Pre-existing numbers, related mathematics and consequential physical theories are generally used for the treatment of new scientific problems. In this memoir we outline the research conducted by various mathematicians, physicists and chemists over the past two decades who have shown that the inverse approach, the construction of new numbers, related new mathematics and consequential new physical theories from open physical, chemical and biological problems, leads to new intriguing formulations of increasing complexity called iso-, geno- and hypermathematics for the treatment of matter in reversible, irreversible and multi-valued conditions, respectively, plus anti-isomorphic images called isodual mathematics for the treatment of antimatter.