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    Hi Buffy, thanks so much for your answer. A major issue is that the UK system doesn't allow "changing majors." The closest I could get would be joining the Cambridge Part III (masters) course in math though I would likely be restricted to taking the more physics-ey courses such as QFT. It might help persuade PhD admissions that I can do serious math but wouldn't fill in knowledge gaps. I'm well aware of how much math I'm missing but am struggling to find a practical way to catch up. Have you heard of anyone doing the full catch-up during a PhD? Eg by being granted an extra year? Commented Apr 21, 2023 at 14:53
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    Few doctoral programs have much of a time limit and for those that do it is more like seven years, after which questions get asked. But note that the US undergrad degree is more general than a UK degree with lots of general education courses. The three courses I mentioned would also let you know if your "love of theory" is solid. Especially the algebra course, I'd guess. Commented Apr 21, 2023 at 15:06
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    @Buffy your comment about time limits for PhD degrees applies to universities in North America but in UK and Europe PhDs are intended to finish much faster. Questions will be asked far before 7 years and at least at Oxford, the chances of staying in the program beyond 7 years is close to 0. Commented Apr 23, 2023 at 7:19