Topological quantum field theory (TQFT) is a powerful organizing framework for many areas of mathematics and physics. Born from 1980s algebraic topology—through discoveries such as Donaldson invariants and the Jones polynomial—and with quantum physics interpretations initially provided by Atiyah, Witten, and others, TQFTs are today a vital tool for studying quantum matter. TQFTs describe the effective theories of topological insulators, give frameworks for theories of quantum computing, and provide an ideal language for understanding symmetries of quantum systems, including recent…