the boolean pythagorean triples problem has been a long-standing open problem in ramsey theory: can the set $n = {1,2,3,…}$ of natural numbers be partitioned into two parts, such that neither part contains a triple $(a, b, c)$ with $a^2 + b^2 = c^2$ ? a prize for the solution was offered by ron graham over two decades ago. we show that such a partition is possible for the set of integers in $[1,7824]$, but that it is not possible for the set of integers in $[1,m]$ for any $m > 7824$. of course, it is completely infeasible to attempt prove this directly by examining all $2^m$ possible partitions of $[1,m]$ when $m = 7825$, for example. we solve this problem by using the cube-and-conquer paradigm, a hybrid sat method for hard problems, employing both look-ahead and cdcl solvers. an important role is played by dedicated look-ahead heuristics, which indeed allowed us to solve the problem on a cluster with 800 cores in about 2 days. due to the general interest in this mathematical problem, our result requires a formal proof. exploiting recent progress in unsatisfiability proofs of sat solvers, we produced and verified a proof in the drat format, which is almost 200 terabytes in size. from this we extracted and made available a compressed certificate of 68 gigabytes, that allows anyone to reconstruct the drat proof for checking. these techniques show great promise for attacking a variety of similar computational problems arising in combinatorics and computer science.