The mathematics of geothermal energy involves the application of various mathematical methods to explore and optimize how geothermal heat from the Earth's interior can be harnessed for energy production and heating. Geothermal energy is derived from the heat generated by the Earth's formation and ongoing radioactive decay, with the temperature increasing significantly with depth, a concept known as the geothermal gradient. High-gradient areas, particularly along tectonic plate boundaries like the Ring of Fire, are prime locations for geothermal energy projects.

Mathematicians and engineers utilize models such as Lagrangian–Eulerian flow models to understand fluid movement and its implications for geothermal reservoirs, while stochastic and geometric models help in optimizing energy extraction processes. Additionally, geothermal heat pump systems have been developed to transfer heat for building heating and cooling, though large-scale water movement can lead to geological concerns such as subsidence.

Electricity can also be generated from geothermal resources, with power plants utilizing steam to drive turbines. Despite the advantages of geothermal energy, including its low greenhouse gas emissions and reliability compared to other renewable sources, its adoption has been slow due to perceived limitations in quality sites and the high initial capital costs. Nonetheless, renewed interest in geothermal energy is evident, especially amid global concerns about climate change.