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For questions arising from topics discussed during the Polymath5 project, which tried to solve the Erdős discrepancy problem.

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Experimental mathematics leading to major advances

Didn't the work of Candès and Tao on compressed sensing begin by a computer experiment by Candès that gave results "too good to be true"? See: http://www.ams.org/samplings/math-history/hap7-pixel.pdf
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