  The Hardy--Littlewood prime $k$-tuples conjecture has long been thought to be
completely unapproachable with current methods. While this sadly remains true,
startling breakthroughs of Zhang, Maynard, and Tao have nevertheless made
significant progress toward this problem. In this work, we extend the
Maynard-Tao method to both number fields and the function field
$\mathbb{F}_q(t)$.
