AMSEcast

In this wide-ranging conversation, Ahmed El-Mokadem explores the deep ideas behind mathematics' most mysterious numbers, revealing how concepts like zero, infinity, irrational numbers, and imaginary numbers challenge both logic and philosophy. He traces how constants such as π, e, the golden ratio, and the Feigenbaum constants appear universally across nature, physics, biology, and technology—suggesting they are discovered features of reality rather than human inventions. El-Mokadem highlights how mathematics repeatedly expands its own boundaries, from accepting imaginary numbers to assigning meaning to divergent infinities through Ramanujan's work. He shows that even chaos follows hidden numerical order, and that numbers long viewed as paradoxical often turn out to be indispensable. Throughout, mathematics emerges not as cold abstraction, but as a living language that reveals structure, mystery, and beauty in the universe. The discussion ultimately invites listeners to see math as a bridge between human curiosity and the deep order of the cosmos.