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[Computational Complexity] How much credit should the conjecturer get? Is Con...

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  • GASARCH
    Theorems are often named after who proved it. The ones who conjectured it are often forgotten. - Mordell s conjecture was solved by Falting. It is now called
    Message 1 of 1 , Aug 14, 2009
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      Theorems are often named after who proved it. The ones who conjectured it are often forgotten.
      1. Mordell's conjecture was solved by Falting. It is now called Faltings' Theorem.
      2. Vazsonyi's conjecture was solved by Joseph Kruskal. It is now called The Kruskal Tree Theorem.
      3. Baudet's conjecture was solved by van der Waerden. It is now called van der Waerden's theorem . Even though van der Waerden's original paper has as its title (roughly translated) On a conjecture of Baudet, Baudet is not well known.
      4. Fermat's last theorem was solved by Wiles. If you type Wiles into Wikipedia you get as options Wiles Theorem which goes to a page whose web address is http://en.wikipedia.org/wiki/Wiles_theorem but whose title on the page is Fermat's Last Theorem. This one may still be in transition from being someones conjecture to someones theorem. It may be for a while. This one is so tied to Fermat that it might always have his name on it somehow.
      If you know of other examples please comment.Is it unfair that the original conjecturers are forgotten? Alexander Soifer thinks so. In his book The Mathematical Coloring Book: Mathematics of Coloring and the Colorful Life of its Creators (reviewed in my latest SIGACT NEWS Book Review Column) he suggests that we should name a theorem after both who conjectures it and who solves it. So what I call
      Van der Waerden's Theorem
      Soifer calls
      The Baudet-Schur-Van der Waerden Theorem.
      (Baudet is known to have conjectured it. Soifer argues convincingly that Schur also conjectured it.) Reading over van der Waerden's own account of how the theorem was discovered (included in Soifer's book) it seems to me that Artin contributed some to the solution of Baudet's conjecture. If standards for co-authorship were weaker then he may have been a co-author. In this alternative universe what I would call
      The Artin-Van der Waerden Theorem
      Soifer would call
      The Artin-Baudet-Schur-Van der Waerden Theorem.
      This is odd since you have prover-conjecturer-conjecturer-prover in the ordering. Perhaps another convention would arise. Perhaps it would be called the ABSV-theorem or ABSW-theorem. Perhaps we are better off, just for the sake of simplicity, using just the prover's name. There have been some fierce battles over who PROVED what. Do we really want to have fierce battles over who CONJECTURED what? I conjecture that we do not.

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      Posted By GASARCH to Computational Complexity at 8/14/2009 09:59:00 AM
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