Synopsis
This paper explores the profound connection between mathematics and philosophy, tracing their shared history through the work of Euclid, René Descartes, and Bertrand Russell. It reveals how philosophical methods, such as Euclid’s deductive reasoning and Descartes’ rationalist approach, directly shaped the development of mathematical principles like geometry, analytic geometry, and even calculus. By examining Russell’s Logicism, the paper demonstrates that modern mathematics is fundamentally grounded in higher logic. Offering a fresh perspective, this work underscores the vital role of philosophical inquiry in shaping the course of mathematical thought throughout history.