The Medical field Gains Additional Mathematical Theorem!

For many decades, the medical sciences have been dominated by Bayes' theorem. The theorem was developed by an English clergyman, Thomas Bayes (1702-1761), and has since been refined by academics, including some academicians from the mathematical and medical fields, to make it more workable. It was first published in the Philosophical Transactions of the Royal Society in London in 1763. The theorem is probabilistic and was not originally developed for this field, though now, it is mentioned in diagnostic research and practice to indicate its importance in decisions about diagnosis.

This article concerns a new mathematical theorem in the field of medical sciences, which Professor Desmond Ayim-Aboagye, who obtained his PhD in Psychology of Religion and later conducted research in Pain Studies at Uppsala University, has propounded. It was first published in Cientperiodique Medical Journal of Neurology and Psychology in 2022 in Canada. The usefulness of this new theorem is that it employs two famous theorems in mathematical analysis to prove the point made by this theorem. They are the Intermediate Value theorem and Bolzano’s theorem, which had already accorded the field of mathematics and its neighboring fields popularity. Karl Weierstrass (1815-1897), the German Mathematician known for the convergence of series and who contributed to the theory of periodic functions, functions of real variables, elliptic functions, Abelian functions, converging infinite products, and the calculus of variations, had contributed to the development of the Intermediate Value theorem.

Researchers and practitioners in medical practice will benefit from the use of the Zero State Theorem, which advises specialists on the spread and treatment of infectious diseases, whether in the laboratory or in the field of a country. Professor Ayim-Aboagye used the Set theory principles to propound his Zero State theorem in the first place, but it can easily be understood by any layman or amateur mathematician who is not conversant with mathematics and Set theory. Set theory was first developed by the German Mathematician Georg Cantor two centuries ago, around 1870. Though it was initially rejected, Set theory has today become the ground principles from which all mathematical developments spring.

The Zero State theorem states that if an infectious disease is spreading in different regions, there must have been a point in time when the disease was in a “zero state” and was transmitted by a “patient zero”. This point can be proven using the Intermediate Value theorem and Bolzano’s theorem from mathematical analysis, which state that if a continuous function is sometimes positive and sometimes negative over an interval, it must be 0 at some point within that interval. The Zero State theorem is essential as it reminds practitioners and researchers to search for patient zero to comprehend the initial spread and treatment of a disease.

The author of the Zero State theorem used the German Physician Robert Hermann Koch's postulates to generate fundamental theorems of medical sciences. Among other things, the fundamental theorems of medical diagnosis include three formulations of the theorems. The first theorem states that no disorder exists without symptoms and no symptoms exist without a disorder. The second theorem states that a disorder can be transmitted. Koch's postulates and an extended version by Fredericks and Relman are used to prove the second theorem by demonstrating disease transmission from one individual to another.

Professor Ayim-Aboagye's contributions to medical science have energized these important fields, which have already developed without their own substantive theorems. Today, the African scholar, who may be the first to have contributed to the mathematical fields with his development of mathematical theorems in both Medicine and Economics, stands tall in the scientific domain. We hope his numerous research findings and scientific contributions will encourage many Africans to surge in the academic world.