You first statement is wrong. Mathematicians cannot "trisect the angle", "duplicate the cube", or "square the circle", using only compasses and straight edge. The ancient Greeks knew how to do these using other methods, as you do.
(It was proved, in the late 19th century, that the only numbers that are "constructible with compasses and straightedge" are those that are "algebraic of order a power of two. It can then be shown that "trisecting the angle" and "duplicating the cube" are equivalent to constructing a number that is algebraic of order 2. "Squaring the circle" is equivalent to constructing " " which is not algebraic of any order.)