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Shannon's Information Theory (Trek through Math 5/8) Shannon's Information Theory (Trek through Math 5/8)
By Lê Nguyên Hoang | Updated:2016-02 | Views: 0
Big Numbers, Googol, Googolplex, Graham (Trek through Math 7/8) Big Numbers, Googol, Googolplex, Graham (Trek through Math 7/8)
By Lê Nguyên Hoang | Updated:2016-02 | Views: 0
Self-Reference, Math Foundations and Gödel's Incompleteness Self-Reference, Math Foundations and Gödel's Incompleteness
By Lê Nguyên Hoang | Updated:2016-02 | Views: 6720
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: 13072
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!