"les frontières de l'espace"

This is the third part of the documentary entitled “The Story of Maths”, the sequel to “The Language of the Universe” and “The Genius of the East”. In this part, Marcus du  Sautoy explored Europe. From Urbino, at the northern part of Italy, where the trail of the Renaissance artist Piero della Francesca was born. Piero was the first major painter to fully understand perspective because he was a mathematician and an artist. The use of perspective was a technique that had been lost for 1000 years. Marcus du Sautoy also took the viewers to The Flagellation of Christ, Piero’s masterpiece, but the problem is they do not allow filming in that place because of some reasons, so Prof. du Sautoy just illustrated the picture, but the problem of perspective is on how to represent the 3-dimensional world on a 2-dimensional canvas. Piero used mathematics to solve this kind of problem. His work was the beginning of a new way to understand geometry.

Prof. Marcus du Sautoy took us to the journey going to the north. We explored Europe and known that it had taken over from the Middle East as the world’s powerhouse of mathematical ideas. In France, the villages were named after the mathematicians because they really value their mathematicians, like the village named Descartes in Loire Valley, which was named after the famous mathematician Rene Descartes. Descartes was born in France in 1596. He was a sickly child who lost his mother when he was very young, and because of this, he was allowed to stay in bed until 11 PM. He tried to continue this practice all his life. He thought that the bed was the best place to achieve the meditative state. The house where Descartes used to stay is now a museum dedicated to all things Cartesian. In this museum, his works showed all his philosophical, scientific and mathematical ideas, all of them fit together. Descartes was a mercenary. He fought for anybody who would pay him.

Descartes could not sleep one night thinking about his favorite subject, philosophy. “how can you anything at all?” The key was to build philosophy on the indisputable facts of mathematics. He realized that numbers could brush out the cob weds of uncertainty. He wanted to publish all his radical ideas but he was afraid on how the catholic France would accept it, so packed his bags and left. He found a home in Holland. He became one of the champions of the new scientific revolution which ejected the dominant view that the sun went around the earth.

Descartes went to the old university of Leiden where they value math and science. Prof Henk Bos is one of Europe’s most eminent Cartesian scholars. He is not surprised if the French scholars ended up in Leiden. He said that Descartes merged algebra and geometry so that the formulas and figures go back and forth. This is a dictionary that was published in Holland in 1637, that contains, in the appendix, the proposal to link algebra and geometry. This states that curve is a parabola, an ellipse, and a hyperbola. Descartes may not be the most congenial person but his ideas between algebra and geometry transformed mathematics forever.

Marin Mersenne, a first-class mathematician, encouraged people to read Descartes’s works. His teachings led to a person who became a rival of Descartes, Pierre de Fermat. Fermat would have hardly approved the ideas of using fun and games to advance an interest in mathematics. He wouldn’t have considered it worthless or common to create a festival of mathematics. His greatest contribution to mathematics was to virtually invent the modern number theory. He devised a wide range of conjectures and theorems about numbers including his famous Last Theorem, the proof of which would puzzle mathematicians for over 350 years. Remarkably, he only tackled mathematics in his spare time, because by day he was a magistrate. His hobby and passion is about battling mathematical problems. He used to do much of his work while sitting at the kitchen table or praying in his local church or up on his roof. He took his mathematics very seriously. He managed to find several new patterns in numbers that had defeated mathematicians for centuries. One of his theorems is about prime numbers. If you have a prime number which when you divide by four leaves remainder one. He said that you could always rewrite this number as two square numbers added together. He proved that this theorem works in all prime numbers no matter how big it is, provided it has remainder one when dividing by four. Another one of his theorems is his Little Theorem, the basis of the codes that protect our credit cards on the internet.

But the usefulness of Fermat’s mathematics is nothing compared to greatness of the next mathematician, Isaac Newton. Newton came from France’s great rival. He was born at Woolsthorpe, and grew up at Grantham. He was the greatest among all the mathematicians. He came back from Cambridge to Lincolnshire during the great plague of 1665, when he was just 22 years old. In two years, he developed a new theory of light, discovered gravitation, and scribbled out a revolutionary approach to mathematics, the calculus. The calculus enables us to work out the exact speed and also the precise distance travelled at any moment in time. It can deal with all the things and can describe the moving world, in contrast with the Greeks, which was a very static geometry. It is also the only way you can deal with the mathematics of motion or with change. This enables us to really understand the changing world, the orbits of planets, and the motions of fluids.