This course traces the evolution and application of the scientific method emphasizing the synergy between mathematical and scientific reasoning. Beginning with Al-Khwarizmi, whose work in algebra and algorithms laid the foundation for systematic inquiry, the course progresses to Viete's "Introduction to the Analytic Art," showcasing the advancement of modern mathematical techniques. Descartes'"Discourse on Method" and "Geometry" extend the connection between reasoning and scientific investigation. Francis Bacon's "Novum Organum" shifts the focus to empirical research and inductive reasoning, formalizing the scientific method as a tool for discovery. Works of Harvey and Linneaus are also examined. This course offers students a deep understanding of how the scientific method has been developed and applied across disciplines, shaping the trajectory of human knowledge and understanding.