Solving an Unsolvable Math Problem

In “The Psychology of Invention in the Mathematical Field,” published in 1945, Jacques Hadamard quotes a mathematician who says, “It often seems to me, especially when I am alone, that I find myself in another world. Ideas of numbers seem to live. Suddenly, questions of any kind rise before my eyes with their answers.” In the back yard, Zhang had a similar experience. “I see numbers, equations, and something even—it’s hard to say what it is,” Zhang said. “Something very special. Maybe numbers, maybe equations—a mystery, maybe a vision. I knew that, even though there were many details to fill in, we should have a proof. Then I went back to the house.”

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