## Math in the Physical Sciences## Chemistry and Math |

## What is the Boltzmann equation? |

In the late 1860s, British physicist James Clerk Maxwell (1831–1879) and Austrian theoretical physicist Ludwig Edward Boltzmann (1844–1906) developed the Boltzmann equation to predict how a gaseous material distributes itself in space, along with how it responds to various environmental factors, such as temperatures, pressure, or velocity—all combined into what is called the kinetic theory of gases.

For almost 140 years, the equation remained unsolved, but in 2010 researchers found solutions to the 7-dimesional equation using modern mathematical techniques. Overall, they used partial differential equations and harmonic analysis to prove that the equation does have solutions. This not only helps scientists understand the probability of where molecules exist, but also explains how molecules just glance off one another rather than collide head on, apparently a dominant way collisions work for the full equation.