Riemann geometry: Einstein had to look around for the mathematics that could describe General Relativity. Before that nobody would have guessed that curved geometry has anything to do with space-time and gravity.
I think one of the best example is the binary system, the representing of numbers in 0 and 1 by diving them by 2. This is how every processor, ram, HDD, SSD,.. etc keep data and how digital communications work. Also the whole Boole algebra is the basics of how computer processors calculate numbers.
In 1605 Francis Bacon discussed a system whereby letters of ...
There are many examples of a physical significance given to abstract mathematical ideas.
One of the most prominent is the spacetime as introduced in general relativity. In general relativity a mathematical framework is given that informs you about the structure of space. It even relates space with time, thereby introducing new physical stuff, i.e., spacetime....
I don't know if this can be counted for as physics, but to my knowledge the radon transformation was mostly something mathematicians thought about without any application. Now, it is widely used (and necessary) to transform images in tomography.
The following quote is from C. N. Yang, delivered at a 1979 symposium dedicated to the geometer Chern: "When I met Chern, I told him that I finally understood the beauty of the theory of fibre bundles and the elegant Chern–Weil theorem. I was struck that gauge fields, in particular connections on fibre bundles, were studied by mathematicians without ...
Physics cannot help giving physical significance to things. But, yes, the first item on your list should have been
Developed as a mathematical "sudoku" game generalizing rotations, in the late 19th century, by Sophus Lie, Felix Klein, Friedrich Engel, Henri Poincare, and, as associated applied mathematical structures by James Joseph ...
The so-called Cantor set was described by
Georg Cantor, 1884 (or H. J. S. Smith, 1875?)
Sets with "fractional" dimension were described by
Felix Hausdorff, 1918
Investigated thoroughly by
A. S. Besicovitch, 1930s - 1950s
But these were only mathematical abstractions.
Benoit B. Mandelbrot, 1960s and later
claimed relevance of these sets in ...