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One step forward, one step back: A puzzle approach to Erdős’ discrepancy problem

by Dana Ernst

Published February 13, 2015 in Science

In the 1930s, the famous Hungarian mathematician, Paul Erdős, thought that for any infinite sequence of +1 and -1, it would always be possible to find a finite subsequence consisting of every nth term up to some point summing to a number larger than any you choose. But Erdős could not prove his conjecture, which he referred to as the "discrepancy problem." About a year ago, Lisitsa and Konev published a proof that is a significant step towards proving Erdős' problem. Their computer-assisted proof resulted in headlines such as "Wikipedia-size maths proof too big for humans to check" because their proof is as large as the entire content of Wikipedia, making it unlikely that it will ever be checked by a human being. In this episode of FAMUS, we will tinker with Erdős’ puzzle and attempt to wrap our heads around its difficulty.

This talk was given at the Northern Arizona University Friday Afternoon Mathematics Undergraduate Seminar (FAMUS) on Friday, February 13, 2015.