The Story of Maths 3: Frontiers of Space

The third series of The Story of Maths is entitled “Frontiers of Space”. It talks about the great mathematicians of Europe, which is the powerhouse of mathematics, and their contributions.

Let’s start in the Northern part of Italy. Piero della Francesca is a renaissance artist and at the same time a mathematician. His work “Flagellation of the Cross” used perspective style/technique.  It is seen in his work that three-dimensional can be represented into a two-dimensional canvass.  This perspective technique leads to understanding geometry.

In France is where a mathematician-philosopher was born, named Descartes. He was sickly as a child and wa nns allowed to stay in bed until 11 A.M. Because of this situation, most of his contemplation took place in his bed.  According to him, his bed is the best place to achieve mathematics.  One of his questions in mind is, “How could you actually know anything at all?” Then, he had a dream, which philosophy should build on mathematics; that “numbers” brush away uncertainty.

Because questioning of faith or religion is a violation in France, Descartes went to Holland to have the freedom to pursue his love for mathematics and philosophy. There, he merged algebra and geometry.

On the other hand, Pierre de Fermat made use of mathematics as fun and games. Pierre loves looking for patterns of numbers as it is his past time playing with mathematics. His contributions are: modern number theory, last theorem, prime numbers and little theorem.

In Britain, the famous Isaac Newton was born. Almost everyone knows him because of his great contribution in physics, the Law of Gravity. The other contribution of Newton in the field of mathematics is calculus. Studying calculus does not just get the speed and distance, but the precise speed and distance of a moving car. It made sense of 0 divided by 0 and it is widely used by engineers and physicists. It is through calculus that we understand the changing world, according to Newton.   But he did not publish his discovery of calculus. He just kept it to himself and maybe some of his friends. For him, it was just a hobby to learn these things, that he gave no importance.

Meanwhile in Northern part of Germany, Gottfried Leibnitz also discovered calculus. He was aware that Newton had the same work as his, but they had different ways of discovering such work. He published his work that made Newton unhappy. He was in trouble because Leibnitz became his rival. Because of this situation, the German royalties recognized that it was Leibnitz who first popularized and published calculus while Newton was given the honour as the first who discovered calculus. But Newton was still not happy about it that he accused Leibnitz of plagiarism. Leibnitz was hurt of the accusation because he was a fan of Newton, and in the first place it was he who developed calculus.

In Switzerland, there’s a dynasty of mathematicians- the Bernoulli’s. This family is a fan of Leibnitz and said to be his disciples. They developed the calculus of Leibnitz. They developed particularly the calculus of variations. During the visit of Marcus in Switzerland, he met the descendant of Leonhard Euler. The Euler’s are also said to be a dynasty of mathematicians.

Another mathematician is Carl Friedrich Gauss. He’s said to be the Prince of Mathematics. But no one knew him except for the people in Brunswick, his hometown. He’s the first person to explain the imaginary numbers clearly. Through these imaginary numbers that we understand radio waves and it is the key to quantum physics.

Janos Bolyai discovered hyperbolic geometry where the sides of the triangle are bent. And lastly Bernhard Riemann from Northern Germany discovered the high dimensional or multidimensional geometry.

I’ve realized that geometry, algebra, and calculus that I’d learned during my high school days have a purpose and importance in our lives. I thought they were only for the mathematicians’ own benefit- to discover theories just to add to the past theories and have additional credits to their work. But I’ve learned from the video, that they derived their equations or work from the activities of our lives, such as the application of calculus. I’ve also learned about some backgrounds of the mathematicians, their lives and how they came up with their discoveries.

Bringing us to the places where the mathematicians were born gives us the “feel” of being in the same place as of the host. It gives us an interaction with them through their works and place. There are just some shots that are not related. But I like how the host delivers his spiels. He has a good sense of humour. He inserts slightly non-sense but funny side comments. One example was when he was in a boat going to Russia and he talked about that last night drinking spree with the mathematicians. Funny side comments have added life  to the presentation.