Embark on a captivating journey through the evolution of computational science in this keynote address from JuliaCon 2020. Prof Linda Petzold shares her extensive experience, from programming with punch cards to developing sophisticated algorithms for differential equations. Explore the challenges and breakthroughs in solving Ordinary Differential Equations (ODEs) and Differential-Algebraic Equations (DAEs), including the development of LSODA and DASKR. Discover applications in various fields such as computational combustion, solar power, spacecraft trajectories, and chemical vapor deposition. Delve into discrete stochastic simulations and their relevance in biological systems, including circadian rhythms and COVID-19 modeling. The talk concludes with a Q&A session addressing software engineering challenges in scientific computing, modeling biological systems, and the intersection of differential equations and machine learning.