In the 19th century, a German mathematician named Carl Jacobi developed an interesting insight:

Many hard math problems become easier to solve when you flip them around and work backwards.

He famously preached to his students, "Man muss immer umkehren."

Translation: Invert, always invert.

As it turns out, this idea echoes across history, showing up in a variety of places before and after Jacobi...

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