What’s so sexy about math?- A TED Talk by Award-winning mathematician Cédric Villani
Villani is a funny-looking man. He wears a three-piece suit, a colorful velvet cravat, pocket watch, center-parted shoulder-length hair, and large spider brooch on his left lapel.
There is typicality about him, that is reminiscent of many thinkers, mathematicians, scientists, and philosophers who the world doesn’t seem to understand.
Honestly, the title was very enticing. Because I do believe that math is very, very sexy.
The great mathematician André Weil likened this — no kidding — to sexual pleasure. But noted that this feeling can last for hours, or even days, claiming it is even better than sex.
The Major takeaway of this talk is:
Mathematics allows us to go beyond the intuition and explore territories which do not fit within our grasp.
Cédric Villani
Villani demonstrates the Gauss Curve of Randomness which was used by Einstein, Perrin, Smoluchowski to explain and prove that our world is made of atoms.
The more interesting part of the TED talk was when Villani explained how the internet works, using these random trajectories and using the analogy of a crime scene.
If you were to solve a criminal case, you would sensibly want to first interview the prime witnesses to the crime. You want a first hand, authentic information. Similarly, when you navigate the world wide web, you want the most relevant, useful and concise information on the topic you are searching up. Villani discusses sophisticated Google algorithms to prioritize what web pages show up when we do a google search through a simple and amazing animation.
“Enter PageRank, one of the early cornerstones of Google. This algorithm uses the laws of mathematical randomness to determine automatically the most relevant web pages, in the same way as we used randomness in the Galton Board experiment. So let’s send into this graph a bunch of tiny, digital marbles and let them go randomly through the graph. Each time they arrive at some site, they will go out through some link chosen at random to the next one. (refer to image above)
And again, and again, and again. And with small, growing piles, we’ll keep the record of how many times each site has been visited by these digital marbles.
And look at this: from the chaos will emerge the solution. The highest piles correspond to those sites which somehow are better connected than the others, more pointed at than the others. And here we see clearly which are the web pages we want to first try. Once again, the solution emerges from the randomness. Of course, since that time, Google has come up with much more sophisticated algorithms, but already this was beautiful.”
Experimenting, truly proves that mathematics, makes order out of chaos. Mathematics tells us with100% certainty, of an event that will occur or not. There’s nothing grey in the world of mathematics, it’s all black and white. It’s all crystal clear, it either exists or it doesn’t, it’s true or it’s false. And the beauty is that this is all through abstraction, i.e., using mathematical principles as a guiding light when we tend to go astray to develop terrific models that demonstrate shockingly accurate results in mathematics. Scaling down and exploring of territories that are far, far outside the fit of our mental grasp and relying on something which is beyond intuition; absolution.
Anjali Manchanda
Cedric narrates one of the more striking days or rather nights in his life as a mathematician. At that time, he was staying at the Institute for Advanced Studies in Princeton — for many years, the home of Albert Einstein and arguably the holiest place for mathematical research in the world. And that night he was working on an elusive proof, which was incomplete.
“It was all about understanding the paradoxical stability property of plasmas, which are a crowd of electrons. In the perfect world of plasma, there are no collisions and no friction to provide stability like we are used to. But still, if you slightly perturb a plasma equilibrium, you will find that the resulting electric field spontaneously vanishes, or damps out, as if by some mysterious friction force.”
Yeah, I didn’t get anything from that either. Point being, he was studying an elusive proof. That just refused to happen.
This paradoxical effect is called the Landau damping and is one of the most important in plasma physics, and it was discovered through mathematical ideas. But still, a full mathematical understanding of this phenomenon was missing.
Working through the night, 1 am, 2 am, 3 am, he worked on the elusive proof. To no avail. He went to bed at 4 am, in low spirits. But the next morning when he woke up, the start of the solution suddenly occurred to him!
“Take the second term to the other side, Fourier transform and invert in L2”
Cedric Villani was then awarded the coveted Fields Medal, from the President of India in 2010. The Fields Medal is equivalent to the Nobel Prize in the field of Mathematics.
Now he is working to establish a special museum of Mathematics in Paris so that everybody can appreciate the thrill of mathematical research and share the passionate stories of humans and ideas behind it.
“So in a few years, when you come to Paris, after tasting the great, crispy baguette and macaroon, please come and visit us at Institut Henri Poincaré, and share the mathematical dream with us.”
