We review recent advances on isomathematics, genomathematics and hypermathematics for the invariant representation of reversible, irreversible and multi-valued 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 operator S in the associativity-preserving iso-, geno- and hyper-completions , , of the millenary old associative product of operators , . We then review advances in physics, chemistry and biology which are permitted by iso-, geno- and hyper- mathematics, but impossible for 20th century applied mathematics [1] [2].

Following studies initiated at Harvard University in the early 1980s under DOE support, we outline: 1) The irreversible, Lie-admissible and Jordan-admissible branch of hadronic mechanics (hm) with generalized Heisenberg equation i(dA/dt) = (A, H) = A < H – H < A = ARH – HSA = (ATH – HTA) + {AJH + HJA}, R = T + J > 0, S = –T + J > 0 for the consistent representation of notoriously irreversible nuclear fusions; 2) The experimentally confirmed new bond within a DC arc of natural positively charged Deuterons and negatively charged valence electron pairs into a pseudo-Deuteron, D(1, 2, 1) + = D(–1, 2, 1), which is prohibited by Heisenberg's uncertainty principle despite the extremely big Coulomb attraction between electrons and nuclei, but fully admitted by the hadronic isodeterminism; 3) The new, independently confirmed, HyperFusions of Deuterons and pseudo-Deuteron into the Helium without the Coulomb barrier . We finally review the independent certifications of the sustainable and controllable excess nuclear energy produced by the third Hadronic HyperFusion Reactor www.world-lecture-series.org/dragon-iii without the Coulomb barrier and without the release of harmful radiation.

We first review the initiation by two of us (R. M. S. and T. V.) [1] of the mathematical representation of life, intended as the difference between organic and inorganic molecules, via the Lie-admissible hyperstructural branch of hadronic mechanics representing the size of biological molecules, their contact thus non-Hamiltonian interactions and the irreversibility over time. We then review and expand the studies done in the subsequent paper [2] showing that: 1) The time irreversible hadronic representation of life can be obtained via the addition of the symmetric Jordan brackets to reversible quantum mechanical Lie brackets; 2) The Lie and Jordan admissible axiomatic formulation of hadronic medicine with non-linear, non-local an non Hamiltonian entanglements of molecular constituents operating without the use of a known form of energy; 3) The smooth connection between hadronic uncertainties at small distances and full Einsteinian determinism at classical distances; 4) The quantitative representation by hadronic medicine of some actions by biological entities beyond our sensory perception; 5) The expected diagnostic and curative values of hadronic medicine.