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::I really don't think there's a choice here. If the article is about the paper, which I think it should be, then it should be named after the paper. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 17:49, 19 February 2016 (UTC)
::I looked back and saw your examples. That is a point. Still, no one treats "Cantor's first set theory article" as a name of the paper (whereas for Alpher-Beta-Gamow they arguably do). The current title is a ''description''; that's what offends me the most about it. Descriptions are the last choice for WP article titles. --[[User:Trovatore|Trovatore]] ([[User talk:Trovatore|talk]]) 17:52, 19 February 2016 (UTC)
A better example than the Alpher-Beta-Gamow paper is the Grothendieck paper. The title '''Grothendieck's ''Tôhoku'' paper''' is as descriptive as '''Cantor's first set theory article'''. The former is saying the Wikipedia article is about Grothendieck's paper that appeared in the Tôhoku Mathematical Journal, while the latter is saying the Wikipedia article is about Cantor's first article on set theory.
I think that descriptions for WP article titles should ''only'' be used if there are good reasons for their use. Usually, I would avoid using a description for a WP article title. However, as I pointed out above we are in an unusual case where Cantor was coaxed (or pressured) into choosing a title that has nothing to do with the revolutionary result the article is famous for. Hence, the descriptive title easily beats the title of Cantor's article as measured by the five characteristics of a good Wikipedia article title ([[WP:TITLE]]). We also need to think of readers who come to the Wikipedia article via various links; for example, at least 20 articles have links to "Cantor's first uncountability proof." Not all these readers will be well-versed in math since some of the links are in an easier section of an article. These readers will find themselves at an article with a long name — "On a Property of the Collection of All Real Algebraic Numbers" — that's talking about some unspecified property of the collection of real algebraic numbers. I don't find this reader-friendly at all and I wouldn't be surprised if some readers think they're not at the correct article and just leave.
Also, I like to think of the first sentence of an article as a welcome mat. Starting an article with "Georg Cantor's first set theory article" is far more welcoming.
Finally, some books completely avoid the name of Cantor's paper and use a description similar to the current Wikipedia article title. Here's a couple of examples: Hao Wang, ''Popular Lectures on Mathematical Logic'', p. 119: "Cantor's first paper on set theory was published in 1874." Gerard Buskes and Arnoud van Rooij, ''Topological Spaces: From Distance to Neighborhood'', page 112: "Cantor's first set theory paper was his 1874 paper on algebraic numbers." It seems that they think the article is about algebraic numbers (perhaps the title confused them), but they do go on to cover the article's theorem about the uncountability of the real numbers.
I do like the respectful tone of our discussion and it has challenged me to think about why I have the opinion I do. Perhaps the next discussion we're both involved in will have us in agreement. [[User:RJGray|RJGray]] ([[User talk:RJGray|talk]]) 02:56, 20 February 2016 (UTC)
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