I am a 10th grader and recently I came to know about "Straightedge and Compass Construction". Seriously, I was stunned!!, we can actually predict that what can be constructed and what not by using "Straightedge and Compass" without actually drawing them. But when I tried to understand the concepts, everything just went up to my mind. I am not aware of the words "Field, Subfield,Extension,Tower..etc.." Is there any theorem which I can assume for a while( until I attend abstract or linear algebra class) and which is not beyond my scope(average 10th grader) to handle any kind of Impossibility proofs.
My knowledge: I know much about polynomials, number theory....and everything that you can expect from an average 10th grader.