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83-year-old math problem solved

Proposal by Erdős involving number sequences validated

By
3:32pm, September 25, 2015
puppies and kittens chart

FURRY MATH  The Erdős discrepancy problem examines sequences of 1s and –1s or, in this case, puppies and kittens. The goal is to see how effectively one can minimize the difference between the number of cats and dogs in various subsequences. Here, the difference in each row doesn’t exceed one.

It took more than 80 years, but a problem posed by a mathematician who delighted in concocting tricky ones has finally been solved.

UCLA mathematician Terence Tao has produced a solution to the Erdős discrepancy problem, named after the enigmatic Hungarian numbers wizard Paul Erdős. Tao’s proof, posted online September 18 at arXiv.org, shows that the difference (or discrepancy) between the quantities of two elements within certain sequences can grow without bound, even if someone does the best possible job of minimizing the discrepancy.

“Based on Tao’s stature, I would trust it straightaway,” even though the proof hasn’t yet been peer-reviewed, says Alexei Lisitsa, a computer scientist at the University of Liverpool in England.

While the problem probably doesn’t have real-world applications, Tao says, “the act of solving a problem like this often gives a trick for solving more complicated things.”

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