Jean Morlet developed wavelets as a tool for oil processing. From page "Multiresolution approximation and wavelets", Mallat.
The paper made it clear that work that existed in many different guises and under many different names -- were at heart all the same. From your example with wavelets, I interpret your question as asking about convergent evolution of sorts: the idea doesn't have to be developed into a full blown mathematical theory in all of its roots, but that some similar shapes and structures can be found?
Wavelet -- from Wolfram MathWorld
Denis-Charles Cisinski mentioned in an answer that Heller's homotopy theory of homotopy theories is the same theory as Grothendieck's theory of derivators. Theory Ser. A 66 , — Sign up to join this community. The best answers are voted up and rise to the top. Home Questions Tags Users Unanswered. Undiscovered for a long time before it is realised it is the same concept developed under different names.
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Wavelets might be an example. Do you specify the language? Different languages would be a source of groups of researchers working independently of each other. I've also heard claim that the DeTurck trick was used before DeTurck in renormalization group flow in physics, but that may be historically inaccurate. On a slightly shorter and more competitive time frame, the whole notion of Lorentz-Fitzgerald contraction and Minkowski space was separately realized by different groups in physics and maths.
Recall that Einstein famously didn't believe in this geometrization of space-time until he finally found it useful for the general theory. Willie Wong. I don't recall whether it was used in general relativity before or after this, but I believe whoever did it second was aware of the other. However, my recollection is that everybody was aware of the precedents when they did this.
For example, DeTurck and Kazdan understood what they were doing for the diffeomorphism group was the same as what others were doing for the gauge group in Yang-Mills. About your first comment: I believe De Donder was either 30s or 40s? Brand new Book. Seller Inventory AA Brand new book, sourced directly from publisher.
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