The Number Theory Revival - From Diophantus to Fermat

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.

The number theory revival
Fermat
Diophantus 200-300 AD
Combinatorics - Binomial theorem
Some results of Fermat
Algebraic curves
Folium of Descartes
Newton forms for cubics
Sum of four squares
Fermat's little theorem