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

• Kin vs Group Selection: Evolutionary Biology on Trial By Lê Nguyên Hoang | Updated:2013-12 | Views: 0
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Linear Algebra and Higher Dimensions By Lê Nguyên Hoang | Updated:2013-11 | Views: 740
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Numbers and Constructibility By Lê Nguyên Hoang | Updated:2013-11 | Views: 947
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Entropy and the Second Law of Thermodynamics By Lê Nguyên Hoang | Updated:2013-10 | Views: 1109
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Logarithms and Age Counting By Lê Nguyên Hoang | Updated:2013-10 | Views: 684
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Imaginary and Complex Numbers By Lê Nguyên Hoang | Updated:2013-12 | Views: 1419
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 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 By Lê Nguyên Hoang | Updated:2013-09 | Views: 566
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• High Dynamic Range and Tone Mapping By Lê Nguyên Hoang | Updated:2013-11 | Views: 313
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• The Beauty of Ellipses, Parabolas and Hyperbolas By Lê Nguyên Hoang | Updated:2013-10 | Views: 3072
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• The Surprising Flavor of Infinite Series By Lê Nguyên Hoang | Updated:2013-12 | Views: 1603
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Euler’s Formula and the Utilities Problem By Lê Nguyên Hoang | Updated:2013-06 | Views: 2395
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Proof by Mathematical Induction By Lê Nguyên Hoang | Updated:2013-07 | Views: 2686
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Spacetime of General Relativity By Lê Nguyên Hoang | Updated:2013-12 | Views: 4931
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 PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Does God play dice? By Arthur Marronnier | Updated:2013-05 | Views: 301
For Albert Einstein, the answer is no. But what did he mean? Has the greatest theoretical physicist of all time really missed the bandwagon of quantum physics? What are the real issues of the controversy that has opposed him to the Copenhagen School (Bohr, Heisenberg …)? Back to the physics of the early twentieth century, its history, philosophy and ideas.
, by Arthur Marronnier Researsh intern in Spintronics in Spintec Lab (Grenoble, France)

Education:
2013-2014: Stanford University (Master of Science in Material Science & Engineering)
2010-2013: Engineer degree in École polytechnique (Paris), Solid state physics, X2010
2008-2010: Intensive Preparatory Classes in Mathematics&Physics (undergrad)

• Hypothesis Test with Statistics: Get it Right! By Lê Nguyên Hoang | Updated:2013-11 | Views: 1686
Statistician Johnson recently claimed that up to 25% of published scientific experimental results were just wrong! To see why, let’s get to the bottom of the scientific method! And it’s probably more complicated than you think. In this article, we apply it rigorously to “prove” $\pi=3$. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• The Amazing Physics of Water in Trees By Lê Nguyên Hoang | Updated:2013-12 | Views: 3125
As explained by Derek Muller on Veritasium, the flow of water in trees involves complex physical phenomena including pressure, osmosis, negative pressure, capillarity and evapotranspiration. What seems simple will blow your mind!
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Dynamics, Chaos, Fractals (pt 2) By Scott McKinney | Updated:2013-04 | Views: 413
Dynamical systems such as a system of 3 planetary bodies can exhibit surprisingly complicated behavior. If the initial state of the system is slightly varied, the resulting system behaves in a radically different manner. This “sensitivity to initial conditions” is a key element of what’s become (perhaps disproportionately) well-known as chaos. Using the mathematical notion of iterative systems, we can model such systems and understand how chaos arises out of deceptively simple foundations.
, by Scott McKinney Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.
• A Model of Football Games By Lê Nguyên Hoang | Updated:2013-10 | Views: 1583
Back then, I simulated the outcome of the 2006 World Cup, based on a modeling of football games. This article explains this model and presents its results.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)
• Dynamics, Chaos, Fractals (pt 1) By Scott McKinney | Updated:2013-04 | Views: 1046
The study of dynamical systems, natural or abstract systems that evolve at each instance in time according to a specific rule, is an active and fruitful area of research in mathematics. Its study has yielded insights into the nature of social networks such as Facebook, the spread of diseases such as influenza, and the behavior of the financial markets. In this series of posts, we’ll look in depth at dynamical systems, as well as at the related subjects of chaos theory and fractals, all of which are both interesting and useful for understanding our world.
, by Scott McKinney Graduate student in mathematics and aspiring teacher/entrepreneur in the field of mathematics, education, and internet business. I earned my BA in pure mathematics from Cornell University and have completed one year of postgraduate study in mathematics and education in Ohio State University.
• Poincaré Conjecture and Homotopy By Lê Nguyên Hoang | Updated:2013-08 | Views: 1889
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.
, by Lê Nguyên Hoang PhD Student in Applied Maths at Polytechnique of Montreal.
Engineer of the Ecole Polytechnique, France. (X2007)