## More on Science4All

Complexity Theory, P versus NP, RSA Cryptography (Hiking in Modern Math 2/7) Complexity Theory, P versus NP, RSA Cryptography (Hiking in Modern Math 2/7)

By Lê Nguyên Hoang | **Updated:**2016-02 | **Views**: 1535

Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7) Ergodic Theory, Brownian Motion, Random Walk, PageRank (Hiking in Modern Math 4/7)

By Lê Nguyên Hoang | **Updated:**2016-02 | **Views**: 2331

The Limitless Vertigo of Cantor's Infinite The Limitless Vertigo of Cantor's Infinite

By Lê Nguyên Hoang | **Updated:**2015-12 | **Views**: 2926

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 Self-Reference, Math Foundations and Gödel's Incompleteness

By Lê Nguyên Hoang | **Updated:**2016-02 | **Views**: 4480

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 Type Theory: A Modern Computable Paradigm for Math

By Lê Nguyên Hoang | **Updated:**2016-01 | **Views**: 10956

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 Construction and Definition of Numbers

By Lê Nguyên Hoang | **Updated:**2016-02 | **Views**: 5922

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.