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.
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Numbers and ConstructibilityNumbers and Constructibility By Lê Nguyên Hoang | Updated:2016-02 | Views: 5461 Last summer, I got to discover Morellet’s artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of $\sqrt{2}$! It’s also a strong argument for the existence of this number. In this article, after discussing that, I take readers further by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!

P versus NP: A Crucial Open ProblemP versus NP: A Crucial Open Problem By Lê Nguyên Hoang | Updated:2016-01 | Views: 5847 P=NP is probably today’s most crucial open problem. Not only is it a very theoretical question in computer science and mathematics, but it also has major implications to real world. Its resolution could revolutionize the world. This article gives the definition and major results of P=NP.

Marriage Assignment Problem and VariantsMarriage Assignment Problem and Variants By Lê Nguyên Hoang | Updated:2016-02 | Views: 4825 Marriage problems consist in matching boys and girls. They are a very interesting class of problems that include assignment problems, which have a very large range of applications. Additional results have been found for variants which include the introduction of boys and girls’ preferences, and cases where people cannot be categorized into two groups.

Poincaré Conjecture and HomotopyPoincaré Conjecture and Homotopy By Lê Nguyên Hoang | Updated:2016-01 | Views: 6303 Poincaré conjecture is the most recent major proven theorem. Posited a century ago by Henri Poincaré, this major conjecture of topology was solved by Gregori Perelman. It has revolutionized our understanding of space and raised intriguing questions regarding the global structure of our Universe.

Space Deformation and Group RepresentationSpace Deformation and Group Representation By Lê Nguyên Hoang | Updated:2015-12 | Views: 2048 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.

Game Theory and the Nash EquilibriumGame Theory and the Nash Equilibrium By Lê Nguyên Hoang | Updated:2016-01 | Views: 9906 In the movie “A Beautiful Mind”, the character is John Nash. He is one of the founders of a large and important field of applied mathematics called game theory. Game Theory is the study of human interactions. Its fallouts in economy, politics or biology are countless. This article gives you an introduction to the concepts of this amazing way of thinking.

Model-Dependent RealismModel-Dependent Realism By Lê Nguyên Hoang | Updated:2016-02 | Views: 3192 Introduced by the two renowned theoretical physicists Stephen Hawking and Leonard Mlodinov in their book The Grand Design in 2010, model-dependent realism is a new controversial understanding of the universe. Based on solid logical reasonings and recent developments in physics, this concept may well be an incredible breakthrough for philosophy and science, as well as metaphysics.