After World War II, quite a few mathematicians were attracted to the modeling of phase transitions as this area of physics was seeing considerable mathematical difficulties. This paper studies their contributions to the physics of phase transitions, and in particular those of the by far most productive and successful of them, the Polish-American mathematician Mark Kac (1914–1984). The focus is on the resources, values, and traditions that the mathematicians brought with them and how these differed from those of contemporary physicists as well as the mathematicians’ relations with the physicists in terms of collaboration and reception of results.

In this paper, we examine the history of the idea that noise presents a fundamental limit to physical measuring processes. This idea had its origins in research aimed at improving the accuracy of instruments for electrical measurements. Out of these endeavors, the Swedish physicist Gustaf A. Ising formulated a general conclusion concerning the nature of physical measurements, namely that there is a definite limit to the ultimate sensitivity of measuring instruments beyond which we cannot advance, and that this limit is determined by Brownian motion. Ising’s conclusion agreed with experiments and received widespread recognition, but his way of modeling the system was contested by his contemporaries. With the more embracing notion of noise that developed during and after World War II, Ising’s conclusion was reinterpreted as showing that noise puts a limit on physical measurement processes. Hence, physicists in particular saw the work as an indication that noise is of practical relevance for their enterprise.