Often physicists do something new, and mathematicians later make it rigorous. Generally the physicists couldn’t care less, and as for the mathematicians, they quickly forget the physicists’ part in the story.
Here’s an example in the beloved book by Körner on Fourier series. In 1909 the physicist Jean Perrin, building on Einstein’s paper of 1905, realized that Brownian motion trajectories are continuous but nowhere differentiable. This was made mathematically rigorous in the 1920s by Norbert Wiener and Paul Levy. Körner summarizes Wiener’s construction with the words, “In accordance with Perrin’s prophetic remarks [the Brownian paths] turned out to be continuous and nowhere differentiable”.
Prophetic remarks! Once again, it would seem, a physicist had struck it lucky.
[8 March 2020]