Physical Sciences and Mathematics Commons^™

Deep Mathematical Results Are The Ones That Connect Seemingly Unrelated Areas: Towards A Formal Proof Of Gian-Carlo Rota's Thesis, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When is a mathematical result deep? At first glance, the answer to this question is subjective: what is deep for one mathematician may not sound that deep for another. A renowned mathematician Gian-Carlo Rota expressed an opinion that the notion of deepness is more objective that we may think: namely, that a mathematical statement is deep if and only if it connects two seemingly unrelated areas of mathematics. In this paper, we formalize this thesis, and show that in this formalization, Gian Carlo Rota's thesis becomes a provable mathematical result.