Satz von Schwarz

de

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Satz von Schwarz

Quality:

Symmetry of second derivatives - theorem. Article “Satz von Schwarz” in German Wikipedia has 21.1 points for quality (as of July 1, 2026). The article contains 5 references and 8 sections.

This article has the best quality in English Wikipedia. Also, this article is the most popular in that (German) language version.

Since the creation of article “Satz von Schwarz”, its content was written by 52 registered users of German Wikipedia and edited by 340 registered Wikipedia users in all languages.

The article is cited 31 times in German Wikipedia and cited 520 times in all languages.

The highest Authors Interest rank from 2001:

  • Local (German): #6305 in September 2004
  • Global: #27754 in September 2004

The highest popularity rank from 2008:

  • Local (German): #38943 in June 2020
  • Global: #117357 in October 2019

There are 17 language versions for this article in the WikiRank database (of the considered 55 Wikipedia language editions).

The quality and popularity assessment was based on Wikipédia dumps from July 1, 2026 (including revision history and pageviews for previous years).

The table below shows the language versions of the article with the highest quality.

Languages with the highest quality

#LanguageQuality gradeQuality score
1English (en)
Symmetry of second derivatives
51.7052
2Portuguese (pt)
Teorema de Clairaut-Schwarz
42.0492
3Korean (ko)
이계 도함수의 대칭성
39.8777
4French (fr)
Théorème de Schwarz
25.2796
5Chinese (zh)
二阶导数的对称性
21.1879
6German (de)
Satz von Schwarz
21.0597
7Indonesian (id)
Simetri turunan kedua
14.5868
8Arabic (ar)
مبرهنة شفارز
14.1421
9Russian (ru)
Равенство смешанных производных
13.5253
10Italian (it)
Teorema di Schwarz
12.2457
More...

The following table shows the most popular language versions of the article.

Most popular in all the time

The most popular language versions of the article "Satz von Schwarz" in all the time
#LanguagePopularity awardRelative popularity
1English (en)
Symmetry of second derivatives
929 132
2German (de)
Satz von Schwarz
466 977
3Italian (it)
Teorema di Schwarz
307 107
4French (fr)
Théorème de Schwarz
258 640
5Spanish (es)
Teorema de Clairaut
226 850
6Russian (ru)
Равенство смешанных производных
87 421
7Polish (pl)
Twierdzenie Schwarza
71 310
8Chinese (zh)
二阶导数的对称性
67 651
9Portuguese (pt)
Teorema de Clairaut-Schwarz
59 619
10Japanese (ja)
ヤングの定理
27 151
More...

The following table shows the language versions of the article with the highest popularity in the last month.

Most popular in June 2026

The most popular language versions of the article "Satz von Schwarz" in June 2026
#LanguagePopularity awardRelative popularity
1English (en)
Symmetry of second derivatives
2 820
2German (de)
Satz von Schwarz
1 262
3French (fr)
Théorème de Schwarz
547
4Italian (it)
Teorema di Schwarz
465
5Spanish (es)
Teorema de Clairaut
333
6Russian (ru)
Равенство смешанных производных
303
7Chinese (zh)
二阶导数的对称性
219
8Polish (pl)
Twierdzenie Schwarza
201
9Portuguese (pt)
Teorema de Clairaut-Schwarz
118
10Japanese (ja)
ヤングの定理
99
More...

The following table shows the language versions of the article with the highest Authors’ Interest.

The highest AI

Language versions of the article "Satz von Schwarz" with the highest Authors Interest (number of authors). Only registered Wikipedia users were taken into account.
#LanguageAI awardRelative AI
1English (en)
Symmetry of second derivatives
113
2German (de)
Satz von Schwarz
52
3French (fr)
Théorème de Schwarz
41
4Italian (it)
Teorema di Schwarz
35
5Spanish (es)
Teorema de Clairaut
17
6Chinese (zh)
二阶导数的对称性
14
7Danish (da)
Clairauts sætning
11
8Catalan (ca)
Teorema de Clairaut
10
9Japanese (ja)
ヤングの定理
10
10Portuguese (pt)
Teorema de Clairaut-Schwarz
10
More...

The following table shows the language versions of the article with the highest Authors’ Interest in the last month.

The highest AI in June 2026

Language versions of the article "Satz von Schwarz" with the highest AI in June 2026
#LanguageAI awardRelative AI
1Ukrainian (uk)
Теорема Клеро — Шварца
1
2Arabic (ar)
مبرهنة شفارز
0
3Catalan (ca)
Teorema de Clairaut
0
4Danish (da)
Clairauts sætning
0
5German (de)
Satz von Schwarz
0
6English (en)
Symmetry of second derivatives
0
7Spanish (es)
Teorema de Clairaut
0
8French (fr)
Théorème de Schwarz
0
9Indonesian (id)
Simetri turunan kedua
0
10Italian (it)
Teorema di Schwarz
0
More...

The following table shows the language versions of the article with the highest number of citations.

The highest CI

Language versions of the article "Satz von Schwarz" with the highest Citation Index (CI)
#LanguageCI awardRelative CI
1English (en)
Symmetry of second derivatives
167
2Chinese (zh)
二阶导数的对称性
107
3Polish (pl)
Twierdzenie Schwarza
54
4French (fr)
Théorème de Schwarz
48
5German (de)
Satz von Schwarz
31
6Italian (it)
Teorema di Schwarz
25
7Spanish (es)
Teorema de Clairaut
17
8Portuguese (pt)
Teorema de Clairaut-Schwarz
15
9Catalan (ca)
Teorema de Clairaut
13
10Japanese (ja)
ヤングの定理
13
More...

Scores

Estimated value for Wikipedia:
German:
Global:
Popularity in June 2026:
German:
Global:
Popularity in all years:
German:
Global:
Authors in June 2026:
German:
Global:
Registered authors in all years:
German:
Global:
Citations:
German:
Global:

Quality measures

Interwikis

#LanguageValue
arArabic
مبرهنة شفارز
caCatalan
Teorema de Clairaut
daDanish
Clairauts sætning
deGerman
Satz von Schwarz
enEnglish
Symmetry of second derivatives
esSpanish
Teorema de Clairaut
frFrench
Théorème de Schwarz
idIndonesian
Simetri turunan kedua
itItalian
Teorema di Schwarz
jaJapanese
ヤングの定理
koKorean
이계 도함수의 대칭성
plPolish
Twierdzenie Schwarza
ptPortuguese
Teorema de Clairaut-Schwarz
roRomanian
Simetria derivatei a doua
ruRussian
Равенство смешанных производных
ukUkrainian
Теорема Клеро — Шварца
zhChinese
二阶导数的对称性

Popularity rank trends

Best Rank German:
#38943
06.2020
Global:
#117357
10.2019

AI rank trends

Best Rank German:
#6305
09.2004
Global:
#27754
09.2004

Local AI rank history

Languages comparison

Important global interconnections (July 2025 – June 2026)

Wikipedia readers most often find their way to information on Symmetry of second derivatives from Wikipedia articles about Partial derivative, Hessian matrix, Maxwell relations, Clairauts formula and Greeks. Whereas reading the article about Symmetry of second derivatives people most often go to Wikipedia articles on Hermann Schwarz, Hessian matrix, Alexis Clairaut, Clairauts formula and Schwarz lemma.

Cumulative results of quality and popularity of the Wikipedia article

List of Wikipedia articles in different languages (starting with the most popular):

News from 1 July 2026

On 1 July 2026 in multilingual Wikipedia, Internet users most often read articles on the following topics: 2026 FIFA World Cup, Kylian Mbappé, Erling Haaland, Democratic Republic of the Congo, FIFA World Cup, Harry Kane, Romelu Lukaku, Senegal, Michael Olise, Sadio Mané.

In German Wikipedia the most popular articles on that day were: Demokratische Republik Kongo, Fußball-Weltmeisterschaft 2026, Senegal, Julian Nagelsmann, Erling Haaland, Sadio Mané, Fußball-Weltmeisterschaft 1994, Jürgen Klopp, Fußball-Europameisterschaft 2028, Fußball-Weltmeisterschaft.

About WikiRank

The WikiRank project is intended for automatic relative evaluation of the articles in the various language versions of Wikipedia. At the moment the service allows to compare over 50 million Wikipedia articles in 55 languages. Quality scores of articles are based on Wikipedia dumps from July, 2026. When calculating current popularity and AI of articles data from June 2026 was taken into account. For historical values of popularity and AI WikiRank used data from 2001 to 2026... More information