Two mathematicians, Will Sawin of Columbia University and Mark Shusterman of University of Wisconsin-Madison, recently posted a proof of a version of one of the most famous open problems in mathematics. The result opens a new front in the study of the twin primes conjecture, which has bedeviled mathematicians for more than a century and has implications for some of the deepest features of arithmetic.
The twin primes conjecture concerns pairs of prime numbers with a difference of 2. The numbers 5 and 7 are twin primes. So are 17 and 19. The conjecture predicts that there are infinitely many such pairs among the counting numbers, or integers. Mathematicians made a burst of progress on the problem in the last decade, but they remain far from solving it.
The new proof solves the twin primes conjecture in a smaller but still salient mathematical world. They prove the conjecture is true in the setting of finite number systems, in which you might only have a handful of numbers to work with.