20th century mathematics underlying mainstream physical and chemical theories is local-differential, thus solely permitting the representation of point-like masses. The Italian-American scientist R. M. Santilli accepted such a mathematics for the representation of particles when the masses are at large mutual distances, thus allowing point-like approximations, as it is the case for the atomic structure. Santilli then identified clear limitation of 20th century mathematics for the representation of extended charge distributions or wavepackets in conditions of partial or total mutual penetration, as it is the case for the synthesis of the neutron from a proton and an electron in the core of a star; for the structure of nuclei, stars and black holes; for the molecular bond of two identical valence electrons in singlet coupling; and other composite systems.
When at the Department of Mathematics of Harvard University in the late 1970s, Santilli developed a series of new mathematics for the representation of extended charge distributions or wavepackets when in condition of partial or total mutual penetration, resulting in:
1. The novel, single valued- isomathematics for the representation of composite matter-systems reversible over time of with extended constituents at short mutual distances; 2. The novel, single valued genomathematics for the representation of composite matter-systems or reactions irreversible over time with extended constituents at short mutual distance; 3. The novel multi-valued hypermathematics for the representation of biological matter-systems.
Additionally, Santilli constructed their anti-Hermitean isodual images for the representation of corresponding antimatter-systems in conditions of increasing complexity. These varieties of new mathematics are today collectively addressed by the name of hadronic mathematics, in view of their applications. The special issue of AJMP on the Foundations of Hadronic Mathematics shall review the above novel mathematics and present new advances for the use in subsequent special issues devoted to its applications.