An introduction to iso-, geno- and hyper-mathematics and their applications in physics, chemistry and biology

Abstract

In this work, the author reviews recent advances on isomathematics, genomathematics and hypermathematics that were initiated  by the Italian-American scientist Ruggero Maria Santilli for the invariant representation of reversible and irreversible systems of extended constituents in conditions of deep mutual entanglement with conventional linear, local and potential interactions represented by the conventional Hamiltonian H plus non-linear, non-local and non-potential interactions represented by the Santillian S in the axiom-preserving  iso-, geno- and hyper-completion $A\hat \times B = A S B$ of the millenary old associative product of operators $A\times B =  AB$. We then review and present, apparently for the first time, new advances in physics, chemistry  and biology which are permitted by iso-, geno- and hyper-mathematics, but impossible for 20th century applied mathematics.