New computational methodology gives unexpected answers to two Hilbert problems

A paper titled “Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems,” published in EMS Surveys in Mathematical Sciences describes a recent computational methodology related to the separation of mathematical objects from numeral systems involved in their representation. It allows mathematicians to work with infinities and infinitesimals numerically in a unique computational framework in all situations requiring these notions. The methodology does not contradict Cantor’s, and is based on Euclid’s Common Notion no. 5, “The whole is greater than the part,” applied to all quantities (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). The non-contradictory of the approach has been proven by Italian logician Prof. Gabriele Lolli.