Talk:Common fixed point problem

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{{Connected contributor|User1=WillisBlackburn|U1-declared=yes|U1-otherlinks=William M. Boyce, one of the two mathematicians who solved this problem, is my father.}}

{{DYK talk|28 December|2024|entry=... that in 1967 two mathematicians published PhD dissertations independently disproving the same thirteen-year-old conjecture?|nompage=Template:Did you know nominations/Common fixed point problem}}

I believe that this subject is notable due to:

The significant amount of attention given to the problem during the period when it was unsolved, as evidenced by the sources
The publication of articles and papers about the problem even decades after it was solved (the articles by Brown and McDowell, and the master's thesis by McCroskey)
The continued relevance of Baxter permutations, which arose directly from research into this problem
References to the work of Boyce and/or Huneke in recent research, e.g., "On distal flows and common fixed point theorems in Banach spaces" (https://doi.org/10.1016/j.jmaa.2022.126995), published in 2023, references the "Commuting functions with no common fixed point" paper
Showing up on Math StackExchange and other sites from time to time (e.g., https://math.stackexchange.com/questions/4413605/continuous-function-on-the-unit-interval-with-commuting-compositions)

Progress?

What is "progress toward an affirmative answer" when the correct answer is No? Reword? Tom Permutt (talk) 05:07, 28 December 2024 (UTC)

:The view of mathematicians at the time was that the conjecture would eventually be proven, so the partial solutions were milestones along that path. It could say "progress toward the expected affirmative answer." WillisBlackburn (talk) 18:29, 22 January 2025 (UTC)

Citation needed

Regarding a citation for the statement "Huneke's paper is notable for its first-principles approach to the problem, not relying on any of the work done by earlier mathematicians." My source is Huneke's paper itself. It only has three references: two are to Boyce's dissertation and his Transactions paper, and the third is to Huneke's own dissertation. WillisBlackburn (talk) 17:20, 16 October 2024 (UTC)

Did you know nomination

:I'd like a copy of the Huneke disseration if you could provide it. Do you also have access to the Boyce dissertation? I only have the paper published in Transactions AMS. WillisBlackburn (talk) 21:23, 16 October 2024 (UTC)

::Boyce is {{ProQuest|288201093}}. I appear to have access if you don't, but maybe the Wikipedia Library works for this?

::Incidentally there is a [citation needed] tag and a few sentences at the ends of paragraphs that are not supported by footnotes that should be footnoted. Per WP:DYKCITE, every claim in a DYK article (not counting the summaries of later sourced material in the lead) must have a reference, not later than the end of its paragraph. —David Eppstein (talk) 07:41, 17 October 2024 (UTC)

:::I now have both. I'm going to have to change the statement that Huneke doesn't reference the prior researchers, because his dissertation does. The dissertation also includes a lot of narrative not in the paper he published in Transactions. WillisBlackburn (talk) 14:59, 18 October 2024 (UTC)