Mathematics is distinguished from the sciences by the freedom it enjoys in choosing basic assumptions from which consequences can be deduced by applying the laws of logic. We call the basic ...

The theorems of Hadamard and of Poincaré–Miranda give sufficient conditions for the existence of at least one zero for some continuous mappings from a Euclidean space into itself. The note gives ...

Recent characterizations of probability measures by use of conditional expectations have included many probability measures defined on subsets of the real line. This paper contains results which allow ...

Scientists have for the first time used artificial intelligence to suggest and prove new mathematical theorems. The potential breakthrough came in a collaboration between mathematicians who specialise ...

Figure 1: Schematic illustration of the configurational space, molecular free-energy landscapes and experimental set-up. Finally, to illustrate the power of the method we show the case of molecules I2 ...