Badass Mathematicians - 2: Emmy Noether

(Part 2 of an occasional series where I profile some influential mathematicians. Part 1, covering the volatile Frenchman Evariste Galois, is here )

Emmy Noether was that special type of badass whose contributions to pure mathematics ended up becoming the impetus for much of modern physics. Before we get to that bit of badassery, some details about her life. She was born in Germany in 1882. Father Max was a mathematician also. Wikipedia tells me he names a couple theorems in his own right. Couple of her brothers got doctorates and such. In short, she was part of an academically inclined family.

What a badass bowtie

After going through routine schooling, where she was a pretty good student, she reach a dead end. Society expected her to become a teacher for girls' school. Noether had other ideas. The powers that be at her university saw great ills in allowing mixed education. They let her enroll grudgingly. Within a few years, she hammered out a fine PhD thesis titled "On Complete Systems of Invariants for Ternary Biquadratic Forms". Later she called it crap. Sounds perfectly fine to me, but hey what do I know.

Contemporary mathematical beast David Hilbert invited her to join him at Gottigen university. There, despite toiling hard as a superb professor without pay for the first two years, she produced some solid papers on topics well above my pay grade.

It was there she formulated the theorem that would propel her into the pantheon of badasses. Here's the statement:

"To every differentiable symmetry generated by local actions, there corresponds a conserved current."

Huh? What? Here is what it means in plain (relatively speaking) English: if a physical law does not change under conditions of space and time, it must have a quantity that is conserved.

Badass mathematicians - 1: Evariste Galois

Most people don't tend to think of mathematicians as being badass. Popular convention - so vigorously and boisterously propagated by the media - sees them as hapless dorks. Thick glasses, messy hair and awkward social skills, the world sees the prototypical mathematician as a portrait in pitiful meekness.

On the contrary, the most influential mathematicians throughout history were people with an extraordinary zeal for life and were full of contagious vitality and energy. Sure, a lot of them were shy or preferred to stay isolated, but that was because they preferred to spend their time working on equations, not wasting time engaging in mindless pleasantries. Most of them maintained a healthy interest in music and reading, and some even went as far as to host lavish parties at their houses to entertain their guests.

In this and the next few posts (probably one a week), I want to highlight the lives and personalities of some of the more "colorful" mathematicians throughout the ages.

Let's start with Evariste Galois.

This is Evariste Galois:

"My jacket collar beats your entire outfit!"

Obviously...

I was goofing around on the internet and somehow ended up in the dark, murky world of ultra-technical quantum mechanics/particle physics/mathematics articles on wikipedia.

The article was called Renormalization Group. Don't ask me what it means because I clearly have NO FRICKIN' CLUE. This ain't Kansas anymore.

These technical articles are usually accompanied by an endless stream of very intimidating equations that are just packed with symbols and arcane operations. But something caught my eye. Well, take a look at it:

For any positive Λ′ less than Λ, define S_Λ′ (a functional over field configurations φ whose Fourier transform has momentum support within ) as

Obviously,

Obviously, the obviousness of Z is obvious...

Duhhhhh, right? I mean how can you not know what Z is? Quite obviously, Z equals all that. Looks like someone chewed up a bunch of variables and puked them out. 

Goodbye to a great mathematician

A couple days ago, I read that famous mathematician Benoit Mandelbrot passed away. If you are not a math nerd or a math hobbyist, you probably have never heard of him before. If you are, however, interested in the fascinating aspects of weird geometries and crazy sequences, you probably worship the man. He is credited with inventing fractal geometry, a branch of mathematics that deals with fractals. I will try my best to go briefly over them, but forgive me if I am not able to clearly explain the idea.

In my precalculus class in high school, there were some forbidden (i.e. chapters we were not going to cover in the class) chapters at the back of the book. One day, I flipped through some of them just out of curiosity. I felt a lot like Harry Potter stealthily walking around the forbidden forest. One of these forbidden chapters talked about something called fractals. This intrigued me a lot. I knew what fractions were (thanks to my third grade math teacher), but what kind of  a beast was this fractal?

I talked to my math teacher and he was nice enough to let me borrow a DVD on fractals. Fractals are, roughly put, geometrical entities that have infinite complexity at all levels of magnification. No matter how far you zoom into the object, you will keep unraveling more and more layers of complexity. The coastline of Britain is often used as an example of this. From the sky, it looks more or less uniform, but as you get closer and closer to it, you begin to see all the jagged edges, coves, etc. They also have a property called self-similarity, which basically means that small sections of a fractal share shape and other features with the fractal as a whole.This video illustrates both of these properties: (it shows the Mandelbrot set, named in honor of the man.)




Fractal geometry has been successfully used to calculate Cloud dynamics, formation of galaxy clusters and predict market fluctuations. Combined with cutting-edge computer technology, fractals have also been used to create stunning visual effects in movies.

Goodbye sir, and thank you for inspiring and captivating us.