In Mikhail Bulgakov’s novel “The Master and Margarita,” the protagonist, a writer, burns a manuscript in a moment of despair, only to find out later from the Devil that “manuscripts don’t burn.” While you might appreciate this romantic sentiment, there is of course no reason to think that it is true. Nikolai Gogol apparently burned the second volume of “Dead Souls,” and it has been lost forever. Likewise, if Bulgakov had burned his manuscript, we would have never known “Master and Margarita.” No other author would have written the same novel.
But there is one area of human endeavor that comes close to exemplifying the maxim “manuscripts don’t burn.” That area is mathematics. If Pythagoras had not lived, or if his work had been destroyed, someone else eventually would have discovered the same Pythagorean theorem. Moreover, this theorem means the same thing to everyone today as it meant 2,500 years ago, and will mean the same thing to everyone a thousand years from now — no matter what advances occur in technology or what new evidence emerges. Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary and timeless.
What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind?
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