Explore the resurgence of number theory in this 57-minute lecture, tracing its development from Diophantus to the 17th century. Delve into Fermat's significant contributions, including his famous last theorem, work on sums of squares, Pell's equation, primes, and rational points on curves. Examine the connection between the Binomial theorem and combinatorics developed by Gersonides. Learn about the rational parametrization of the Folium of Descartes using Fermat's technique. Understand Fermat's little theorem through the lens of Gauss's modular arithmetic. Gain insights into the historical progression of number theory and its key figures, including Euler, Lagrange, Legendre, and Gauss.