The Left Out Heroes

It was long ago when mathematics was associated with arts. That is an artist turning out to be a mathematician. The town of Urbino in Italy was the home of the Renaissance artist who first understood perspective. He was Piero della Francesca. Aside from his works mentioned in the film, Piero was also the artist behind the “View of the Ideal City” (maybe you can’t relate with this one if you were not enrolled in Hum2: such great advantage), which can also give you an insight about a vanishing point. Speaking of vanishing point, Piero used this technique to make a two-dimensional set up appear three-dimensional in a painting by means of parallel lines. This technique is an illusion of perspective, wherein mathematics was a tool in unlocking the idea.

The beginning of the 17^th century signaled the beginning of Europe’s title as the world’s powerhouse of mathematical ideas. There is a village in France which was named after the mathematician Descartes, the village of Descartes in the Loine Valley. His mother died when he was young. The bed became his new world where he can meet a lot of shapes and patterns. He always used this area for meditation. Later, Descartes’ house became a museum where people can see his philosophical, scientific and mathematical aspects. This museum also tells that Descartes was once a soldier in the Protestant and Catholic Army and also a mercenary. One night in 1698, Descartes couldn’t sleep thinking about philosophy until he slips into a dream where he discovered that mathematics can be the actual key to uncertainty. He cannot publish his radical ideas in his hometown because he does not know how the Catholic France will accept it. Descartes went to Holland where he found a home in the old university town of Leiden wherein math and science are valued. He was able to connect algebra with geometry and geometry with algebra. Descartes discovered the possibility of navigating geometries of higher dimensions. Under the same century, a Parisian monk named Marin Mersenne, a first-class mathematician, convinced people  to read Descartes’ work on geometry. He was also the one who published the work of Pierre de Fermat.

Fermat’s hobby was solving mathematical problems but he only did it at night because at daytime, he was a magistrate. He used to do it in his kitchen, in the church or in his roof. One of Fermat’s theorems is all about prime numbers. When having a prime number, you can divide it by four and then left with a remainder of one. With Fermat, this number can be rewritten into two square numbers added together. That is 13 = 3² + 2² or 13 = 9 + 4. According to Fermat, this theorem will work regardless of how big the prime number is, but has always a remainder of one when divided by four. Fermat loved to look patterns in numbers and he wanted to prove that these patterns would be there forever.  Did you know   that the codes protecting our credit cards on the internet are based on the scribblings of Fermat? He called this theorem, Little Theorem.

In Britain, there was a mathematician greater than Fermat. He was Isaac Newton. The house where Newton was brought up is still being preserved in the village of Woolsthorpe. Newton was a son of an illiterate farmer but he died shortly after Newton was born. He hated his stepfather but it was this man who pursued him to be a mathematician and not a sheep farmer. Newton was just an average school boy in his time and had a very few friends. During the Great Plaque of 1665, Newton came back to Lincolnshire from Cambridge at the age of 22. In just two years here, he developed a new theory of light, discovered gravitation and the revolutionary approach to maths, the calculus. Calculus is of great use to every engineer, and physicist because it can describe the moving world. The changing world, the orbits of planets, and the motion of fluids can be understood through Calculus. Newton did not put his works into public but just shared it to his friends. His interest was transferred to other areas for he then became a professor, an MP, and then Warden of the Royal Mint in London. But when he heard about a rival who was also a member of the Royal Society having the same idea as him, his interest was again back to mathematics. 

Gottfried Leibniz also discovered calculus shortly after Newton. At the age of 29, he developed differential and integral calculus for just within two months. Aside from being interested with mathematics, Leibniz also got interested in reunifying the Protestant and Roman Catholic churches. He also got a proposal for France to conquer the Egypt and contributions to philosophy and logic. Leibniz was also the one of the first people to invent practical calculating machines that worked the binary system. Unlike Newton, Leibniz published his work and so mathematicians across Europe heard about calculus first from him and not from Newton. Newton did not want to share credit with Leibniz, until such time came when the Royal Society in London was asked to judge between the rival claims. Newton was credited for the first discovery of calculus while Leibniz got the credit for the first publication. In the end, Leibniz was accused of plagiarism and was very hurt. This judgment might be due to the fact that Newton was the President of the Royal Society. Leibniz admired Newton and had never recovered from that occurrence until he died in 1716. After 11 years, Newton died and was buried in the grandeur of Westminster Abbey while Leibniz was buried in a small church in Hanover. At present, it is Leibniz’s mathematics which succeeds, not Newton’s.

In the heart of Europe, Basel, there is one great dynasty of mathematicians, the Bernoullis. Their family were merchants and among the Bernoullis, Johann I is the most smart mathematician. Both Jakob and Johann Bernoulli worshipped Leibniz. They stood up for him against Newton and spread his calculus around Europe. One of the Bernoullis amazing contributions to mathematics was to develop calculus in order to solve a classic problem of the day. That is to design a ramp that will get the ball from the top to the bottom as fast as possible. This problem was solved by calculus through a cycloid, the path traced by a point on the rim of a moving bicycle wheel. This application became known as the calculus of variation, one of the most powerful aspects of the mathematics of Leibniz and Newton.

Leonhard Euler was a good friend of Johann Bernoulli’s son, Daniel. Daniel got him a job in his University in Russia called Peter’s Academy. It is where Euler found his intellectual home. The numbers like e and i was created by Euler. Also, the use of the symbol pi was popularized by him. Combining these numbers together will produce the mathematical formula, e to the power of i is equal to negative one. Euler’s life was not that happy. He had 13 children but only 5 of them reached adulthood. His wife, whom he adored, died at a very young age. Euler started losing most of his eyesight but he still continued his mathematical research. One of Euler’s theorems concerns calculating infinite sums which got him to the top when announced it in 1735. Having one shot glass of vodka and a tall glass, if you keep on adding infinitely many glasses where each one is  a fraction squared, how much will be in the tall glass? This problem was called the Basel problem which Bernoullis tried to solve but failed to. But Euler solved it by calculating the total height of the vodka to be exactly pi squared divided by 6.

France got brilliant mathematicians like Joseph Fourier who worked on sound waves and an analysis which is the basis of MP3 technology today. The town of Gottingen in Germany was the home of the Prince of Mathematics, Carl Friedrich Gauss. His father was a stonemason and it was his mother who recognized his talent and got him the best possible education. At the age of 12, Gauss was already criticizing Euclid’s geometry. At 15, he discovered a new pattern in prime numbers and at 19, he discovered the construction of a 17-sided figure which nobody had known before this time. Gauss used to keep a diary which included some sines and integrals, very different sort of mathematics, the first intimations of the theory of elliptic functions and the Riemann zeta function. Gauss was also the one to explain the imaginary numbers clearly. When he got the fame, ordinary mathematicians would send him their works but he used to ignore it which discouraged some very talented mathematicians that time. Back then, Gauss had done a tower called the Gauss tower and the major purpose of doing this was to discover the shape of the earth, but deeper than this was something to do with the shape of space. According to him, if we were living in a curved universe, there wouldn’t be anything flat. Based on this, he questioned Euclid’s geometry but he never published anything for in the early 19^th century, Euclid’s geometry was seen as God-given and he did not want to argue. 

There was a mathematician in Transylvania who has no such fear as Gauss. He was Janos Bolyai. Janos was a son of a math teacher, Farkas Bolyai. His father has seen him as a mathematical prodigy so his father wrote his old friend Carl Friedrich Gauss requesting him to tutor his son, but Gauss declined. Janos then joined the Army but he still loved mathematics. He studied what he called imaginary geometries where the angles in triangles add up to less than 180. This became known as hyperbolic geometry. In Bolyai’s hometown of Targu Mures, lies a museum containing Bolyai- related artifacts. One of these is the model of Bolyai’s geometry. He published his work in 1831 and his father sent Gauss a copy of it. Gauss wrote back his approval but he did not praise the young boy because according to him it must be himself whom he should praise. Gauss had worked on this before. Jonas Bolyai was unaware that Gauss wrote to another friend saying, “I regard this young geometer boy as a genius of the first order”. He was very disappointed with Gauss. Additional heartache came when a Russian mathematician named Nicholas Lobachevsky published a work the same as him two years earlier. Jonas Bolyai retained unrecognized until he became a little crazy and then died in obscurity in 1860. In contrast, after Gauss died, a university, the units used in measuring magnetic induction, also a crater on the moon would be named after him.

Bernhard Riemann was not like Gauss who just lent support on few mathematicians. Riemann’s father was a minister and got a Christian life. His family was large and poor; all he got was his excellence in mathematics. He went to school in his town in Luneburg, northern Germany. His school was built as a result of Humboldt’s educational reforms in the early 19^th century. He was one of its first students. Riemann was a shy boy and so the head teacher got him the freedom of the school’s library. There, he found a book by the French mathematician Legendre which was all about number theory. His teacher asked him how he was getting into the book and he said “I have understood all 859 pages of this wonderful book”. Riemann became a brilliant mathematician and got famous in 1852 with his lecture on the foundations of geometry. He described the relationship of geometry to the world and sketched out what geometry could be. That happened when he was just 26 years old. His ideas were made concrete 50 or 60 years after. These ideas became the beginning of Einstein’s relativity. Of all those great mathematicians, Riemann was the one to think in higher dimensions. He was only 39 years old when he died in 1866. His mathematics still remains as of the present time and is applied in many ways.

          As I’m watching the movie, I’m also being exposed to the lives of many great mathematicians. I got the insight that they have no such thing as happy family wherein they can get inspiration. Majority of them came from a very sad background. Suddenly, it came to me, what if I were in their place? How would I deal with it? I know many of us need an inspiration whenever we want to achieve something. Like me, my inspiration in doing my best in studies is my family. I always think of them whenever I’m down and wanted to get up. They always serve as my strength next to God. Despite of this fact, these great mathematicians still managed to be at their best and prove to the world that they are of great worth. Without them, technology would be impossible and that will definitely turn us to be lonely human beings. Another thing which I would like to make a point is the way some of our brilliant mathematicians died. I am referring to those mathematicians who died due to great depression, pain and frustration. The reason for these was either someone stole their work or someone already published the same work as them earlier when they decided to, leaving them with nothing. I will always feel sorry for them. They have gone through deep research, done a lot of effort, gave their life to mathematics. But in the end, they just died unrecognized. Thanks to “The Story of Maths”, it enlightened a lot of viewers including me, that those mathematicians popular to us in school were not just the only mathematicians but there were many of them. It’s just that only a few were given credit. I will always value their contributions to the world because if it weren’t for them, we will remain ignorant of the many things our world is ready to give us.