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What are some notable (famous?) instances where the following has occurred.

A particular author proves:

Every P which satisfies Q has property Z.

A few years later (roughly speaking) the same author proves:

Every P has property Z;

thus rendering at least part of their original research article obsolete.

Is such a thing common?

On one hand, the author should be the person most equipped to strengthen their result since they likely tried before, learned some traps to avoid, and got a partial solution.

On the other hand, the author could prefer not to revisit their work to avoid duplication & making their own work obsolete, or simply to do research on different things they find interesting. Maybe they eventually just "quarantine" the problem in order to make better use of their time and mental energy.

On a personal level, I really struggle with "letting a problem go", especially if it's one I've previously solved certain cases of.

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    $\begingroup$ The scenario that you describe does not necessarily render any of the original research article obsolete. For instance, perhaps the proof in the second paper amounts to showing that every P satisfies Q. In fact, I would guess that this is quite common in such scenarios. $\endgroup$
    – Lee Mosher
    Commented Dec 17, 2018 at 14:33
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    $\begingroup$ Not sure about famous instances, but in general it happens more often than not. I'm guilty myself of publishing three papers of the type "A implies B", "A implies C" (with C trivially implying B), and "A is equivalent to D" (with D trivially stronger than C). The paper "A is equivalent to D under extra assumption Q" was published by somebody else in the meantime. I find nothing wrong with it and I do not think anybody else frowns upon it either. Every time you have something interesting to say, it is OK to say it.If later you can say more and in a better way, just consider yourself lucky :-) $\endgroup$
    – fedja
    Commented Dec 17, 2018 at 15:06
  • $\begingroup$ I guess this is a side effect of the infamous "publish or perish". Would mathematicians publish incomplete results if they could get rid of this pressure ? $\endgroup$
    – Sylvain JULIEN
    Commented Dec 17, 2018 at 21:45

1 Answer 1

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Something along these lines happened during the march towards the odd order theorem. Quoting Wikipedia:

The attack on Burnside's conjecture was started by Michio Suzuki (1957), who studied CA groups; these are groups such that the Centralizer of every non-trivial element is Abelian. In a pioneering paper he showed that all CA groups of odd order are solvable. (He later classified all the simple CA groups, and more generally all simple groups such that the centralizer of any involution has a normal 2-Sylow subgroup, finding an overlooked family of simple groups of Lie type in the process, that are now called Suzuki groups.)

Feit, Marshall Hall, and Thompson (1960) extended Suzuki's work to the family of CN groups; these are groups such that the Centralizer of every non-trivial element is Nilpotent. They showed that every CN group of odd order is solvable. Their proof is similar to Suzuki's proof. It was about 17 pages long, which at the time was thought to be very long for a proof in group theory.

The Feit–Thompson theorem can be thought of as the next step in this process: they show that there is no non-cyclic simple group of odd order such that every proper subgroup is solvable. This proves that every finite group of odd order is solvable, as a minimal counterexample must be a simple group such that every proper subgroup is solvable. Although the proof follows the same general outline as the CA theorem and the CN theorem, the details are vastly more complicated. The final paper is 255 pages long.

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  • $\begingroup$ In this case, the authors of each improvement are different. The original question was asking about improvements by the same author. $\endgroup$
    – spin
    Commented Dec 17, 2018 at 16:12
  • $\begingroup$ @spin: the 1960 result about CN groups is due to Feit-Hall-Thompson, and the "full" odd order theorem from 1962/63 is due to Feit-Thompson, so at least most of the authors are the same there. $\endgroup$
    – Sam Hopkins
    Commented Dec 17, 2018 at 16:19

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