Don't get me wrong though. Back in university I loved reading these things and it is still nice to read them. But I would be careful to derive anything beyond amazement from it. It can be very frustrating to see how much you struggle with simple things, while some Indian clerk without any formal education shows you how its done. And you have to admire Hardy's character for not feeling the same way, or at least to a reasonable extend, not showing this feeling.
A man once asked Mozart how to write a symphony. Mozart told him to study at the conservatory for six or eight years, then apprentice with a composer for four or five more years, then begin writing a few sonatas, pieces for string quartets, piano concertos, etc. and in another four or five years he would be ready to try a full symphony. The man said, "But Mozart, didn't you write a symphony at age eight?"
Mozart replied, "Yes, but I didn't have to ask how."
In order to learn/study something, you need unbounded enthusiasm/motivation (though it maybe irrational). Once you have jumped in with both feet, reality will slowly strip the fantasies but hopefully by that time, one's interest is sufficiently solidified that one can settle down to the long grinding road to mastery. It is Emotion which drives one to Action while Rationality modulates it.
The key is to light the fire within one's imagination. Any kindling will do whether sane or not. Everything that the Human Species has achieved has started from here.
PS: For example, Ramanujan himself used to say that the goddess "Namakkal" revealed the theorems to him!