Quanta Magazine Covers Reverse Mathematics

An article just published in Quanta Magazine by Natalie Wolchover covers a recent result from reverse mathematics.  Keita Yokoyama and Ludovic Patey showed that Ramsey’s theorem for pairs is finitistically reducible, i.e., it is $latex \Pi_3$ conservative over $latex I\Sigma_1$. The article explains Ramsey’s theorem, but also Hilbert’s program and its more recent relativizations, i.e., the reverse mathematics program.