Painting, Bed, Apples, Manuscript, Diary and the Picture

( A Review on the Story of Maths 3 : The Frontiers of Space)

Europe became the central powerhouse of the 16^th to 17^th century mathematics. In this documentary, Professor Sautoy walked around the lands of France, London, Netherlands, Germany, Romania and Russia, telling us the lives of some of the most famous Western mathematical aces whose outstanding contributions made a great impact on today’s world.

            Centuries ago, painters had a hard time portraying a three dimensional scene, for example, in a two dimensional canvass. It was until the Italian Renaissance era that the artist Piero della Francesca, discovered and fully understood how to make such thing possible. His painting the Flagellation of Christ showed his mastery of perspective. Here, the parallel lines from the walls and floor tile all meet at a single vanishing point. This creates an illusion of distance and gives depth and realistic factor to the drawing. Objects close to the person’s viewpoint seemed to be bigger than distant things. Enthusiasts studied the rules of perspective and practice it day and night. Since then, most of the artists’subjects ranged from the portrayal of a classroom scene, hallways, pathwalk and buildings seen at a given distance and angle. Also, architects were able to communicate their ideas and designs better using single, two point, three point ( that’s like looking up or down) and four point ( for curved and other related surfaces) perspective.

            Next, the professor drove us around Descartes village (in France), named after the genius who was born in that place. For me, it was a good thing that he and his colleague showed us the very pillars where Rene lived. I have always been interested about how mathematicians are in their homes – what are their hobbies aside from mental torture. Well, I learned that lying in bed was Descartes’favorite hobby. Many can relate to that. I, myself love doing that and I am willing to do that for the rest of the day. But, not everyone, while chilling on their mattresses and couch, can perceive thoughts that will later be turn into postulates, theorems and formulas. Descartes can do more. Aside from his theory of equations, rules of signs ( used to find positive and negative root/s of an algebraic number), the Cartesian coordinate system, invention of the usage of indices to express powers of numbers, he also contributed in the study of optics and became the father of modern philosophy.

            “One thing good about mathematics is you can do it everywhere,” Professor Sautoy pointed out. True. Laboratories and observatories are not that necessary. One could just have to have that burning lust for math, stored knowledge, a couple of textbooks and other references and most importantly, food( brain will need lots of glucose for that stuff). Also, doing things with friends who share the same passion as we have is totally fun and in a lot of cases, most productive. Pierre de Fermat of Beaumont-de- Lomagne, France, worked with his philosopher and scientist friend, Blaise Pascal in investigating about figurate numbers. Afterwards, he was able to give the world new system of calculating probabilities. He was also being thanked for, for his contributions in differential calculus.

            From France, we arrived at the streets of London. I noticed the professor to be more confident, natural and articulate this time. He was finally telling us about his own country and the people of Britain who made marks in math.  “I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me,” a quote by Isaac Newton, the English natural philosopher, physicist and mathematician. Wow, he was that genius. Most people exert so much effort in solving nerve-wrecking math problems while he, as he said, was just playing with numbers.

            Undeniably, Newton’s name is familiar to almost all of the people especially in his motherland. His works on the three laws of motion, modern study of optics and invention of the reflecting telescope earned him fame, respect and admiration. One of his most important contributions is his laws on universal gravitation speaking that all bodies are affected by gravity, a force. Falling apples are popular examples to illustrate this. Probably, the most important thing he did in the field of math is translating his ideas into what we know as the modern calculus. The professor ended his Newton report with a quote “through the power of calculus, we have a way of describing with mathematical precision, the complex, ever-changing world”. Big words.

            At the heart of Europe, a German mathematician shared almost the same thoughts as Newton had of calculus and he developed these thoughts independently from his rival. Gottfried Leibniz reached the top because of what he has done but a number of critics accused him of plagiarizing Newton’s works. Arguments as to who will be the rightful person to credit calculus to arose. After a couple of years, it was decided to attribute that field of math to the two. Most mathematicians though said that Leibniz’s methods were better compared to Newton’s “clumsy and difficult to use notations.” His manuscript showed his ideas on the Law of Continuity and developed calculating machines that basically made use of the binary number system. Unlike other mathematicians, he believed in God and created philosophies such as optimism and sufficient reason which states that "There must be a sufficient reason [often known only to God] for anything to exist, for any event to occur, for any truth to obtain.¹

            It runs in the blood.

The Bernoulli family of Switzerland produced a number of great mathematicians. Genes, genes and genes! Dr. Fitzgerald, the director of the Bernoulli archives, took Professor Sautoy around a part of the Basel University dedicated in honor of the Bernoullis.  An interesting problem was presented. How should a ramp be designed in order to allow a ball to travel from top to bottom at the shortest possible time? Straight and curved ramps are no answers. Cycloid takes on the scene. As quoted by Prof. Sautoy , “ this application of calculus by the Bernoulli’s which became known as the calculus of variation has become one of the most powerful aspects of the mathematics of Leibniz and Newton”. “ Investors use it to maximize profits, engineers exploit it to minimize energy use and designers apply it to optimize construction”.

            Daniel, a Bernoulli, taught at the Russian University on 1725. Among his noteworthy accomplishments are the creation of e and the usage of the symbol i for the imaginary numbers, popularization of the use of π , and development of a new theory in music. He is also known for the kinetic theory of gasses and fluid dynamics. I vaguely have any idea of those things. Anyway, thanks to Dani for the concepts underlying airplane wings; if it were not for him, travelling by the air would only mean death.

           

Birds of the same father flock together.

            Leonard Euler , a Swiss physicist and mathematician, was the Bernoulli’s family friend. His influence on mathematics is so vast. This versatility was shown in his works on trigonometry, algebra, mechanics, astronomy, fluid dynamics, infinitesimal calculus, exponential functions and logarithms and more. However, if one asks a random man who Euler is or if he has heard of that name in the first place, he will probably give 30 seconds silence or a straightforward “no” as answers. That’s the sad truth of being a mathematician sometimes.

             Crowns are no proofs to show that he is the prince of Mathematics. Carl Friedrich Gauss of Germany was also a physical scientist who, at a grade school age showed unbelievable mastery in mathematics when he instantly add up the integers from 1 to 100 by noticing that the sum was 50 pairs of numbers, each summing to 101. As he grew old, he made significant works on electricity and magnetism, the number theory, differential geometry and etc. Interestingly, he thought of a polygon with 17 sides, known as the 17-gon.

            Mythical creatures were said to inhabit Transylvania, a region in Romania. For the past centuries, this place has been the subject of haunted stories, gothic dramas and all works of romanticism. That is fiction. Here is a fact. The works of Janos Bolyai, one of the founders, of non-Euclidean geometry is found in this place. He developed a rigorous geometric concept of complex numbers as ordered pairs of real numbers² Fun fact. Professor Sautoy shared that the only photo people have of Bolyai was on a money bill, which was not actually his face but of someone else’s.

            Riemann, a German descent, was a shy and sickly boy who showed great calculation abilities at a young age. Having a Lutheran pastor as a father greatly influenced his early years. He studied theology but his professor, Gauss, urged him to focus his life on mathematics instead. Poverty was not a hindrance for him to succeed. The University of Berlin became his learning sanctuary, and from there, he developed a geometrical system which became one of the bases for Einstein’s theory of relativity.

            The documentary shared enormous information in a span of an hour. Honestly, for me, there could be moments of boredom listening to the speakers in the entire video but the knowledge it had imparted on us was great that one can safely say it is worthy to watch. The show ended with the statement “ but without these golden age from Descartes to Riemann, there will be no calculus, no quantum physics, no relativity- more of the technology we have today but even more important than that, their mathematics blew away the cobwebs and allow us to see the world as it really is , the world much stranger than we really thought.”

References:

1.                                “Gotffried Wilhelm Leibniz”. Online. Retrieved: http://en.wikipedia.org/wiki/Gottfried_Wilhelm_Leibniz, 11 January 2014

2.                                “Janos Bolyai”. Online. Retrieved: http://en.wikipedia.org/wiki/J%C3%A1nos_Bolyai, 11 January 2014

Glory to God

 

JPMC