Incidentally, this topic gave rise to a much larger theory, namely mirror symmetry (unrelated to reflection at everyday mirrors). Please take the following account of the history with some grain of salt, I'm not an expert on this topic.
After counting lines on a smooth cubic surface, you could also count lines on other manifolds, for instance three-dimensional ones given by a quintic polynomial (these are examples for "Calabi–Yau manifolds"). Also you could count curves of degree two, three, and so on instead of lines, which are curves of degree one. The calculations get increasingly harder: The case of degree two curves was only settled in 1986.
It therefore came as a surprise when a group of physicists (Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes) announced in 1991 a formula for calculating the result for curves of any degree. They did so by inventing a new technique, mirror symmetry, in which one relates the "complex geometry" (as in "complex numbers") of the manifold on which you're counting curves to the "symplectic geometry" of a certain other manifold, dubbed mirror of the original one.
Many aspects of mirror symmetry are still widely non-understood and many conjectures are motivated and made plausible by physical arguments.
After counting lines on a smooth cubic surface, you could also count lines on other manifolds, for instance three-dimensional ones given by a quintic polynomial (these are examples for "Calabi–Yau manifolds"). Also you could count curves of degree two, three, and so on instead of lines, which are curves of degree one. The calculations get increasingly harder: The case of degree two curves was only settled in 1986.
It therefore came as a surprise when a group of physicists (Philip Candelas, Xenia de la Ossa, Paul Green, and Linda Parkes) announced in 1991 a formula for calculating the result for curves of any degree. They did so by inventing a new technique, mirror symmetry, in which one relates the "complex geometry" (as in "complex numbers") of the manifold on which you're counting curves to the "symplectic geometry" of a certain other manifold, dubbed mirror of the original one.
Many aspects of mirror symmetry are still widely non-understood and many conjectures are motivated and made plausible by physical arguments.
https://en.wikipedia.org/wiki/Mirror_symmetry_(string_theory... https://en.wikipedia.org/wiki/Homological_mirror_symmetry