What is the name of the mathematical science in Isaac Asimov's 'Foundation' series?

The mathematical science in Isaac Asimov’s “Foundation” series is psychohistory.

Hari Seldon develops psychohistory as a mathematical discipline combining history, sociology, psychology, and statistics. Its central premise is that the behavior of enormous populations can be predicted probabilistically, even though the actions of individual people remain unpredictable. Seldon uses it to foresee the collapse of the Galactic Empire.

Psychohistory cannot simply control the future or predict every event. Its forecasts work only at a vast social scale and under particular assumptions, including a sufficiently large population and the absence of unusual individuals disrupting the statistical pattern. This is why the character known as the Mule becomes such a major threat to the Seldon Plan.

Readers sometimes confuse psychohistory with sociology, but sociology is a real-world social science, while psychohistory is Asimov’s fictional mathematical extension of it. “Positronics” and “robotics” belong to Asimov’s robot stories and are unrelated to Seldon’s predictive science.