A student cannot be greater than his master.

There is no count to the number of lessons we can learn from the simple formulas found in our maths.
I was sleeping yesterday when, after a religious service, the thought occurred to me: a student cannot be greater than his master. Right, yeah, I do believe that. But how is that translated in the maths? I wanted to know.
I was thinking about it when the thought of sets and subsets came to mind. I thought of all the maths problems I had solved and of my maths teachers , both those loved and hated; those feared and respected. I realized one truth then: The solution space of a student, any student, is a subset of his teacher’s.
The solution space of a student cannot be greater than his master’s. A student cannot do much maths, cannot solve more advanced maths than his teachers. One would never realize it unless you take the count yourself. I’d give a reward to anyone who can prove than he can solve more complex maths than his teacher? Excepting – exceptions are always the rule in life.
Excepting:
THE STUDENT HAS TO DO A CHANGE OF PARADIGMS. I recall this term from one of Steven Corby’s books. I think it was the “Seven habits of highly successful people?” Please forgive me if I am wrong.
So, how can we do a paradigm change in solution space and maths solutions.
1. By derivation. A derivation is like a creative activity. To be able to derive a solution space different from the teacher(s)’s, the student has to be a teacher himself. A derivation is like creating a complexity out of simple objects. But although this is a paradigm change, yet there must, I say, must still be taints of the inspiration and influences of his original teachers. So, there can be no total claim that the new teacher can have a solution space greater than his own teachers, just a more complex derived space.
2. Or By intersection. While still keeping the original solution space, by intersecting with another school of thought, a school of thought with a different paradigm, he can create a new solution space that is greater than his original teacher(s)’s.
But the two options above result in complexities and complexities result in more problems to solve. What if the teacher does not succeed? Then back to the original solution space of his teacher(s) is he/she going to be going to.
You see why I have to agree with that maxim: A student cannot be greater than his teachers?