The number theory revival | Math History | NJ Wildberger

Author: Insights into Mathematics

After the work of Diophantus, there was something of a lapse in interest in pure number theory for quite some while. Around 1300 Gersonides developed the connection between the Binomial theorem and combinatorics, and then in the 17th century the topic was again taken up, notably by Fermat, and then by Euler, Lagrange, Legendre and Gauss. We discuss several notable results of Fermat, including of course his famous last theorem, also his work on sums of squares, Pell’s equation, primes, and rational points on curves. The rational parametrization of the Folium of Descartes is shown, using the technique of Fermat.
We also state Fermat’s little theorem using the modular arithmetic language introduced by Gauss.

Screenshot PDFs for my videos are available at the website These give you a concise overview of the contents of the lectures for various Playlists: great for review, study and summary.

My research papers can be found at my Research Gate page, at

My blog is at, where I will discuss lots of foundational issues, along with other things.

Online courses will be developed at The first one, already underway is Algebraic Calculus One at Please join us for an exciting new approach to one of mathematics’ most important subjects!

If you would like to support these new initiatives for mathematics education and research, please consider becoming a Patron of this Channel at Your support would be much appreciated

Here are all the Insights into Mathematics Playlists:

Elementary Mathematics (K-6) Explained:
Year 9 Maths:
Ancient Mathematics:
Wild West Banking:
Sociology and Pure Mathematics:
Old Babylonian Mathematics (with Daniel Mansfield):
Math History:
Wild Trig: Intro to Rational Trigonometry:
Wild Linear Algebra:
Famous Math Problems:
Probability and Statistics: An Introduction:
Boole’s Logic and Circuit Analysis:
Universal Hyperbolic Geometry:
Differential Geometry:
Algebraic Topology:
Math Seminars:

And here are the Wild Egg Maths Playlists:

Triangle Centres:
Six: An elementary course in pure mathematics:
Algebraic Calculus One:
Algebraic Calculus Two:

Video source Youtube

Leave a Comment

20 − 11 =