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I suggest this as an accompanying wiki page, which has PhD dissertations that contain a solution for an open problem in the style of Big-List questions, with regard to the well-known paradigm thinking that mathematical research In Problem Solution and theory building . The theories are temporarily developed to solve famous open problems, but sometimes the concrete problems they solve through the possibilities that a new theory is opened.
Can you call modern mathematicians who have already developed a significant new theory in their doctoral students (or earlier in their career) or put the basics of a new research area?
John Forbes Nash Jr. got a Nobel Prize for his.
nash earns a Ph.D. Degree in 1950 with a 28-page dissertation on non-cooperative games.
The work written under the supervision of the doctoral consultant Albert W. Tucker contained the definition and characteristics of the Nash equilibrium, a decisive concept in non-cooperative games. It won the Nobel Memorial Prize in Economics in 1994.
There are many examples. Here are a few who come to mind:
Simon Donaldsons Thesis The Yang-Mills equations to Bald distributors contain the first main steps in his work on the differentiation topology of four distributors. The following paraphrases its abstract. He gave a new proof of a set of Narasimhan and Seshadri, which characterizes these holomorphic bundles via a projective curve that adds a flat connection and it used to prove the simplest interesting case of assumption of Hitchin and Kobayashi. He examined the module space of self-duel connections on a simply connected four distributor and used them to close obstacles to the realization of a matrix as crossing pairing at the second cohomology of such a distributor.
John Tates Thesis is a well-known example, although I'm not competent to summarize it. It has its own Wikipedia page.
Doctoral thesis of Mikio Satos (based on some already published work) led the theory of hyperfunctions as limits of holomatophen functions. See this poll by P. Schapira and this interview with SATO. (Nothing about Satos education is standard.)
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