## Introduction

The polymath we are going to talk about today is Benoit Mandelbrot who lived from 1924 to 201, one of the smartest people that has ever lived. Some of you may have never heard of this name before, but trust me, he has done amazing things in science which we will get into right now.

## Benoit Mandelbrot and Fractals

Alright, so who exactly was Benoit Mandelbrot? Well, he was basically the guy who discovered this thing, which is called a fractal.

What is a fractal exactly? Fractals are basically these rough shapes which show self-similarity on different scales. If you zoom in on a fractal, the parts will look the same as the entire thing. You can see that in this fractal right here, which is called the Mandelbrot set, named after Benoit Mandelbrot himself who discovered it. If we zoom in at like the neck of this snowman figure, we see little copies of the snowman emerging.

This can go on forever. If you plot one of these computers then you can keep zooming in forever, to infinity, and you will still see new details emerging and more copies that look similar to the original snowman. But of course computers cannot really produce images that are really infinite, so depending on the technology it would stop being zoomable at some point. But in theory these fractals are infinitely complex.

So, you might be thinking that since these images are so complex, basically infinitely complex, that you have to enter like very difficult formulas or codes in the computer to plot these images. Well, actually the exact opposite of that is true, and that is one of the fascinating and beautiful things about fractals. You can create these staggering images with very simple formulas. The formula that lies at the heart of the Mandelbrot set is $z^2 + c$. That’s it, you just have one variable z, you square it and then you add a constant number to it. But here is the trick which allows for this formula to become infinitely complex.

What you do with this formula is iterate it. Iterate means that you repeat the procedure over and over again. So every time you start out with certain numbers for z and for c, whatever the outcome is, you put that outcome back in the value of z. Then you square this new value again, add c to it again, and keep going. Then, depending on how the number for z behaves after we iterate it over and over again, the computer knows whether to color that number black, or with any of the different colors that you can see. That is how the Mandelbrot set is plotted.

Before we had any of the crazy super computers we have today, Benoit Mandelbrot had to do to this mostly by himself, with a little bit of help of old fashioned computers of the 70s and 80s. He was working at IBM at the time. IBM stands for International Business Machines and is a company that produces and sells computer hardware, software, hosting and other things. IBM is also a research center and is the inventor of the floppy disk, the hard disk drive, the SQL programming language, and more. Benoit Mandelbrot worked at this company for around 35 years, and in 1980 he used IBM’s computers to make a visualization of the Mandelbrot set.

## Other Fractals

The Mandelbrot set is not the only fractal we can find. There are millions, billions, perhaps infinitely many more we can make on the computer. Here are some more beautiful images of fractals.

The last one is actually not a computer generated image. This is a vegetable called Romanesco broccoli. It’s just a type of broccoli, but every part of it shows self similarity to the whole thing. That’s of one of the beautiful things of fractals. A lot of things in nature show these fractal patterns, and we can understand them better if we can model them ourselves on the computer.

Trees are also fractals.

Fractals are found everywhere in nature. Thanks to Mandelbrot, we can now better understand these rough, self-similar things in nature. The reason we call Mandelbrot a polymath is not only because he discovered fractals, but because he helped find applications for fractals in many sciences outside of mathematics.

## Benoit Mandelbrot’s Career

Benoit Mandelbrot has made contributions to sciences like physics, economics, medicine, cosmology (for those of you who don’t know cosmology is the science that studies the universe), he also had contributions in engineering, geology which is the science that studies the earth, and much more. He didn’t stop at fractals and his knowledge of math and geometry in general, but used this knowledge to step outside of his own boundaries and help other sciences advance too.

What is interesting about Mandelbrot is that he made so many advances in science, but didn’t have a completely standard career for these achievements. Yes he did a phd right after he got his masters degree, and then worked at a French research facility after for 6 more years, but he started a 35 year long career at IBM when he was 34. Here he would also work on the practical applications of his ideas. During this career he also took breaks every once in a while to teach at Harvard. At the end of his career he also became a tenured professor at Yale university.

We can see from his career that he was on the one hand working on the theoretical side of things, publishing papers and books, but also doing work for practical matters, doing research for a company that makes inventions and provides products for clients.

His career really shows us insights on how to be more polymathic. He never stopped to challenge himself and always tried to make new discoveries. After he did his phd and worked in France as a researcher, he could have basically stayed there for the rest of his life and be done with it. But he constantly took on new positions, new ways of working and new ways in which he could develop his ideas. He also couldn’t have gotten so far without using the state of the art technology of the time at IBM. If he didn’t take on the job there, he might have never discovered the Mandelbrot fractal, and became known as the father of fractals.