Carl Jacobi, the nineteenth-century German mathematician, developed a reputation as someone who could solve especially hard and intractable problems. He learned that to do that most easily, Man muss immer umkehren, which translates to “One must invert, always invert.” To invert means to turn an assumption or approach upside down, to work backward, to ask, “What if the opposite were true?” Inversion can help you discover obvious insights you have missed because you’re looking at the problem from only one point of view. It can highlight errors in our thinking. It can open our minds to new ways
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