New discoveries happen not when you master a predetermined set of knowledge fields, although this helps. New discoveries take place only when you are courageous enough to challenge pre-set fields of knowledge themselves.
One of the biggest problems with education today is the assumption on which it is build. The assumption too often go like this: (a) a student lacks knowledge; and (b) education is that which fills the lack or the "void" in the student. The structure here, as you can see, is a Master/Slave hierarchical structure in which the student is perceived and treated as slave and the master are the teachers and the education apparatus.
In each case, the logic here is simple: For the student to succeed they must submit to the master.
There are many issues with this authoritarian structure including how information and knowledge are shaped by putting knowledge, facts, history, etc. into a master/slave paradigm in the first place. On a psychological level, the student is constantly and continually reminded of their lack. Examinations on this view are but constant reminders that the student is already a failure even if they answer all the questions correctly. They are a failure because they have, under their own power, submitted to the examination, which is, at the same time, submitting to the story that their lack determines the very nature of learning as such.
Lack = being as student.
It is only when the student realizes that they are not defined by their lack that they will overcome, in a single moment of inspiration, their own enslaved or colonialized submission to a matrix of disempowerment. When this happens, a new world is formed, even if only in the mind of the liberated student. When the taste of this new world touches the tongue of one's desire, the chains of the master/slave dialectic will fall to the ground and no power in the world can force them back into the prison-house of enslavement again.
Lack = traditional education
Liberation = living into one's owe desires (anti-student)
The power of learning, of thinking, and of being-in-the-world is found in the courage to overcome the hierarchical structure that only functions by repeating the boring story that you lack your own being. A true education is precisely the liberation from this structure, and for that you only need the courage to BE, you!