le-nguyen.hoang Lê Nguyên Hoang

Je suis en thèse à Polytechnique Montréal en mathématiques appliquées, après avoir étudié à l'École Polytechnique à Palaiseau.
Je travaille sur des problèmes de conception d'horaires personnalisés, de modélisation des préférences et de conception de mécanismes.
J'ai lancé, un site d'articles de vulgarisation scientifique de qualité, auquel tout candidat ou diplômé d'un Master ou doctorat peut contribuer.
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    What's Einstein's gravity? General relativity explained! Science4All 15

    Last time, we saw that Einstein explains the falling of the apple by the upwards acceleration of the ground. This is Einstein's happiest thought. But wouldn'...
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    Are astronauts weightless? Einstein's happiest thought - Science4All #14

    In 1907, Einstein had the happiest thought of his life - definitely one of the greatest thought ever. An ingenious but surprisingly simple thought...
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    La Magie des Maths de Prépa (2/2) - L'analyse

    Dans cette série, je propose de vous révéler la magie des mathématiques des classes préparatoires aux Grandes Écoles. Ce second épisode porte sur l'analyse.
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    The Unlikely Correctness of Newton’s Laws - S4A

    By stressing the weirdness of Newton's laws with Veritasium videos, this article dives into a deep understanding of classical mechanics.
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    La Magie des Maths de Prépa (1/2) - L'algèbre

    Dans cette série, je propose de vous révéler la magie des mathématiques des classes préparatoires aux Grandes Écoles. Ce premier épisode porte sur l'algèbre.
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    La Magie des Maths de Prépa - Bande Annonce 2

    Voici la 2ème bande annonce du documentaire sur la magie des mathématiques des classes préparatoires. Le documentaire sera composé de deux épisodes d'une heu...
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    Univalent Foundations of Mathematics - S4A

    A consortium of today's greatest mathematicians have laid out new foundations. They all lie upon one single axiom, called univalence. With univalence, our Arabic numbers aren't just like natural numbers; They are natural numbers. Univalence also has unforeseen and mesmerizing consequences.
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    Homotopy Type Theory and Higher Inductive Types

    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.
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    Type Theory: A Modern Computable Paradigm for Math - S4A

    In 2013, three dozens of today's brightest minds have laid out new foundations of mathematics, which better fits both informal and computationally-checkable mathematics. Have a primer of this upcoming revolution, with this article on type theory, the theory that the book builds upon!
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    The Tortuous Geometry of the Flat Torus - S4A

    Take a square sheet of paper. Can you glue opposite sides without ever folding the paper? This is a conundrum that many couldn't figure out. While John Nash did answer yes, he couldn't say how. Finally in 2012, Borrelli and his collaborators finally made it! And it is spectacularly beautiful!
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    The Thrilling Physics of Resonance - S4A

    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 visual by playing with head massagers!
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    The Greatest Feat of Mathematics: Euler’s Identity - S4A

    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.
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    The New Big Fish Called Mean-Field Game Theory

    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 maths in the making!
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    Pluto is NOT (not?) a Planet - S4A

    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!
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    The Most Troubling Experiments on Human Behavior

    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.
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    Vehicle Routing and Heuristics in Operations Research

    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!
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    Kin vs Group Selection: Evolutionary Biology on Trial

    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!
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    Linear Algebra and Higher Dimensions - S4A

    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.
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    Numbers and Constructibility

    Last summer, I got to discover Morellet's artwork on inclined grids. Amazingly, this artwork is a display of the irrationality of ?2! It's also a strong argument for the existence of this number. In this article, after discussing that, I take readers further!
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    Entropy and the Second Law of Thermodynamics - S4A

    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!
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    Imaginary and Complex Numbers

    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.
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    Beauty, the Driving Force of our Quest for Truth - S4A

    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!
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    High Dynamic Range and Tone Mapping

    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!
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    Euler’s Formula and the Utilities Problem

    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! It is nothing less than the gateway to the wonderful world of algebraic topology!
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    The Surprising Flavor of Infinite Series

    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. Surprisingly though, his proof can be rigorously and naturally justified!
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    Ma Thèse en 180 Secondes

    Prestation de Lê Nguyên Hoang, étudiant à l'École Polytechnique de Montréal, à la grande finale du concours Votre soutenance en 180 secondes, au 81e Congrès de l'Acfas.
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    Proof by Induction - S4A

    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!
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    Hypothesis Test with Statistics: Get it Right!

    How does the scientific method really work? It's probably more complicated than you think. In this article, we apply it rigorously to "prove" ?=3. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!
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    The Amazing Physics of Water in Trees

    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!
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    A Model of Football Games - S4A

    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.
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