Physical law and the quest for mathematical understanding

The theoretical physics of the first quarter of the twentieth century --centering around relativity theory and nonrelativistic quantum mechanics--has had a broad influence mathematically. The main achievement of theoretical physics in the following half-century was the development of quantum field theory or QFT. Yet the mathematical influence of QFT still belongs largely to the $21^{st}$ century, because its mathematical foundations are still not well-understood.