"In my paper the fact the XY was not equal to YX was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme...and I was not able to solve it."

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When the boy begins to understand that the visible point is preceded by an invisible point, that the shortest distance between two points is conceived as a straight line before it is ever drawn with pencil and paper...the fountain of all thought has been opened to him...the philosopher can reveal him nothing new, as a geometrician he has discovered the basis of all thought.

— Johann Wolfgang von Goethe