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From Encyclopedia of Mathematics
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This project is based on an electronic version of the "Encyclopaedia of Mathematics", published by Kluwer Academic Publishers until 2003, and by Springer after that. The encyclopaedia goes back to the Soviet Matematicheskaya entsiklopediya (1977), originally edited by Ivan Matveevich Vinogradov.

The electronic version had its formulae written in $\rm \TeX$, which were saved as png images. On its way through the various publishers the original $\rm \TeX$ source code was lost, therefore, to edit a formula in one of these original pages requires to retype the code for that formula from scratch.

For the project, it will be of big help to transcribe the old pages. To make this easy, it was decided to use MathJax, which allows to use Plain $\rm \TeX$ or $\rm \LaTeX$ for formulae encoding.

Some help on this is given on the help pages.

The installed software and extensions for this project can be seen here: Special:Version. This collection may be updated and extended.

Comments

Please add comments and/or suggestions here:

This is a useful page, but it should be more visible. Maybe the navigation toolbar should contain it (among "main page", ..., "help"). --Boris Tsirelson 08:14, 14 December 2011 (CET)

I have added a link to this page on the Help:Contents page. Nathan Brothers 17:28, 16 December 2011 (EST)

The footer "How to Cite this Entry" is appropriate for articles, but probably not for user pages etc. --Boris Tsirelson 15:05, 14 December 2011 (CET)

I have transmitted your proposals to the admins. Ulf Rehmann 22:44, 14 December 2011 (CET)

I rewrote Measurable space; please look. In particular, in the bibliography I gave links to MathSciNet (following a suggestion by Ulf Rehmann); but for now they use my private template User:Boris Tsirelson/MR; if you like it, please move it into Template:MR (with needed changes, if any). --Boris Tsirelson 21:43, 20 December 2011 (CET)

Ok, I have made MR a global template and have added a ZBL template as well, see Measurable space. --Ulf Rehmann 22:53, 21 December 2011 (CET) Same for Tamagawa number --Ulf Rehmann 00:38, 23 December 2011 (CET)
Good news: even working with no subscriptions, clicking a Zbl link I still get a review, in contrast to an MR link (MR says: "For users without a MathSciNet license, Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews.)".
That corresponds to Zbl's policy: They do allow up to three requests even to non subscribers. --Ulf Rehmann 10:40, 23 December 2011 (CET)
Bad news: even working with an MSC subscription (via my university), clicking a Subject Classification link I get:
A username and password are being requested by http://ams.math.uni-bielefeld.de. The site says: "MathSciNet Authentication".
--Boris Tsirelson 10:13, 23 December 2011 (CET)
That is different here: Under a vpn connection I do get access -- even from my home notebook, and I can switch on and off that access by using or not using vpn (as it should happen). But: after switching on, I have to reload the EoM page before my browser realizes that access is given.--Ulf Rehmann 10:40, 23 December 2011 (CET)
And still, the MSC template is not good for primary-only cases, because the "ParserFunctions" extension is missing. --Boris Tsirelson 10:21, 23 December 2011 (CET)
Unfortunately that is true. An updated software version which should fix this hopefully will be installed in early January. --Ulf Rehmann 18:44, 23 December 2011 (CET)
Here is an MSC template which works correctly, but without #if clause: User:Rehmann/sandbox/MSC --Ulf Rehmann 00:33, 7 January 2012 (CET)
Wow! --Boris Tsirelson 08:16, 7 January 2012 (CET)
MSCwiki links added to help non MSN supported readers (not perfect for secondary MSC)--Ulf Rehmann 14:10, 7 January 2012 (CET)

Our readers

It seems, most of EoM articles are targeted at graduate math students and professional mathematicians; but some are accessible to an interested layman. I try to collect these; for now, starting on "A", "B". --Boris Tsirelson 10:36, 14 December 2011 (CET)

Absolute value + Additivity + Algebra + Algebra, fundamental theorem of + Algebra of sets + Analytic geometry + Arabic numerals + Arithmetic mean + Arithmetic root + Assertion + Associativity + Axiomatic method

Ball + Bayes formula + Bell inequalities + Benford law + Bernoulli experiment + Bernoulli random walk + Bertrand paradox + Binary tree + Binomial distribution + Bit

Should we introduce (two or more) levels, and mark articles accordingly? --Boris Tsirelson 11:17, 15 December 2011 (CET)

I am not sure. Maybe it is good to just have a list (category) of articles which are suited for non professionals, in order to attract such readers. --Ulf Rehmann 13:21, 15 December 2011 (CET)

Preferred style

Many articles have (near the end) the section "Comments" (and often also the second "References" section after "Comments"). What does it mean? And should we follow this pattern when editing and creating articles? --Boris Tsirelson 11:22, 15 December 2011 (CET)

This is due to the history of the encylopaedia. It underwent various (print and electronic) editions, which not always resulted in a rewrite of an article, but just in an update by amending a comment (sometimes there are several, each with its own reference list). There is no need to follow this pattern now since wikipedia does allow better ways of updating.--Ulf Rehmann 13:21, 15 December 2011 (CET)

I guess, some day the use of our new templates will become a part of recommendations posted on our help pages. Here is another question of style.

I observe a typical pattern in the existing articles: the title, mentioning a notion, is immediately continued by the definition of the notion. Sometimes a slanted text in between gives some context or some synonims.

I propose to use a definition style using a complete sentence with predicate consisting of copula+predicative, as this is common in (written) English. Synonyms could be given, maybe after a prefix "also:" and with an extra page for that synonym referencing to the actual page.Context extensions of some notion should be given within the text, if there is no need to distinguish against other uses of that notion, in which case a disambiguation page should be used. See below my suggestions.--Ulf Rehmann 19:43, 23 December 2011 (CET)

Examples:

Binary relation
A two-place [[Predicate|predicate]] on a given set.
Preferable: A binary relation is a two-place [[Predicate|predicate]] on a given set.--Ulf Rehmann 19:43, 23 December 2011 (CET)
Spectral density
of a stationary stochastic process or of a homogeneous random field in n-dimensional space
The [[Fourier transform|Fourier transform]] of the covariance function of a stochastic process which is stationary in the wide sense...
Preferable: In this article, the spectral density of a stationary stochastic process or of a homogeneous random field in n-dimensional space is described.--Ulf Rehmann 19:43, 23 December 2011 (CET)
Inter-quantile width
inter-quantile distance, inter-quantile range
Preferable: Also: inter-quantile distance, inter-quantile range --Ulf Rehmann 19:43, 23 December 2011 (CET)
The difference between the lower and upper quantiles of the same level (cf. [[Quantile|Quantile]]).

But in rare cases the definition appears much later (as in Berwald connection).

Maybe here a link to the text part giving the formal definition could be placed under the title.--Ulf Rehmann 19:43, 23 December 2011 (CET)

On Wikipedia the pattern of the beginning is different: the title is not a part of the definition; an example:

Binary relation
In [[mathematics]], a '''binary relation on''' a [[set (mathematics)|set]] ''A'' is a collection of [[ordered pair]]s of elements of ''A''.

Thus, what is our preferred style for the start of an article? --Boris Tsirelson 17:28, 23 December 2011 (CET)

Since our language is English, we should use full sentences for definitions, as said above.--Ulf Rehmann 19:43, 23 December 2011 (CET)

Subject classification

What I find more important is to classify articles by MSC (Mathematical Subject Classification) and possibly categorize them according to that. This classification should be done so that it is easily recognizable by bots collecting bibliographic info. Of course MSC is subject to change over time, and there should be a tool to update such a classification easily over the whole collection. (We are lucky, since such a change did just happen via MSC 2000 --> MSC 2010.) Does anybody know if there exist wikimedia extensions which do support a suitable classification (and possibly its update)?--Ulf Rehmann 13:21, 15 December 2011 (CET)

For now I added MSC codes to our categories. It will be much easier to update categories than all articles. About bots collecting bibliographic info, I have no idea. But probably a template can help. Do you know which text should appear on articles to this end? Boris Tsirelson 20:51, 15 December 2011 (CET)
Some html meta tag would do the job like
<meta name="description" content="2010 Mathematics Subject Classifiction 20-XXX" />
and
<meta name="keywords" content="associative algebras, Galois theory, ..." />.
But I think that ought to be done on a pagewise basis. --Ulf Rehmann 12:47, 17 December 2011 (CET)
As an experiment, I added "<nowiki><meta name="keywords" content="probability" /></nowiki>" to the end of "Probability"; it is invisible, but appears on the generated html as "<p><span class="tex2jax_ignore"><nowiki><meta name="keywords" content="probability" /></nowiki></span></p>". Will it do the job? --Boris Tsirelson 16:39, 17 December 2011 (CET)
It seems one cannot put some <meta> tag outside the <body> section of some wiki page (unless there is some wikimedia extension wich helps??). So maybe you just omit the <meta ... /> tag. But apparently at the time being, Google's bots don't visit the EoM pages at all.--Ulf Rehmann 19:33, 25 December 2011 (CET)
Not quite so. I just took an old article (not "Measurable space", this is too recent), asked Google for "interest in abstract differential equations is that the so-called mixed problems" and got the first answer: "Differential equation, abstract - Encyclopedia of Mathematics". --Boris Tsirelson 21:13, 25 December 2011 (CET)
Too slow. On my preprint server, articles are recognized by google within a few days.--Ulf Rehmann 21:49, 25 December 2011 (CET)
It is rumored that Google, seeing a new page, returns to it after some days; if it is changed, Google treats it as volatile, and visits frequently; otherwise it does not. But anyway, (a) I doubt we can hope for a high Google rank, and (b) I doubt we can have many visitors. Just because mathematicians are a small population. Students are a larger population, but these are not our readers, I guess. --Boris Tsirelson 23:04, 25 December 2011 (CET)
But (a),(b) are true for my preprint server as well... --Ulf Rehmann 23:35, 25 December 2011 (CET)

Categories

Concerning categorization I propose to use the sectioning scheme used by the International Congresses of Mathematicians as shown below (I have added the respective two digit MSC codes - please amend/correct):

ICM sectioning scheme, cf. ICM 2010 Corresponding MSC 2010 two digit codes
1. Category:Logic and foundations 03
2. Category:Algebra 06,08,12,13,15,16,17,18,19,20
3. Category:Number theory 11
4. Category:Algebraic and complex geometry 14
5. Category:Geometry 51,52
6. Category:Topology 54,55,57
7. Category:Lie theory and generalizations 22
8. Category:Analysis 26,28,30,31,32,33,40,41,42,43,44
9. Category:Functional analysis and applications 46,47,48
10. Category:Dynamical systems and ordinary differential equations 34,37 (39)
11. Category:Partial differential equations 35
12. Category:Mathematical physics 70,74,76,78,80,82,83,85
13. Category:Probability and statistics 60,62
14. Category:Combinatorics 05
15. Category:Mathematical aspects of computer science 68
16. Category:Numerical analysis and scientific computing 65,68
17. Category:Control theory and optimization 49,93
18. Category:Mathematics in science and technology 81,86,90,91,92,94
19. Category:Mathematics education and popularization of mathematics 00,97
20. Category:History of mathematics 01
List of preliminary MR, Zbl, and MSC templates. --Ulf Rehmann 23:30, 12 January 2012 (CET)
This is obsolete, pleass see below. --Ulf Rehmann 00:16, 27 January 2012 (CET)
The tableau (or some variants) has been used by IMU for the recent ICM section setup, see ICM 2010. (Cf. also: more verbal, ICM 2006, ICM 1998 --Ulf Rehmann 13:21, 15 December 2011 (CET), modified: 19:33, 25 December 2011 (CET)
A good idea; I shall do. --Boris Tsirelson 15:54, 17 December 2011 (CET)
I've made a template here and used it in Tamagawa number. It would be better to use the template "[ 2010 Mathematics Subject Classification {{{1}}}{{#if:{{{2|}}}|,({{{2}}})|}} ]", since the call {{MSC|11F70}} should not generate "11F70,()". Unfortunately, the "ParserFunctions" extension is still missing.
An "MSC" template is worth using, since (1) changing it one can change the appearance of all MSC at once, and (2) in 2020 :-) one can instruct the template to replace some codes with new ones. --Boris Tsirelson 16:57, 18 December 2011 (CET)
--Boris Tsirelson
I have set up some algebra (etc.) subcategories with some new template User:Rehmann/sandbox/MSCtop‎. (Eventually all the MSC templates should be combined as soon as we will have the ParserFunctions extensions or so.) --Ulf Rehmann 23:29, 7 January 2012 (CET)
We need an msc macro which automatically produces not only the entry+link for the primary/secondary number, but also inserts the respective [[Category:<blah>]] line entries to categorize the pages. But this requires (at least) the ParserFunctions extensions, maybe more.--Ulf Rehmann 00:35, 8 January 2012 (CET)
The existing MSC template does not work correctly for such cases as [ 2010 Mathematics Subject Classification MSN: 60-01 | MSCwiki: 60-01  ]. --Boris Tsirelson 13:09, 12 January 2012 (CET)
Yes, I know. That cannot be resolved without "#if"-clause, so I drafted another template User:Rehmann/sandbox/MSC-X for this special purpose (middle entry an hyphen '-') (and nagged the sysadmins again for installing #if). --Ulf Rehmann 16:44, 12 January 2012 (CET)
Here is a list of all the (preliminary) MR. ZBL, and MSC templates. --Ulf Rehmann 23:26, 12 January 2012 (CET)
ParserFunctions works! Wow! --Boris Tsirelson 09:43, 19 January 2012 (CET)
Yes, that's good. It also offers some nice string handling functions. For further new extensions, see Special:version.--Ulf Rehmann 11:07, 19 January 2012 (CET)
New MSC & categorization templates

Here are new categorization templates. It suffices to inlude an MSC entry in a page, then the template will automatically add the respecitve categories to that file. Please use them from now and let me know any problems you might encounter. --Ulf Rehmann 23:41, 26 January 2012 (CET)

Yes, I did it on Absorbing state, and strangely, it got three categories "Markov chains", "Probability and statistics", "Probability theory and stochastic processes". Before it had only the "Markov chains" category (this being a subcategory of "Markov processes" and so on, according to MSC). Is it the intended behavior? --Boris Tsirelson 09:14, 27 January 2012 (CET)
Yes: According to our table above the MSC 60Jxx requires an entry in "13. Category:Probability and statistics". The MSC yields two other categories 60-XX Category:Probability theory and stochastic processes and 60Jxx Category:Markov processes. --Ulf Rehmann 11:17, 27 January 2012 (CET)
Usually (I mean, in Wikipedia) members of a subcategory are not members of the category. See for example [1] and [2]. Otherwise high-level categories will be terribly overpopulated. --Boris Tsirelson 14:45, 27 January 2012 (CET)
That's right. However, right now there is no big danger of any overpopulated categories like that, and it is more cumbersome to click one's your way through all analysis or algebra related subcategories in order to find out what is there. If this changes, it is very easy to remove files of a big subcategory from some supercategory, since this requires only to remove one entry in Template:Category. This is the advantage of a list controlled categorization: Entries are generated "on the fly" every time a page is called.
OK, I see. --Boris Tsirelson 19:10, 27 January 2012 (CET)
Well, "Absorbing state" probably is now as it should be (please check).
And please look at "Category:Distribution theory"; any remarks?
As a consequence, now "Category:Probability and statistics" contains subcategories of different levels: both "Category:Probability theory and stochastic processes" and "Category:Limit theorems"; should it be so?
Maybe not. I had seen this last night as well for Category:Number theory and a few others, my solution was to use MSCwiki for indicating their MSC, which is not a good idea, as this will cause confusion. I now have modified Template:Category so that it does >not< categorize if called from a category page, so those pages have to be categorized by an explicit entry. --Ulf Rehmann 00:43, 28 January 2012 (CET)
(But do not bother about "Category:Probability", I'll delete it, but only after rerouting all links to it.) --Boris Tsirelson 21:16, 27 January 2012 (CET)
I wonder whether such a concept could be introduced for references as well. Generating the pagewise lists over a global list (or several such, the entries being already pre-formated) would ease to control the pagewise reference lists. Certainly many related pages share quite some reference entries. After all, TeX has a similar system (bibtex). --Ulf Rehmann 15:54, 27 January 2012 (CET)
Yes, I recall that such means are used on Citizendium in chemistry and biology articles, but not in math articles. I am not sure that the result is worthy of the effort. I also wonder, in which namespace the bibliographic entries will be. Mainspace? No, it is for articles only. Templates? No, it is editable by admins only. --Boris Tsirelson 19:09, 27 January 2012 (CET)
Technical Categories

How about a few "technical categories"? I think of "Category:TeX encoded" and "Category:TeX encoding wanted".

People interested in editing certain pages but technically less skilled could just enter an entry [[Category:TeX encoding wanted]] and advertise these in order to get it converted by some $\rm \TeX$ freak. --Ulf Rehmann 11:52, 27 January 2012 (CET)

No objections. --Boris Tsirelson 14:48, 27 January 2012 (CET)

Here is this tex thing: Template:TEX. The state of the categories needs to to be updated.

One could think of more categories which reflect the state of pages, concerning their actualization state or the state of their references. --Ulf Rehmann 17:42, 29 January 2012 (CET)

The tableau again

But why is 37 in "Category:Partial differential equations"? It should be only in Category:Dynamical systems and ordinary differential equations. --Boris Tsirelson 16:55, 28 January 2012 (CET)

Probably because of mutual references between 35, 37, Hamiltonian and these KDF and NLS stuffs. But maybe you are right: if some article belongs into both that should be decided for that article individually. --Ulf Rehmann 19:28, 28 January 2012 (CET)
Yes; now "Approximation by periodic transformations" does not belong to "Category:Partial differential equations", which was rather unexpected (at least to me). --Boris Tsirelson 20:17, 28 January 2012 (CET)

References

Now, having ParserFunctions, we can choose a style for refs (and support it by templates).

For now refs are coded like that: 

<table><TR><TD valign="top">[1]</TD> <TD  valign="top">
H. Cartan,   S. Eilenberg,   "Homological algebra" ,  Princeton Univ. Press  (1956)
</TD></TR><TR><TD  valign="top">[2]</TD> <TD valign="top">
A. Grothendieck,    "Sur quelques points d'algèbre homologique"  ''Tohoku Math. J.'' ,  '''9'''  (1957)  pp. 119–221
</TD></TR></table>

and rendered like that:

[1] H. Cartan, S. Eilenberg, "Homological algebra" , Princeton Univ. Press (1956)
[2] A. Grothendieck, "Sur quelques points d'algèbre homologique" Tohoku Math. J. , 9 (1957) pp. 119–221

At least, we can create template(s) that save us the trouble of writing all these "<table><TR><TD..."

The best is probably the $\LaTeX$-like automatic numbering; but I doubt we can do it. If we cannot, then articles are not easily editable (not quite "wiki-wiki"), since a new source inserted in the middle of the list requires manual change of many numbers (both in the refs list and, worse, throughout the article). I did it several times working on "Measurable space"; not nice. No wonder that linking by numbers is not used on Wikipedia. On the other hand, our articles tend to be much less volatile than these of Wikipedia. Any comment?

--Boris Tsirelson 12:38, 19 January 2012 (CET)

The mediawiki equvalent of the table above is
{|
|-
|valign="top"|[1]||valign="top"| H. Cartan, S. Eilenberg, "Homological algebra" , Princeton Univ. Press (1956)
|-
|valign="top"|[2]||valign="top"| A. Grothendieck, "Sur quelques points d'algèbre homologique" ''Tohoku Math. J.'' , '''9''' (1957) pp. 119-221
|-
|}
which looks much easier and renders like this:
[1] H. Cartan, S. Eilenberg, "Homological algebra" , Princeton Univ. Press (1956)
[2] A. Grothendieck, "Sur quelques points d'algèbre homologique" Tohoku Math. J. , 9 (1957) pp. 119-221
In fact, the strings |valign="top" probably can be omitted:
[1] H. Cartan, S. Eilenberg, "Homological algebra" , Princeton Univ. Press (1956)
[2] A. Grothendieck, "Sur quelques points d'algèbre homologique" Tohoku Math. J. , 9 (1957) pp. 119-221
However, this concept conflicts with our earlier convention to use '|' as a separator between MR and Zbl numbers. Maybe that should be modified.
--Ulf Rehmann 20:55, 19 January 2012 (CET)
If you want automatic numbering, why not simply:
  1. H. Cartan, S. Eilenberg, "Homolthogical algebra" , Princeton Univ. Press (1956)
  2. A. Grothendieck, "Sur quelques points d'algèbre homologique" Tohoku Math. J. , 9 (1957) pp. 119-221
But why numbering at all? As has been said above: If there are references by number then automatic numbering (or manual renumbering) requires changing of the references, too, and if there are no references numbers are not used. In the text, references like (Cartan-Eilenberg, 1956) are more friendly to the reader. Personally, I prefer bibliographies in chronological order, possibly split in recommended reading, references, and historical sources.
--Peter Schmitt 23:35, 19 January 2012 (CET)
One may want numbered or labeled references, since this allows precise referencing, like "Thm. 1: <blah>. For proof cf. [42, p. 456f]" or the like. --Ulf Rehmann 00:35, 20 January 2012 (CET)
"Thm. 1: <blah>. For proof cf. [Cartan-Eilenberg, p. 456f]" is only slightly longer, carries the same information, and may often be understood without looking on the references. --Peter Schmitt 02:37, 20 January 2012 (CET)
One needs a reference list anyway, since most citations are from journals (and you don't want to quote the stuff say from ref 2 above inline). This could be achieved by using <ref "name"> ... </ref> tags and the {{reflist}} template, but then the automatically created list won't be sorted. So your proposal could be achieved if one uses just alphanumeric tags for each ref (as is often done in math literature) and sort the list by hand (unless a template is found to sort some list??) -- no renumbering needed in case of new refs.--Ulf Rehmann 13:08, 20 January 2012 (CET)

(unindent)
By a (not very extensive) search I found [3]and [4]. --Peter Schmitt 18:56, 20 January 2012 (CET)

Thanks. How would one make these programs work within a wikimedia template? --Ulf Rehmann 19:36, 20 January 2012 (CET)

Username: acceptable and unacceptable

Is it written somewhere, which usernames are acceptable here?

No, its not (yet), finger glitch, corrected.--Ulf Rehmann 11:51, 26 January 2012 (CET)

As far as I see, "TrialAndError" is rejected, while "AgelessMale", "Abrar.p496" etc. are accepted. On Wikipedia, almost every name is acceptable. On Citizendium, only real names are (thus, "Rafael.greenblatt" would be " "Rafael Greenblatt" on CZ). We should publish a rule before punishing for its violation. --Boris Tsirelson 10:57, 26 January 2012 (CET)

Sure.--Ulf Rehmann 11:51, 26 January 2012 (CET)

Time zones

I just noticed that the history pages display UTC/GMT, while the time stamps produced by signatures are CET. In order to avoid confusion, they should give UTC, too. --Peter Schmitt 01:18, 28 January 2012 (CET)

Something is wrong

I try to edit Convergence of measures as usual (just adding MSC and category); but as a result the page becomes empty. (Twice.) --Boris Tsirelson 16:26, 7 February 2012 (CET)

I cannot confirm this: I edited the page twice, the first time under my admin account, and by adding MSC, the second time under my account TestUser with just ordinary user permission, and by adding the tex category "TeX wanted". Everything worked fine, as it seems. --Ulf Rehmann 19:00, 7 February 2012 (CET)
Rather mysterious. I got it again, this time on Cramér theorem. I added
{{MSC|60F10}}
[[Category:Limit theorems]]
did "Show preview" (nothing strange here) and then "Save", and got the empty page! --Boris Tsirelson 20:08, 7 February 2012 (CET)
More observations. This time I was not asked to answer an arithmetic question; but the previous time I was, with the explanation "since you are adding an external link". More: I use exactly the same browser and system as all the time before. --Boris Tsirelson 20:12, 7 February 2012 (CET)
And now, on User:Boris Tsirelson/sandbox1 I got again "Your edit includes new external links" but nevertheless the page did not get blank. --Boris Tsirelson 20:17, 7 February 2012 (CET)
And now it went smoothly on Cramér theorem with the same procedure as I did before.
But I also note that the behavior of the edit window changes (another reaction to right-click). --Boris Tsirelson 20:27, 7 February 2012 (CET)
How to Cite This Entry:
EoM:This project. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=EoM:This_project&oldid=20890
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