Read this very carefully:
http://www-history.mcs.st-and.ac.uk/Biographies/Feynman.html
"Richard, [Feynman] learned a great deal of science from Encyclopaedia Britannica and taught himself elementary mathematics before he encountered it at school. He also set up a laboratory in his room at home where he experimented with electricity. In particular he wired circuits with light bulbs, he invented a burglar alarm, and he took radios apart to repair damaged circuits. When he entered Far Rockaway High School his interests were almost entirely mathematics and science."
So instead of going to University early why not get a set of Encyclopedia Britannica, read through maths & physics articles (only!), get an expensive electronics hobby kit to build all these kinds of things, and experiment with fixing your friend's broken down electronic equipment?
I've been bouncing around John Gribbin's "Q is for Quantum" recently - an encyclopedia of quantum physics - and I can see how doing that might develop flexibility of mind.
"At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education."
Note the stress on *recreational* mathematics - same as Wilczek.
"He entered MIT in 1935 and, after four years study, obtained his B.Sc. in 1939. He went there to
study mathematics but, although he found the courses easy, he became increasingly worried by the abstraction and lack of applications which characterised the course at this time. He read Eddington's Mathematical Theory of Relativity while in his first year of studies and felt that this was what he wanted from mathematics. His mathematics lecturers presented him with the view that one did mathematics for its own sake so Feynman changed courses, taking electrical engineering. Very quickly he changed again, this time moving into physics."
I just read a biography of Dirac and Eddington's book was very important to him as well!
So put that on the "must buy" list...
"He took Introduction to Theoretical Physics, a class intended for graduate students, in his second year. There was no course on quantum mechanics, a topic that Feynman was very keen to study, so together with a fellow undergraduate, T A Welton, he began to read the available texts in the spring of 1936. Returning to their respective homes in the summer of 1936 the two exchanged a series of remarkable letters as they tried to develop a version of space-time..."
Here the important points to take are:
(i) he really stretched himself by taking a tougher course. Watson (the DNA guy) said he did exactly this as well, taking tough Math classes that biologists were not expected to take...)
(ii) He found a friends to discuss these things with at the highest level - I always felt jealous of Einstein's coffee bar lifestyle where he would go and chat with friends who later became almost as famous as him! If only I had had famous friends! ... But I didn't get chatting to the brightest guys in my class, so it's partly my fault - SO *push yourself forward socially* make friends with the bright guys and talk about important stuff.
(iii) Don't moan that your school doesn't have a class in string theory/LQG/whatever , plough through the tough books, with your like-minded pals, in the breaks! And try and have your own ideas, push them to the limit...
"By 1937 Feynman was reading Dirac's The principles of quantum mechanics and seeing how his highly original ideas fitted into Dirac's approach. In fact Dirac became the scientist who Feynman most respected throughout his life."
Another must read book! (Not too early though ... you need a couple of years of the toughest theoretical physics classes in Uni. before thinking of this...)
"He had the best grades in physics and mathematics that anyone had seen, but on the other hand he was close to the bottom in history, literature and fine arts."
Lesson: Focus on what's most important! UK citizens don't have this problem so much, they don't have to do "history, literature and fine arts." at Uni. They just do physics. So you might want to consider Manchester, like Bohr :), or Lancaster or even Cambridge (wish I had!)
"His doctoral work at Princeton was supervised by John Wheeler, and after finding the first problem that Wheeler gave him rather intractable, he went back to ideas he had thought about while at MIT. The first seminar that he gave at Princeton was to an audience which included Einstein, Pauli and von Neumann. Pauli said at the end..."
Lessons: Find the best mentors, listen to them, use them, hang out with them, but when it comes to the crunch go with your own ideas...
"At twenty-three ... there was no physicist on Earth who could match his exuberant command over the native materials of theoretical science. It was not just a facility at mathematics (though it had become clear ... that the mathematical machinery emerging from the Wheeler-Feynman collaboration was beyond Wheeler's own ability). Feynman seemed to possesses a frightening ease with the substance behind the equations, like Einstein at the same age, like the Soviet physicist Lev Landau - but few others."
But as his "lucky" schooling shows it wasn't (necessarily) some "divine spark" that gave him this ability - it was the things he did, the books he read, the courses he took, the people he talked to. You can't reproduce a "divine spark" (if it exists) but there is much in his life worth pondering on and emulating.
And for you educators out there: Why don't you encourage a culture similar to that encountered by Einstein and Feynman? Why not:
(i) Invite the bright students to the coffee bar for long bull sessions...
(ii) Create reading groups to get reading Eddington's book over the second summer break and Dirac's over the third.. ask them to come up with their own ideas for a theory of space time or Quantum Gravity.
(iii) Act like Wheeler (see "Geons" for another great biography...)
