It was the math exam that got me into MIT with advanced standing. MIT was actually the first school I ever attended. I entered as a sophomore, took physics, and finished in three years. I was interested in applying my knowledge of mathematics, and I was able to do that the moment I got into a physics course. Theoretical physics is not difficult when you know the laws and the necessary mathematics.
Experimental physics can be very difficult.
I didn't have anybody special, but John Slater is one of the professors I remember particularly well. The University of Nancy in France was trying to make contacts here at MIT, and in 1924, I was recommended for entrance there. I was given an experimental problem to work on, building a small, 10-megahertz oscillator and measuring its Q value, and we published an article on it. I received a degree for this work, but French degrees are not the same as American degrees. The only academic degrees that really matter are the ones backed by the French government.