Archimedes' principle says that the upward buoyant force that is exerted on a body submerged in a fluid is equal to the weight of the displaced fluid. There is no mathematical literature on Archimedes' principle except for two articles co-authored by the speaker. This is because the principle can be easily derived from standard macroscopic laws of physics regarding pressure. I will show how the principle can be derived from Newtonian mechanics applied to "ideal gas" consisting of point particles. Besides the derivation from a "lower level" theory, the main novelty is that the macroscopic floating object is allowed to move, unlike in the traditional proof.
The talk is based on joint research with Mauricio Duarte, Carl-Eric Gauthier, Robin Graham, Jacek Małecki and Jaime San Martin.