Tsao, Hung-ping (2019). Evolutionary mathematics and science for life contingency investigation. In: “Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)”, Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 3, March 2019; 72 pages. Lenox Institute Press, PO Box 405, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM3-MAR2019; ISBN 978-0-9890870-3-2. —————ABSTRACT: This chapter will start with the accumulation function and use the geometric point of view to generalize and simplify the theory of interest. Then survey the laws of mortality from both points of view of stochastic theory and traditional actuaries. There is a thorough discussion and simple visualization of Balducci and uniform distribution of deaths assumptions of mortality rates of fractional ages. Two least square-fit cubic survivorship functions for fitting the Male Table of 1958 CSO are presented. Various complicated exposure formulas for a mortality study are obtained by a simple inspection of the valuation schedule in demography. Life insurance and annuities are first introduced in three different points of view: deterministic, stochastic and dynamic. Then the uniform representation of a general life contingency function and its derivative is defined in such a fashion that deferred, term, endowment, life insurance and life annuity with level or varying benefit and premium can be treated all in one shot.