says that the limit of the function (1+x)^{1/x} at x=0 is related to the critical point of x^{1/x} because of the existence of the one parameter family of functions that you cooked up, it doesn't belong here. It is a novel synthesis, not appearing in published reliable sources. That's not allowed here. Sławomir Biały (talk) 23:20, 18 June 2015 (UTC)

Whether it is original research is debatable, and needs additional editors' comments to achieve consensus. As I have stated and argued above, the verified sources are limx→0 (1+x)(1/x) = e and f(x)max x(1/x) = e. The one parameter family of functions is straightforwardly verifiable from the sources, and -- per "SYNTH is when two or more reliably-sourced statements are combined to produce a new thesis that isn't verifiable from the sources. If you're just explaining the same material in a different way, there's no new thesis." -- the proposed change is precisely explaining the sourced material in a different way and is not a novel synthesis. Bwisialo
I beg to differ: "The properties of the two functions can be shown to be continuous with one another via the function (n+x)(1/x)." This certainly qualifies as a "new thesis". This includes a statement that "properties" are "continuous", whatever that might mean. Supposing that we remove this statement, all that remains is a statement that \lim_{x\to 0}(1+x)^{1/x}=e, which already appears elsewhere in the article in context. The section under discussion is a short, precise, and clear discussion of the Steiner problem and Euler's theorem on the infinite tetration. It does not need a red herring about the limit \lim_{x\to 0}(1+x)^{1/x}. Sławomir Biały (talk) 01:00, 19 June 2015 (UTC)
What you have quoted is a provisional draft statement that may commit SYNTH unintentionally due to wording. Another provisional, revisable statement could be the following:

The global maximum for the function

 f(x) = \sqrt[x]{x} = x^{\frac{1}{x}}

occurs at x = e. This functional property of x(1/x) is related to the limit property of the function

\lim_{x\to 0} \left( 1 + x \right)^{\frac{1}{x}} = e:

the two functions are instances of

 f(x) = (n+x)^{\frac{1}{x}},

where x(1/x) occurs at n = 0, and (1+x)(1/x) occurs at n = 1. From n = 0 to n = 1, the minima and maxima of (n + x)(1/x) form a continuous curve from the global maximum of x(1/x) until converging on the limit coordinates of (0, e).Bwisialo

And your reference supporting this new proposed addition...? Sławomir Biały (talk) 02:37, 19 June 2015 (UTC)
The first two functional properties are verified; that the two functions are instances of (n + x)(1/x) is straightforwardly verifiable; and the final sentence is merely a description of the graphic representation of plugging in different values for n. Bwisialo
Not what I'm asking for. What's the source that the limit of the function (1+x)^{1/x} has anything to do with the extrema of x^{1/x}. Your saying these functional properties are related. If there's no source for this strong claim, you'll need to publish this elsewhere first. We don't accept original arguments. Sławomir Biały (talk) 04:01, 19 June 2015 (UTC)
In using the word "related," I don't intend to mean anything other than what is stated in the subsequent statement in the remainder of the passage. That can be reworded. — Preceding unsigned comment added by Bwisialo (talkcontribs) 04:33, 19 June 2015 (UTC)
The section under discussion is about how e arises as an extremum of x^{1/x}. If what you propose to add is not connected with this after all, then it is redundant with material in the article already. If the family of functions (n+x)^{1/x} is a notable family and published reliable sources have discussed its connection with the mathematical constant e, then we can include some discussion of it in the article. The appropriate context for discussing this family of functions would be determined by how the sources in question make that connection. But this is all hypothetical, because you've been asked to present sources several times, yet haven't done so. Sławomir Biały (talk) 14:04, 19 June 2015 (UTC)
It is more correct to say that the section under discussion is about e: Properties: Exponential-like Functions. The proposed addition is about the functional properties of x(1/x) and (1+x)(1/x) considered as instances of (n+x)(1/x), which exhibits maxima and minima converging toward a limit. As such, e: Properties: Exponential-like Functions is the appropriate context for the proposed change. Again, the proposed change is intended to be a way of "explaining the same material in a different way," which is neither redundant nor asserts a new thesis. It is intended to be a way of explaining the functional properties of x(1/x) (a maxima property) and (1+x)(1/x) (a limit property) in relationship to one another.
The issue under dispute seems to come down to this: Does (n+x)(1/x) need to be in published works in order to be used in the section/article as way of explaining functional properties of exponential-like equations? Does (n+x)(1/x) count as original research? Ultimately, I consider (n+x)(1/x) as an explanatory way of representing a set of routine calculations, which fall within the guidelines of acceptable use and which do not constitute original research -- the calculations being: using various values between 0 and 1 and graphing the results.Bwisialo
No, this is not the issue. You need to find sources that relate (n+x)^{1/x} to the mathematical constant e, which is the subject of this article, and that do so in a way that connects the limits of one function to the extrema of another, using this family of functions. As far as I can tell, none of what you have said here actually does what you say it does, namely "explaining the functional properties of x(1/x) (a maxima property) and (1+x)(1/x) (a limit property) in relationship to one another." Indeed, all you have shown is that there is a one parameter family of functions between two given functions. That's true for any pair of functions at all, so it cannot be used to "explain" how a property of one is related to a different property of another. Although it's true that \lim_{x\to 0}(1+x)^{1/x}=e and the maximum of x^{1/x} is at x=e, you cannot assert that these are related "because the family (n+x)^{1/x}". That's a classic non sequitur fallacy, and surely requires a source: WP:SYN. And no, WP:CALC is absolutely not about this. And regardless of how we read "routine" there, a precondition of WP:CALC is that you get consensus, which you clearly do not have. If you disagree, go ahead and ask for clarification at WP:OR/N, but you're not likely to get a very different response there. Sławomir Biały (talk) 14:33, 5 July 2015 (UTC)
As I stated in my previous post, and as I read your post, the issues under dispute concern questions of sources and original research. You are certainly correct that consensus is required. To clarify a few other points, however, I would add the following. First, "explaining" does not necessarily mean, and does not in this case mean, anything more than "describing" something in a particular way. Your addition of "because of" states a new thesis and goes beyond what the proposed change is intended to state. Second, for what it's worth, it is not true that "any pair of functions" can be related to one another as instances of a single-parameter family; and the only single-parameter family that relates x(1/x) and (1+x)(1/x) is the one used in the proposed change, though this is not the point of the proposed change.Bwisialo
Yes, consensus is required, and I don't see consensus emerging from this discussion. Instead, you've asserted on the one hand that your one parameter family "explains" something (which it does not), and on the other that it does not (in which case it is irrelevant and so already covered in the article). Here you continue to defend your one-parameter family as being relevant, because you labor under the mistaken belief that this family is uniquely defined. In actual fact, any two real-valued continuous functions on an interval are homotopic. The homotopy is not uniquely defined, as you maintain. It is trivial to find many such examples for the pair of functions x^{1/x} and (1+x)^{1/x}. For example, nx^{1/x} + (1-n)(1+x)^{1/x}, x^{n/x}(1+x)^{(1-n)/x}, etc... This is why, to mention your example in connection with the mathematical constant e, we need reliable sources that make the connection. If we eliminate the original research from your proposed change, all it contains is the following two pieces of encyclopedically useful information: \lim_{x\to 0}(1+x)^{1/x}=e and that the maximum of x^{1/x} occurs at x=e. Both of these facts are already covered in the article. Sławomir Biały (talk) 11:38, 8 July 2015 (UTC)
You are correct concerning homotopy. I should have been more specific in using "single-parameter." I should have said, "the only single-parameter, single-term defined family...." As for the remainder of your points, our disagreements have already been stated. And yes, other editors' input would be required for a consensus to emerge. Bwisialo 01:37, 9 July 2015 (UTC)
You're still wrong. For example, (n+x + n(1-n)x^{2015})^{1/x}, ((1-n^2) + x)^{1/x},(x+\sin(n\pi/2))^{1/x}, (etc...) are each one "term", or at least do not consist of more "terms" than your original example. I suggest that you drop the assertion that the family you've given is somehow special, that invoking it is an exception to WP:OR because of its specialness and WP:CALC. We really can't use this unless you have a reference linking it to the mathematical constant e. It's that simple. Sławomir Biały (talk) 13:16, 9 July 2015 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── I am here because Sławomir Biały pinged WT:MATH. Having quickly glanced over the discussion and the proposed change, it is my opinion that the addition runs afoul of rules about original research by synthesis and proper weight: while the basic claim (this is a family that interpolates two cases involving the number e) is correct, for us to include this in the article there should be some some source that writes about this particular family in the context of the number e. --JBL (talk) 14:55, 9 July 2015 (UTC)

Fair enough. I tried to advance as far as I could arguments in favor of the proposed change, but I understand the arguments against it. Thank you. Bwisialo — Preceding undated comment added 17:17, 9 July 2015 (UTC)

In reverting the proposed change below JohnBlackburne writes, "rv as consensus for change and clear opposition after lengthy discussion." The change below is entirely different than the previously proposed change and it is verifiable with a cited source. There has been no discussion of the change below, and the change below resolves the problem of original research with a cited source. Proposed change:

Several properties of exponential functions can be connected with the exponential inequality
e^t \ge 1+t\,

where et = (1 + t) only at t = 0.[1] Based on this inequality expression, e1/x ≥ 1 + 1/x and, hence, e ≥ (1 + 1/x)x, such that

f(x) = \left( 1 + \frac{1}{x} \right)^x
The global maximum of \sqrt[x]{x} occurs at x = e.

is an increasing function with a horizontal asymptote at y = e. More generally,

\lim_{x\to\infty} \left( 1 + \frac{n}{x} \right)^x = e^n.

Additionally, the above exponential inequality can be used solve Steiner's Problem. The expression

 e^{\frac{x-e}{e}} \ge 1+ {\frac{x-e}{e}}\,

can be reduced to \sqrt[e]{e} \ge \sqrt[x]{x}\,, yielding the solution that the global maximum for the function

 f(x) = \sqrt[x]{x} = x^{\frac{1}{x}}

occurs at x = e. — Preceding unsigned comment added by Bwisialo (talkcontribs)


  1. ^ Dorrie, Heinrich (1965). 100 Great Problems of Elementary Mathematics. Dover. p. 44-48; 368. Retrieved 13 July 2015. 
We can use some of this. I have added the inequalities to a new section on properties, to do with inequalities. Arguably these are more fundamental than the connection with Steiner's problem. I have included the proof of Steiner's problem, with edits. Sławomir Biały (talk) 12:01, 13 July 2015 (UTC)

287,000 digits in 1988 and 1,000,000 in 1992[edit]

I (Richard Nungester) found e to 1,000,010 decimal places 1992-02-12. This precedes the currently listed table entry of 1994-04-01 by Nemiroff & Bonnell. I posted the program header in a Usenet post 1993-10-05 that includes the program date, algorithm (with 4 enhancements of my own), execution platform, execution timing, and results (first 20 and last 20 digits). I still have the Turbo Pascal 6.0 1-file 1360-line program with "Modified Date" tag of 1992-02-12. It can still be run. I am a novice at Wikipedia editing and submission guidelines. How should I proceed? Rick314 (talk) 20:54, 21 June 2015 (UTC)

I also recovered my 1988-05-24 files resulting in 287,187 decimal places, done on an HP-150 with 8 MHz 8088 CPU in 30.8 hours. This was over twice Wozniak's prior results with algorithmic improvements explained in the source code file header, so seems worthy of another table row entry. I am planning on uploading the key files to Wikipedia Commons and referencing them as proof. Please let me know if anything else would be expected before I go forward with this. Rick314 (talk) 00:00, 26 June 2015 (UTC)
I don't think it's a good idea to add these. The one beating Wozniak, since it was actually "published" online, seems like it would be more appropriate that the other, unpublished one. Most of the entries of the table are really problematic, falling on the wrong side of sources like WP:SELFPUB, WP:RS. This post is just one indication of why Wikipedia keeping "it's own" list of numerical records is a bad idea: such a list is inherently problematic. I think the table should be reduced, including only those records that are notable in the sense of having been published in reliable sources, or possibly those self-published by experts with a proven publication record. (The latter would be the most generous interpretation of WP:SELFPUB.) Sławomir Biały (talk) 23:13, 28 June 2015 (UTC)
Thank you Slawomir. Your comments and links were very helpful, but I do hope to continue with my table changes. Regarding WP:SELFPUB keep in mind that changes to the table are only a statement about what I did and seem to fit the exceptions given there. WP:RS seems to apply to whole Wikipedia articles not just lines in an existing table in an article. My reference to the 1993 Usenet post (above) and references to the 1988 source code and 1992 source code show dates, algorithms and results (first and last digits, in the file headers). These programs can still be compiled and executed, and I have have 3rd-party verification of my complete output. The 1988 program is clearly the predecessor of the Usenet-described 1992 program (with only its 2 additional algorithm enhancements). So I think I am ready to proceed with the table updates, but further comments are welcome. Rick314 (talk) 02:54, 8 July 2015 (UTC)
That exception to SELFPUB is typically for biographical articles (a better link is WP:SPS; for some reason WP:SELFPUB links to the incorrect subsection). This is not an article about you or your accomplishments, and so that exception does not apply. WP:RS does indeed apply to all sources used in an article. Sławomir Biały (talk) 11:22, 8 July 2015 (UTC)
Slawomir: You say "is typically for", meaning the application of the rule sited is unclear to begin with. "This is not an article about you or your accomplishments" is true, but the lines I will add to the table are exactly about me and my accomplishments just as the other lines in the table are about individual accomplishments. Existing references already violate the logic you are trying to defend. For example, the reference for 1994 Nemiroff & Bonnell says "Email from Robert Nemiroff and Jerry Bonnell" (the 2 people claiming the accomplishment and therefore not a third party) and then refers to a web page (not an email) published by them. The 1999 Gourdon reference says "Email from Xavier Gourdon to Simon Plouffe", and again sites a web page (not an email) written by Gourdon claiming verification by Gourdon (not a third party). I could go on. Just look at what already exists in the table. But I think all those entries should stay. There is no doubt the people listed did what they say they did. Look at my documentation referenced in this discussion above. It is actually better than several already existing table references and I have emails that confirm third-party (not me) verification of my results. Or are you just saying that I can't update the article page but someone else can on my behalf? Could other knowledgeable Wikipedia authors please join in with an opinion? Rick314 (talk) 03:47, 9 July 2015 (UTC)
That is an incorrect reading of SELFPUB that probably should be clarified at the actual policy page. The exemption is only for articles about a person, their works, activities, etc. For example, in an article on a Grothendieck topology we could cite self-published work of Alexander Grothendieck. But it's pretty clear that the policy does not intend an exemption for random people on the internet to cite their own unpublished or self-published works referring to their accomplishments, views, activities, etc. Indeed, WP:SPS specifically says that self-published media are largely not acceptable as sources. Anyone can claim that their self-published sources are about their views or accomplishments, so the mantra "It's about my accomplishments" is not a get-out-of-jail-free card that can just be invoked whenever someone thinks their own self-published sources deserve mentioning in an article that is not specifically about them (also, see WP:COI). Anyway, your statement that this is just about your accomplishments is wrong. You aren't just claiming that you computed some number of digits, but that number of digits was a record. That's a factual statement about the world that requires a reliable source. You would need to make a very strong case that the source you want to cite is reliable for making such a statement about the world, and that the exemption at WP:SELFPUB applies. When there is a disagreement over the interpretation of policy, WP:CONSENSUS needs to be established, and I think it is very unlikely that any consensus will emerge from this marginal interpretation of the reliable sources guideline. If you want a wider input, you can drop a note at the reliable sources noticeboard, but I can basically guarantee that the response there will not be very different from my own.
As for the other entries in the table, I believe that at least some of them should be removed. Xavier Gourdon is a published expert, so this actually would fall under the exemption mentioned at WP:SPS, but that is not a very strong case. I'm all for removing entries on the table that lack secondary sources. Anyone with a computer can compute billions of digits of e, as the case of Alexander Yee shows. Sławomir Biały (talk) 11:43, 9 July 2015 (UTC)
Slawomir: Rather than continuing to discuss this with me, I see you concluded you are right and deleted much of the Known Digits table, substituting the incorrect statement "Since that time [1978], the proliferation of modern high-speed desktop computers has made it possible for amateurs to compute billions of digits of e." Let's continue this discussion at the math project page Wikipedia_talk:WikiProject_Mathematics#E_(mathematical_constant) where your knowledge of the subject and Wikipedia editing rights are brought into question. Then we can return here after that is resolved. Rick314 (talk) 04:53, 10 July 2015 (UTC)
See Wikipedia_talk:WikiProject_Mathematics#E_(mathematical_constant) and I think we are done here. In summary, the answer to my original How should I proceed? is that I first need to have my work published by the right person in the right place (details in the discussion) and then it could be added to the table. The same applies to others whose table entries were removed by Slawomir. Thanks to all who participated in this discussion. Rick314 (talk) 18:10, 11 July 2015 (UTC)


Hi, I'm not a mathematician, I came here after reading the article on Conlon Nancarrow, who wrote a piece for player piano ([1]) in the ratio of e:π. From the ==History== section I followed the link to Bernoulli where a note in Jacob Bernoulli#References appears to say that his published solution of 1690 was the answer to his own self-posed problem, published in 1685. To clarify the chronology of this History section, I wonder if this could somehow be worked into the sentence, such as

"The discovery of the constant itself is credited to Jacob Bernoulli,[7][8] who in 1690 published an attempt[9]<ref>Note from the above Bernoulli article</ref> to find the value of the following expression (which is in fact e): ..." >MinorProphet (talk) 12:03, 3 August 2015 (UTC)