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The Amplitude Heathen, 1986
In 1986 mathematicians named Park and Taylor took the scattering amplitude for two gluons coming in at high energy and four gluons going out at low energy. They couldn't do it on supercomputers, they needed to compute them billions of times per second. And then a little bit later they guessed one term expression that turned out to be equivalent. That was like, okay, where did that come from? This is a pointer into a deep realm beyond space and time but no one, I mean, what can you do with it?