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trees and plants
Hello.Well, this is a general question.when solving a math problem what are the ways the mind finds to prove the problem?How about giving new definitions for abstract objects or posing new problems on your own?What are the motivations to do these things?Should they be of very high value to be accepted?Should they be very difficult or be interesting to be accepted?I know that Aristotle in ancient Greece tried to solve problems other posed and he also posed his own problems and then tried to solve them.Is this done today in math or physics?Are mathematicians of two kinds, problem solvers and theory builders?What are theory builders?Thank you.