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!
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).
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!
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!
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.
How does the scientific method really work? It's probably more complicated than you think. In this article, we apply it rigorously to "prove" π=3. This will highlight the actually mechanism of the scientific method, its limits, and how much messages of experiments are often deformed!
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.
Glaciers are spectacular phenomenons of nature. The physics they are based on is surprising, while the geological role they have is essential. In this article, we discuss these facts, as well as their retreats and their dangers.
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 by discussing what numbers can be constructed geometrically, algebraically, analytically or set theoretically using the power of mathematics!
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.
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!
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!
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!
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!
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.
Claude Shannon may be considered as the single most influential person of the 20th Century, as he laid out the foundation of the revolutionary information theory. Yet, unfortunately, he is virtually unknown to the public. This article is a tribute to him. And the best way I've found is to explain some of the brilliant ideas he had.
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.