Mayer’s theory of gas condensation (1937–1970): phase transitions and mathematical reasoning

Abstract We study the origins and reception of the statistical mechanical theory of gas condensation put forward by the American scientist Joseph E. Mayer in 1937. Promising the first single and unified treatment of the gas and liquid phases of molecule assemblies on a solid theoretical footing, the theory was praised by Mayer’s contemporaries as a breakthrough. Mayer’s mathematical reasoning was, however, soon the subject of much debate, and while some of his peers accepted his reasoning, others questioned its validity on various grounds. With the intermission of World War II, it was first in the 1950s that the valid parts of the reasoning could be separated from the questionable ones, which meant that most physicists dropped the theory as a research object. The paper addresses Mayer’s mathematical reasoning and its reception, as well as the impact of the theory on physics. The theory helped put the problem of a statistical mechanical theory of phase transitions on physicists’ agenda as well as highlight the importance of mathematical sound reasoning in this area.