Applying for a mathematics PhD in the US after getting a BSc degree from Imperial
Most US students enter doctoral studies after &quot;only&quot; a bachelors degree. It isn't a reach at all. But expect there to be coursework and exams. The coursework is something like what you would get in a masters, but is intended primarily to prepare you for the qualifying examinations. Serious dissertation research often starts after you've done a couple of years of other things. But you aren't likely to finish in three years from where you are now. Expect something like twice that.