[BLANK_AUDIO] I'm sure you have a lot of questions now. Why do six and not others? Because I just choose them. You could have as a question; hey, Gandhi is not there? No. Spinoza is not there? No. No woman; no. Newton is not a philosopher. Mm. So I cannot answer all of those questions. I just made my own selection, because I have my preference. That's easy. Such a lecture of course is subjective. And the way I teach is the way I am. So, at least we have six guys. And now we will walk, we will have walked different walks in this world of ideas. Six walks, number one, history of mathematics. And that's the privilege to have guides on the long period of time, more than 2,000 years and different countries. Because you can have, like some distance and you see things that otherwise you can not see. History of mathematics. All of us, all of us, we are using mathematics constantly. Sometimes it's good to remember different things. So, how do we start? Maybe with a little reminder. At the beginning, you have Egyptians. Egyptians were mostly geometric. Their field was geometry. They built pyramids. They did a lot of things. Of course they were mathematicians, but mostly geometry was their field. Algebra, came much much later, around the Middle Ages, and through a completely unexpected way. Through the Arab world. Where at one, two, three, four, are called Arab digits. And they brought something which was unknown in the time of Greek and Roman. For example zero, the zero, the figure zero didn't exist. At, if you take for example, Roman digits like L, X, V; they didn't have the zero it only came 1,000 years after. So, in the beginning it was like two main influence, geometry from the Egyptians, and algebra from the Arabs. Al-ge-bra, algorithm, it's not a coincidence. And of course they both bring completely different expertise. And the genius of DeCartes. You remember DeCartes? I selected DeCartes first. Well again, because this is my way. But what did Descartes? He put geometry and algebra together. If you take this, this two axis, x and y, we call them Cartesian axis. Because of him. Descartes was a philosopher, but he loved mathematics, and he has this incredible, brilliant idea to combine, to combine geometry and algebra. And it's like something I put, like with those arrows you can see like putting together. And the key to creativity, lecture number five we will talk a lot about creativity. But creativity is very often about combining things not connected before. And definitely Descartes was a combiner. Now, we have, of course, Descartes as he offer a tool to a lot of giants. Two of them are include in my set of six: Newton and Leibniz. They're both incredible genius, but they were, of course using Descartes's tool, the x and the y. And both claimed, Newton and Leibniz both claimed to have invented the calculus. The calculus, so the integrals, derivatives, et cetera, et cetera. So this is just a sample of the way you can talk about mathematics. When you take a lot of distance and you use my guides.