In the late 1860's-1870's, physicists James Clerk Maxwell and Ludwig Boltzmann made one of science's many leaps of faith in using a certain equation to predict how gaseous material distributes itself and responds to change. They used the Boltzmann equation:
which modeled the gaseous behavior REAL well under experimentation, even though it was assumed at the time for gases to actually be comprised of molecules. The study on this equation was funded by the NSF (duh) and conducted by Penn math professors Philip Gressman and Robert Strain. Using PDE's and harmonic analysis, modern 50 year old techniques woot, they described locations of gas molecules probabilistically and predicted particular locations (an area I'm all about right now after using probability models last summer about crime locations in LA county). View the full article about the discovery in the science daily.
Way to go guys, did old Boltzmann proud!!!! Work that beard boy.