I remember reading an interview with Vladimir Arnold where he tells the following anecdote about Hassler Whitney. I don't have the interview in front of me, so some of the details may be not quite correct, but if memory serves, the story goes on like this.
Whitney used to study music in America and at some point decided to spend a year in Germany. He arrived in G\"ottingen where it turned out that he had to take a course outside his main subject of study, which was music. He asked which one of the courses was the most difficult one. It turned out the most difficult subject was quantum mechanics. Whitney enrolled on that course. After the first lecture he came to see the professor and said
-- I was one of the best students in Yale in my year, Herr Professor; how come I didn't understand a single word of the lecture?"
--Well, you see, there are some prerequisites for this course. You have to know calculus and linear algebra and ....
-- Are there any books where I can read all this up?
It took Whitney a couple of weeks to work through the books the professor told him to read. In a month Whitney was able to follow the course, and he decided to switch to mathematics at the end of the semester.
Arnold tells this story to illustrate the dangers of early specialization.