The first generation of computers (vacuum tube-based) emerged from WWII for scientific, military, or business purposes. In this pioneering time, the term “mathematical machines” was also used to distinguish them from human computers. This talk presents a working software simulator of the Belgian Mathematical Machine (MMIF), a little-known computer funded after WWII by IRSIA-FNRS and inaugurated 70 years ago at the Bell Company in Antwerp. We will show, including using the stepping mode, how it deals with programs and data using separate "RAM" drums (Harvard-style) and carries out computations with a high-precision floating-point calculation unit. You will discover the not-so-odd instruction set, coding style and how complex functions required for applications in ballistics and thermodynamics were implemented as a specific library. In addition to releasing the simulator as Open Source, the NAM-IP museum also publicly archived the available technical documentation.