By Lê Nguyên Hoang, Not an Ordinary Seminar, GERAD.
For one hour, I will take you through some of the most amazing recent subfields of mathematics. From computational theory to chaos theory, from infinity to ergodicity, from mathematical physics to category theory, we will be unveiling mind-blowing results of modern mathematics. Although primarily aimed at non-mathematicians, it should be of great interest to everyone.
Complexity Theory, P versus NP, RSA Cryptography (Hiking in Modern Math 2/7)
By Lê Nguyên Hoang | Updated:2016-02 | Views: 0
Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7)
By Lê Nguyên Hoang | Updated:2016-02 | Views: 0
The Limitless Vertigo of Cantor's Infinite
By Lê Nguyên Hoang | Updated:2015-12 | Views: 4182
No one believed him. Not even fellow mathematicians. They thought he was wrong. They thought he was crazy. Even he ended up doubting himself and went crazy. And yet, he had mathematically proved it all. Georg Cantor had figured out how to manipulate the infinite. Even more remarkable, he showed that there were actually several infinities; and some are bigger than others!
Self-Reference, Math Foundations and Gödel's Incompleteness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 6722
Although highly appreciated by artists, self-reference has been a nightmare for mathematicians. It took one of the greatest, Kurt Gödel, to provide a better understanding of it. This article deals with paradoxes, recursion, fractals and Gödel's incompleteness theorems.
Type Theory: A Modern Computable Paradigm for Math
By Lê Nguyên Hoang | Updated:2016-01 | Views: 13078
In 2013, three dozens of today's brightest minds have just laid out new foundation of mathematics after a year of collective effort. This new paradigm better fits both informal and computationally-checkable mathematics. There is little doubt that it will fundamentally change our perspective on rigorous knowledge, and it could be that, in a few decades, the book they published turns out to be the bedrock of all mathematics, and, by extension, all human knowledge! Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!
Construction and Definition of Numbers
By Lê Nguyên Hoang | Updated:2016-02 | Views: 9313
Although they have been used for thousands of years, an actual definition of numbers was given less than a century ago! From the most fundamental level of set theory, this article takes you to the journey of the construction of natural, integer, rational, real and complex numbers.
Self-Reference on XKCD.
Self-Reference and Apparent Self-Reference on Cut the Knot.