In this paper we develop a formal framework to measure the efficiency gains of introducing new concepts in mathematics. We first define what we mean by a mathematical theory. We then define a coefficient η which turns out to be positive if a change in the formalism of a theory results to be a gain. In this sense, mathematical research is seen as a continuous optimization process. We also provide a formal proof, demonstrating that finding the maximum possible value of η is in general a non-computable problem, implying that the discovery of new mathematical ideas is an intrinsically creative process that cannot be automated by an algorithm. Finally, we discuss the implications of these findings for the "saturation" of mathematical branches, the role of artificial intelligence in research, and the ontological nature of the mathematical landscape.
Francesco S. Giannice (Sun,) studied this question.