- Feb 24, 2016
More At: https://www.quantamagazine.org/smaller-is-better-why-finite-number-systems-pack-more-punch-20190211/It’s one thing to turn a cartwheel in an open field. It’s another to manage it in a tight space like a bathtub. And that, in a way, is the spirit of one of the most important results in number theory over the past two decades.
The result has to do with the “sum-product problem,” which I wrote about last week. It asks you to take any set of numbers and arrange them in a square grid, then fill in the grid with either the sums or the products of the crosswise pairs.
The sum-product problem states that the number of distinct sums or products will always be close to N2 (where N stands for the number of numbers used to make your grid).