Explore the historical controversies and debates surrounding the development of Calculus in this 49-minute lecture. Delve into the criticisms faced by Newton and Leibniz's groundbreaking ideas, despite their impressive achievements. Examine problems with differential and integral calculus, the nature of curves, the role of imaginary numbers, and the St. Petersburg paradox in probability theory. Learn about the influential critics, including members of the Bernoulli family, a Dutch physician, and an English bishop. Discover how these debates motivated 18th-century mathematicians like Euler and Lagrange to establish more logical algebraic foundations for calculus, leading to further developments in limits, continuum theory, and modern axiomatic approaches to real numbers. Gain insight into the ongoing challenges in mathematics that trace back to ancient Greek times and continue to impact the field in the 21st century.