What do French, German, and Russian texts call the Cauchy-Schwarz inequality?

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Discussion Overview

The discussion revolves around the naming conventions of the Cauchy-Schwarz inequality in different languages, specifically French, German, and Russian. Participants explore how this mathematical concept is referred to in various texts and the implications of these differences in nomenclature.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • Some participants assert that the inequality known as "Cauchy-Schwarz" in English is referred to as "Cauchy's inequality" in France, "Schwarz's inequality" in Germany, and "Bunyakovsky's inequality" in Russia.
  • One participant mentions specific English texts that refer to the inequality as either "Cauchy-Schwarz" or "Cauchy," but expresses a lack of experience with texts in French, German, or Russian.
  • Another participant suggests that the naming differences may reflect a form of intellectual patriotism, noting their own experience of only encountering the term "Cauchy-Schwarz."
  • A participant introduces the full name "Cauchy-Bunyakovsky-Schwarz," emphasizing the chronological order of the mathematicians' contributions.
  • One participant shares their experience with a German professor who referred to it as "the inequality of Schwarz," indicating that there may be some validity to the claims about different names.
  • Another participant compares the naming of the Cauchy-Schwarz inequality to the Cech-Stone compactification, noting that naming conventions can vary significantly between regions.

Areas of Agreement / Disagreement

Participants express differing views on the naming of the inequality, with no consensus reached on the most accurate or accepted term across languages. The discussion remains unresolved regarding the validity of the claims about naming conventions.

Contextual Notes

Participants' claims are based on personal experiences and observations of naming conventions in various texts, with no definitive sources cited to confirm the accuracy of these claims.

Fredrik
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I was once told that the inequality that most books in English seem to call "the Cauchy-Schwarz inequality" is called "Cauchy's inequality" in France, "Schwarz's inequality" in Germany (or Austria or whatever...I'm too lazy to find out where he's from), and "Bunyakovsky's inequality" in Russia and other countries that used to be part of the Soviet union. I'm just curious if this is true. Have you encountered the inequality in a text written in French/German/Russian? What was it called?
 
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Fredrik said:
I was once told that the inequality that most books in English seem to call "the Cauchy-Schwarz inequality" is called "Cauchy's inequality" in France, "Schwarz's inequality" in Germany (or Austria or whatever...I'm too lazy to find out where he's from), and "Bunyakovsky's inequality" in Russia and other countries that used to be part of the Soviet union. I'm just curious if this is true. Have you encountered the inequality in a text written in French/German/Russian? What was it called?

I have Apostle's Linear Algebra book and he calls it Cauchy-Schwarz. I have Bartle's Real Analysis book and he calls it Cauchy. Both are English. So, I haven't read a French or German or Russian book, but it is interesting that some things have so many different names.
 
Sounds like intellectual patriotism, but I myself haven't seen the inequality labeled anything other than Cauchy-Schwarz.
 
Cauchy-Bunyakovsky-Schwarz. Chronologically.
 
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I had a german professor, and he always called it the inequality of Schwarz. So there could be some truth to the story :biggrin:

I always call it the inequality of Cauchy-Bunyakovsky-Schwarz though...It's the same with the Cech-Stone compactification. In america it's called the Stone-Cech compactification. In eastern europe they reverse the order...