Numerical infinities and infinitesimals open new horizons in computations and give unexpected answers to 2 Hilbert problems

In the last issue of the prestigious journal EMS Surveys in Mathematical Sciences published by the European Mathematical Society there appeared a 102 pages long paper entitled “Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems” written by Yaroslav D. Sergeyev, Professor at Lobachevsky State University in Nizhni Novgorod, Russia and Distinguished Professor at the University of Calabria, Italy (see his Brief Bio below). The paper describes a recent computational methodology introduced by the author paying a special attention to the separation of mathematical objects from numeral systems involved in their representation. It has been introduced with the intention to allow people to work with infinities and infinitesimals numerically in a unique computational framework in all the situations requiring these notions. The methodology does not contradict Cantor’s and non-standard analysis views and is based on the 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 proved by the famous Italian logician Prof. Gabriele Lolli. This computational methodology uses a new kind of supercomputer called the Infinity Computer (patented in USA… Read full this story

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