## Einstein’s first proof

Steven Strogatz walks us through the first mathematical proof Albert Einstein did when he was a boy: a proof of the Pythagorean theorem.

Einstein, unfortunately, left no such record of his childhood proof. In his Saturday Review essay, he described it in general terms, mentioning only that it relied on “the similarity of triangles.” The consensus among Einstein’s biographers is that he probably discovered, on his own, a standard textbook proof in which similar triangles (meaning triangles that are like photographic reductions or enlargements of one another) do indeed play a starring role. Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come to this deflating conclusion, and each of them describes the steps that Einstein would have followed as he unwittingly reinvented a well-known proof.

Twenty-four years ago, however, an alternative contender for the lost proof emerged. In his book “Fractals, Chaos, Power Laws,” the physicist Manfred Schroeder presented a breathtakingly simple proof of the Pythagorean theorem whose provenance he traced to Einstein.

Of course, that breathtaking simplicity later became a hallmark of Einstein’s work in physics. See also this brilliant visualization of the Pythagorean theorem

P.S. I love that two of the top three most popular articles on the New Yorker’s web site right now are about Albert Einstein.

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