Suppose someone wrote a paper about X two decades ago. A modern reader realizes the X paper sheds light on an unrelated idea Y. Do we have any information on how often this happens? How often is this just "I figured out Y for a different reason, and while doing my lit review I realized that the X paper is also relevant for Y"?

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I expect this information is reasonably well documented in histories of particular currents of thought. I have no idea how often it happens in absolute terms, but I feel it must be relatively common because I have encountered it as an amateur reader of papers.

A good example is ET Jaynes' work on maximum caliber, which is a variational principle for dynamical systems. It might be cheating because it is well-understood to be a controversial concept, but the insights concerned entropy. Jaynes' specialty was Statistical Mechanics, for which he had employed information-theoretic notions of entropy in order to account for the lack of knowledge of the microstates. When Jaynes' was writing, physics used the Clausius formulation of 2nd Law of Thermodynamics, which he found unsatisfactory for the problem of prediction because it says nothing about intermediate states before reaching equilibrium. In Physical Chemistry they used a different one, which came from work by G.N. Lewis, who used the Gibbs formulation of the 2nd Law. It is insights drawn from the subtleties of Gibbs' work concerning entropy that gave Jaynes the predictive power he was interested in. Lastly, Jaynes had the work of Clifford Truesdell who was writing around the same time in the field of Continuum Mechanics, and working to expand that approach to fully cover thermodynamics. Truesdell's work persuaded Jaynes that the other approaches were in fact wrong.

So here was a case where one physics researcher (Jaynes) borrowed math ideas from communication (Shannon), then read older work from chemistry (Lewis), leading to much older work in early thermodynamics that had new insights (Gibbs), and confirmed by more recent work in a different field of math (Truesdell). All of these insights went into his work on maximum caliber.

In a similar vein, a lot of Truesdell's writing consists of going back to the early days of thermodynamics and finely sifting the insights therein. He writes well and carefully, but is animated and polemical; I recommend reading him to anyone interested in thermodynamics.

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Half of my scientific career appears to be shaping up into repeatedly doing this...

Since most papers don't include much metadata this will be really hard to figure out (also, which citations count as central to the insight?). I agree knowing the answer to this would be very interesting. My impression has been that Kuhnian style shifts do generally involve someone going back to the assumptions of the current paradigm and realizing that a different direction is now plausible given what has been discovered in the interim. E.g. the modern era is built on set theory and point estimates. In order to make progress rebasing on distributions natively might have to happen.

Citations can be used as the metadata. One of the closest corresponding things in cliometrics are 'sleeping beauty' papers, which instead of the usual gradual decline in citation rate, suddenly see a big uptick many years afterwards. The recent 'big teams vs small teams' paper discussed sleeping beauty papers a little: You could also take multiple discovery as quantifying repetition, since one of the most common ways for a multiple to happen is for it to happen in a different field where it is also important/useful but they haven't heard of the original discovery in the first field.

There's a nice version of this with Ed Boyden on how old papers helped lead to the hot new 'expansion microscopy' thing (funded, incidentally, by OpenPhil):

I would not count such a thing as an "old paper" but a "primary reading" of a "new" paper. But this might be because I am pessimistic about academic speed and the reach of papers.