Euclid Division Lemma: Origins & Legacy

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Discussion Overview

The discussion revolves around the origins and naming of the Euclid Division Lemma, exploring historical context, the implications of naming conventions in mathematics, and the contributions of Euclid versus later mathematicians.

Discussion Character

  • Historical
  • Meta-discussion

Main Points Raised

  • Some participants question why the term "Euclid lemma" is used if Euclid did not discover it, suggesting a need to understand the historical naming conventions.
  • One participant interprets that while Euclid could perform division, he may not have been aware of the existence and uniqueness theorem related to it.
  • Another participant notes that the term "Euclidean division" was introduced in the 20th century, indicating a shift in terminology that may not reflect Euclid's original contributions.
  • A participant references Stigler's law of eponymy, arguing that many concepts are named after those who popularized them rather than their original inventors.
  • One participant emphasizes that Euclidean concepts are primarily geometric, suggesting that naming Euclid's algorithm after him is justified due to its geometric nature.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the name "Euclid lemma" and the implications of historical naming practices. There is no consensus on whether Euclid's contributions warrant the naming of the lemma after him.

Contextual Notes

Participants discuss the historical context of naming conventions and the evolution of mathematical terminology, highlighting the complexity of attributing discoveries in mathematics.

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Suyogya said:
If the euclid division lemma was not discovered by euclid himself, then why was the name "euclid lemma"? (https://en.wikipedia.org/wiki/Euclidean_division#History)
From the same article, "it seems that he did not know the existence and uniqueness theorem". My interpretation is that he (Euclid) could perform the division, but was unaware of the details of existence and uniqueness.
 
Further down in the same section of the wiki it says:
Wikipedia said:
The term "Euclidean division" was introduced during the 20th century as a shorthand for "division of Euclidean rings".
 
A case of Stigler's law of eponymy: Nothing is named by its inventor/discoverer, including this law.
Often things are named after people who made something more widely known, or extended existing knowledge a lot.
 
Euclidean are usually all geometric concepts, a flat geometry until Bolyai. His Elements were for 2000 years the first and most important books in mathematics. It is somehow natural to name Euclid's algorithm after him, as it is basically a geometric question.
 

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