Mathematics is the art of giving the same name to different things.
Quote of the Week 15
“Mathematics is the art of giving the same name to different things.”
Triggered by the use of a variation of the quote by Robert Fuchs on LinkedIn.
“Poetry is the art of giving different names to the same thing.”
“La Mathématique est l’art de donner le même nom à des choses différentes.”
In 1908, the Fourth International Congress of Mathematicians was held in Rome. During the Congress, the mathematician Jean-Gaston Darboux presented an address written by Henri Poincaré entitled “L’avenir des mathématiques,” and Poincaré included the paper as a chapter in his book Science et Méthode. An authorized English translation by George Bruce Halsted appeared as the chapter “The Future of Mathematics” in The Foundations of Science, first published in 1913.
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Out of context, it is possible to misinterpret “giving the same name to different things” as saying that words in mathematics are used in confusing or misleading ways, using the same word to label very different concepts. However, it is clear that Poincaré’s intent was very different: he was instead emphasizing that otherwise completely different objects can share some similar structures and properties, and mathematics can use a terse word or phrase to identify and describe in detail these common features.
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Almost every modern source pairs the subject quotation in this column with a similar sounding one: “Poetry is the art of giving different names to the same thing.” ... The original connection between these two quotations appears to be the article, “Three Great Synonyms: Relation, Transformation, Function,” by Cassius Jackson Keyser, which was first published in the journal Scripta Mathematica in 1935. In the paper, Keyser stated that he shared the Poincaré quotation with an unnamed poet, who quickly responded with the alternative quotation [Keyser 1947, p. 218]. So, according to Keyser, the quotation on poetry was in response to Poincaré, not the other way around.
Source: Quotations in Context
Another contrasting quote posted on Twitter/X:
“Machine learning is the art of giving different names to the same thing.”
― Yi Ma
Mathematics is the art of giving the same name to different things(Henri Poincaré). Machine learning is the art of giving different names to the same thing. pic.twitter.com/CIsxItQbeW
— Yi Ma (@YiMaTweets) July 1, 2023
Related to the original quote:
“Mathematics is only the art of saying the same thing in different words.”
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