I read that Ed Witten's 1990 Fields Medal was somewhat controversial among mathematicians, because even though no one questioned his deep conceptual understanding of important new mathematical ideas, his work was not considered rigorous enough to deserve the medal. For example, Wikipedia claims that
Witten's work [on Chern-Simons theory and topological quantum field theory] was based on the mathematically ill-defined notion of a Feynman path integral and was therefore not mathematically rigorous, [although] mathematicians were [later] able to systematically develop Witten's ideas.
Moreover, the actual discovery that his Fields Medal nominally awarded was an innovative new simpler proof of the positive energy theorem, which had already been proven.
What are some examples of theorems that Witten discovered that were not previously known, such that there is consensus across the mathematical community that (a) the hypothesis and conclusion of the theorem are completely and unambiguously mathematically well-posed and (b) the proof is completely mathematically rigorous?
Edit: I don't mean theorems that Witten proposed non-rigorously which were then later made rigorous by mathematicians (of which there are many). I mean theorems for which Witten himself provided the rigorous version. (I know there are eternal philosophical debates between mathematicians about the relative importance of imprecise conjectures vs. precise conjectures vs. rigorous proofs for statements that end up being correct. But presumably both correctness and proof are important for the kind of work that the Fields Medal's purpose is to recognize.)
Let a famous mathematician answer this question on the contributions of Edward Witten: On the work of Edward Witten, by Michael Atiyah.