Could a universe without border, not go on and on forever?

Poincaré not only gave an answer, he also proposed a fundamental conjecture…

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Poincaré Conjecture and Homotopy Poincaré Conjecture and Homotopy

By Lê Nguyên Hoang | **Updated:**2016-01 | **Views**: 6934

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.

Can you glue opposite edges of a square? Relativity 7 Can you glue opposite edges of a square? Relativity 7

By Lê Nguyên Hoang | **Updated:**2016-03 | **Views**: 0

Euler's Formula and the Utilities Problem Euler's Formula and the Utilities Problem

By Lê Nguyên Hoang | **Updated:**2016-01 | **Views**: 12121

I was a kid when I was first introduced to the deceptively simple utilities problem. It's only lately that I've discovered its solution! And it's an amazing one! Indeed, it provides a wonderful insight into some fundamental mathematics, including Euler's formula! This is nothing less than the gateway to the wonderful world of algebraic topology!

Homotopy Type Theory and Higher Inductive Types Homotopy Type Theory and Higher Inductive Types

By Lê Nguyên Hoang | **Updated:**2015-12 | **Views**: 7434

In this article, we explore the possibilities allowed by higher inductive types. They enable a much more intuitive formalization of integers and new mind-blowing definitions of the (homotopical) circle and sphere.