1. Zugzwang
    08 Jun '07
    20 Nov '14 21:401 edit
    My hypothesis is that we are taught early tends to have a disproportionate
    influence upon us, though it's possible to unlearn some of our early lessons.

    As a young student, I became interested in the mathematics of paper folding.
    Yet I soon abandoned my interest because I lacked a mentor who shared
    any interest in it. Indeed, I was strongly discouraged and advised to stop
    wasting my time wondering about non-classical methods of construction.
    Going back to the ancient Greeks, a compass and and a straightedge were
    the only tools allowed in geometric construction.

    Speaking of the ancient Greeks, there was a famous 'Delian problem', in
    which the oracle of Delphi challenged people to construct a cube with
    exactly twice the volume of an existing cube. This has been proven
    (in 1837) to be impossible with only a compass and a straightedge.


    In 1936 Margherita Piazzolla Beloch (1879-1976), an Italian mathematician,
    proved that, given a length L on a paper, she could fold a length that was
    exactly the cube root of L. This could lead to solving the Delian problem.
    The 'Beloch fold' showed that origami can solve general cubic equations.
    Unfortunately, her work seems to have remained obscure for decades.

    Contrary to what my early teachers had told me, paper folding evidently
    has been recently receiving an increasing amount of mathematical study.
    An early 'discouraging word' can be enough to alter one's path.