In existographies, Constantin Caratheodory (1873-1950) (CR:16) was a German mathematician, a student of the Berlin school of thermodynamics in 1900, who is noted for his pure axiomatic mathematical interpretation of thermodynamics, specifically his so-called Caratheodory's theorem (or theorem of Caratheodory, as it has come to be called), centered around a proof of the necessary relation between the Pfaffian form, differential quantities of heat, and the integrating denominator. [1]“We can derive the whole theory, without assuming the existence of heat, i.e. a physical quantity that differs from the usually mechanical quantities.”
In his work he reformulated the first and second laws of thermodynamics as the first and second axioms. He then introduced two assumptions differing from the traditional approach, one that heat was reduced to mechanical work and second that the system was treated mainly as an adiabatic process instead of a cyclic process. [1]
“The problem as it seemed to many scientists was to explain in terms of the real laws of physics (like Maxwell’s and Einstein’s) why entropy never decreased. Perhaps the most penetrating analysis of this question was given in 1909 by the German mathematician C. Caratheodory. His work did not commend itself generally, however, because it did not arrive at the wanted result. What Caratheodory proved was that either entropy could never decrease or it could never increase, but he couldn’t say which! To agree with the observed situation, it was still necessary to make an arbitrary choice.”
— Fred Hoyle (1981), Evolution From Space: a Theory of Cosmic Creationism (Ѻ)