The Mathieu group $M_{23}$ is a Galois group over $\mathbb{Q}$

Researchers studying the inverse Galois problem realized 25 of the 26 sporadic finite simple groups as Galois groups over $\mathbb{Q}$ during 1984-1989. We complete this program by proving that the last remaining sporadic group, the Mathieu group $M_{23}$, occurs as a Galois group over $\mathbb{Q}$.