Mathematicians have found solutions to a 140-year-old, seven-dimensional equation that were not known to exist for more than a century, despite its widespread use in modeling the behavior of gases. During the late 1860s and 1870s, physicists James Clerk Maxwell and Ludwig Boltzmann developed this equation to predict how gaseous material distributes itself in space and how it responds to changes in things like temperature, pressure or velocity. Solutions of the equation, beyond current computational capabilities, describe the location of gas molecules probabilistically and predict the likelihood that a molecule will reside at any particular location and have a particular...