Discover a new field of science with the latest no-prerequisite articles:

• The Tortuous Geometry of the Flat Torus The Tortuous Geometry of the Flat Torus
  By Lê Nguyên Hoang | Updated:2014-03 | Views: 0
  Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many of the greatest modern mathematicians, like Gauss, Riemann, and Mandelbrot, couldn’t figure out. While John Nash did answer yes, he couldn’t say how. After 160 years of research, Vincent Borrelli and his collaborators have finally provided a revolutionary and breathtaking example of a bending of a square sheet of paper! And it is spectacularly beautiful!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The Thrilling Physics of Resonance The Thrilling Physics of Resonance
  By Lê Nguyên Hoang | Updated:2014-03 | Views: 2850
  From the destruction of bridges and buildings to the foundations of electromagnetism and quantum mechanics, through their uses by radios or our ears,resonance is a counter-intuitive underlying phenomenon which shapes our reality. But amazingly, they can be made amazingly visual by playing with head massagers!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The Greatest Feat of Mathematics: Euler’s Identity The Greatest Feat of Mathematics: Euler’s Identity
  By Lê Nguyên Hoang | Updated:2014-03 | Views: 2280
  In 1988, Euler’s identity was elected most beautiful theorem of mathematics. It has been widely taught worldwide. But have you ever stopped to really sense the meaning of this incredible formula? This article does., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The New Big Fish Called Mean-Field Game Theory The New Big Fish Called Mean-Field Game Theory
  By Lê Nguyên Hoang | Updated:2014-02 | Views: 1381
  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!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Pluto is NOT (not?) a Planet Pluto is NOT (not?) a Planet
  By Lê Nguyên Hoang | Updated:2014-01 | Views: 326
  In 2006, Pluto was officially demoted from its planetary status. When we dig a little bit, this isn’t much of the surprise. What’s more interesting is rather why it ever was regarded as a planet, as the History of Pluto highlights a magic enterprise that science is!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The Most Troubling Experiments on Human Behavior The Most Troubling Experiments on Human Behavior
  By Lê Nguyên Hoang | Updated:2014-03 | Views: 534
  We all intuitively think of ourselves as independent creatures with strong free will. However, many disturbing experiments about fashion, conformity, obedience, environment, choice and opinions have been troubling this idea we make of ourselves. These ought to be lessons of humility for all of us., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Santa Routing and Heuristics in Operations Research Santa Routing and Heuristics in Operations Research
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 1683
  Designing routes to visit customers has become one of applied mathematicians’ favorite optimization problems, as companies offer millions to solve them! This article discusses the clever technics they have come up with, and use them to help Santa deliver toys to kids all over the world!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Kin vs Group Selection: Evolutionary Biology on Trial Kin vs Group Selection: Evolutionary Biology on Trial
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 516
  In 2010, a controversial article published in Nature violently criticized the last 40 years of developments in evolutionary biology, triggering an ongoing war within the scientific community. This article explains the essence of the controversy!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Linear Algebra and Higher Dimensions Linear Algebra and Higher Dimensions
  By Lê Nguyên Hoang | Updated:2013-11 | Views: 1329
  Linear algebra is a one of the most useful pieces of mathematics and the gateway to higher dimensions. Using Barney Stinson’s crazy-hot scale, we introduce its key concepts., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Numbers and Constructibility Numbers and Constructibility
  By Lê Nguyên Hoang | Updated:2014-02 | Views: 1296
  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!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Entropy and the Second Law of Thermodynamics Entropy and the Second Law of Thermodynamics
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 4887
  The second law of thermodynamics is my favorite law in physics, mainly because of the troubling puzzles it raises! Indeed, what your professors may have forgotten to tell you is that this law connects today’s world to its first instant, the Big Bang! Find out why!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Logarithms and Age Counting Logarithms and Age Counting
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 1021
  Amusingly, the age difference between a 45-year-old man and a 25-year-old woman doesn’t seem as big as the age difference between them 20 years earlier, when the woman was a little 5-year-old girl. This remark was the insight the late science popularizer Albert Jacquart liked to give to his readers to explain logarithms. This article pays tribute to the great scientist by introducing age difference as he liked to tell it., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Imaginary and Complex Numbers Imaginary and Complex Numbers
  By Lê Nguyên Hoang | Updated:2014-02 | Views: 1761
  My first reaction to imaginary numbers was… What the hell is that? Even now, I have trouble getting my head around these mathematical objects. Fortunately, I have a secret weapon: Geometry! This article proposes constructing complex numbers with a very geometrical and intuitive approach, which is probably very different from what you’ve learned (or will learn)., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Beauty, the Driving Force of our Quest for Truth Beauty, the Driving Force of our Quest for Truth
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 696
  According to Matthew Colless, the most important aspect of science is beauty. Not only is it what inspires scientists and their quests, I’d even claim that it’s also the compass that guide them in their quests, in a deeper and more surprising way that one can imagine!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• High Dynamic Range and Tone Mapping High Dynamic Range and Tone Mapping
  By Lê Nguyên Hoang | Updated:2013-11 | Views: 393
  Our eyes are amazing! Even today’s cameras are nowhere near competing with them. However, the recent development of high dynamic range (HDR) and tone mapping technologies creates new possibilities to get images nearly as awesome as what our eyes really see!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The Beauty of Ellipses, Parabolas and Hyperbolas The Beauty of Ellipses, Parabolas and Hyperbolas
  By Lê Nguyên Hoang | Updated:2013-10 | Views: 4426
  The conic sections, that is, ellipses, parabolas and hyperbolas, are too often presented analytically. Yet, their amazing beauty is actually their spectacular geometry, as well as their omnipresence! This article presents plenty of illustrative descriptions of their uncountable applications!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• The Surprising Flavor of Infinite Series The Surprising Flavor of Infinite Series
  By Lê Nguyên Hoang | Updated:2014-01 | Views: 2288
  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!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Euler’s Formula and the Utilities Problem Euler’s Formula and the Utilities Problem
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 3465
  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!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Proof by Mathematical Induction Proof by Mathematical Induction
  By Lê Nguyên Hoang | Updated:2014-03 | Views: 2857
  This article explores the potency of proofs by induction with 4 different stunning puzzles, from a lock puzzle and a lion issue, to the monk problem and the pencil conundrum!, by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)
• Spacetime of General Relativity Spacetime of General Relativity
  By Lê Nguyên Hoang | Updated:2013-12 | Views: 5475
  Most popular science explanations of the theory of general relativity are very nice-looking. But they are also deeply misleading. This article presents you a more accurate picture of the spacetime envisioned by Albert Einstein., by Lê Nguyên Hoang Lê Nguyên Hoang
  PhD Student in Applied Maths at Polytechnique of Montreal.
  Engineer of the Ecole Polytechnique, France. (X2007)