My name is Lê and I believe that the greatest challenge in education is to make science and math appealing.
This is why I aim at bringing enthusiasm and excitement to the readers’ learning experience.
I now run a Robustly Beneficial wiki, mostly on AI ethics, which has come to fascinate me!
Space Deformation and Group RepresentationSpace Deformation and Group Representation By Lê Nguyên Hoang | Updated:2015-12 | Views: 2772 All along the 20th century, pure algebraists have dug deep into the fundamental structures of mathematics. In this extremely abstract effort, they were greatly help by the possibility of representing these structures by space deformations, which could then be understood much better. This has led to breakthroughs, including the proof of Fermat's las theorem. This article introduces the ideas of group representations.
Type Theory: A Modern Computable Paradigm for MathType Theory: A Modern Computable Paradigm for Math By Lê Nguyên Hoang | Updated:2016-01 | Views: 12992 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!
Cryptography and Number TheoryCryptography and Number Theory By Scott McKinney | Updated:2016-01 | Views: 19345 Over 300 years ago, a mathematician named Fermat discovered a subtle property about prime numbers. In the 1970's, three mathematicians at MIT showed that his discovery could be used to formulate a remarkably powerful method for encrypting information to be sent online. The RSA algorithm, as it is known, is used to secure ATM transactions, online business, banking, and even electronic voting. Surprisingly, it's not too difficult to understand, so let's see how it works.
Non-Euclidean Geometry and Map-MakingNon-Euclidean Geometry and Map-Making By Scott McKinney | Updated:2016-02 | Views: 11475 Geometry literally means "the measurement of the Earth", and more generally means the study of measurements of different kinds of space. Geometry on a flat surface, and geometry on the surface of a sphere, for example, are fundamentally different. A consequence of this disparity is the fact that it is impossible to create a perfectly accurate (flat) map of the Earth's (spherical) surface. Every map of the Earth necessarily has distortions. In this post we look at a few different methods of map-making and evaluate their distortions as well as their respective advantages.
The New Big Fish Called Mean-Field Game TheoryThe New Big Fish Called Mean-Field Game Theory By Lê Nguyên Hoang | Updated:2016-01 | Views: 18609 In recent years, at the interface of game theory, control theory and statistical mechanics, a new baby of applied mathematics was given birth. Now named mean-field game theory, this new model represents a new active field of research with a huge range of applications! This is mathematics in the making!
Probabilistic Algorithms, Probably BetterProbabilistic Algorithms, Probably Better By Lê Nguyên Hoang | Updated:2016-02 | Views: 2010 Probabilities have been proven to be a great tool to understand some features of the world, such as what can happen in a dice game. Applied to programming, it has enabled plenty of amazing algorithms. In this article, we discuss its application to the primality test as well as to face detection. We'll also deal with quantum computers, as well as fundamental computer science open problems P=BPP and NP=BQP.
The Surprising Flavor of Infinite SeriesThe Surprising Flavor of Infinite Series By Lê Nguyên Hoang | Updated:2020-01 | Views: 11492 1+2+4+8+16+...=-1, as proven by Henry Reich on Minute Physics! Now, as a mathematician, I must say that his proof is far from being rigorous. In fact, anyone familiar with the surprising flavor of infinite series should not find it convincing. Surprisingly though, his proof can be rigorously and naturally justified! Find out how!
Duality in Linear Programming
