In the early/mid twentieth century, there were a number of "great mathematicians" working on theoretical physics directly and indirectly related to atomic weapons research. I think this area will have a number of examples with "great political commitments."
I want to briefly mention The ManhattanProject, but first I want to point out the (sort of) null hypothesis: the people involved in that work had "great political commitments," that what they were working on was for the national interest.
For this question, I wanted to add a mention for Oppenheimer. It is true he was an accomplished physicist, and even made important contributions to the field, but in a period of many important discoveries I'm not sure he would ever rise to qualifying as a truly "great mathematician." One area he did excel in was task management and coordinating people, which is how he landed as the head of Los Alamos Laboratory.
This is just a bit of background to mention Oppenheimer's "great political commitments." After the war,
Oppenheimer recommended putting control over atomic energy into the hands of an international agency. Appointed a key advisor to the newly created Atomic Energy Commission, a position that offered him an important voice in Washington and a top-secret security clearance, he spoke out for moderation as tensions between the Soviet Union and the United States began to escalate. He advised against the development of the hydrogen bomb, a device with unlimited destructive power, and took a stand against building nuclear powered aircraft and submarines. [emphasis mine]
(Without going into details, he was stripped of his authority and removed from this position)
“The Oppenheimer hearings had a tremendous impact on the nuclear arms race,” says Mark Samels, executive producer of AMERICAN EXPERIENCE. “Once Robert Oppenheimer’s voice of moderation was silenced, the U.S. began building an arsenal of tens of thousands of nuclear weapons, and the Soviet Union followed suit. The result was a standoff between the world’s two largest superpowers that lasted for nearly fifty years.”
(quoted from "The Trials of J. Robert Oppenheimer", released on PBS. reference: https://www.pbs.org/wgbh/americanexperience/films/oppenheimer/#part01 )
The above quote seems to imply that Oppenheimer was the sole thing standing between the USA and nuclear weapons development, which seems a bit exaggerated. Surely there were other forces and institutional inertia at play. But I like to think there is an alternative universe where his non-proliferation stance prevailed.