Saturday, January 18, 2014

From Descartes to Riemann, with Love

                How a person formulates a theory and finds evidences for it to become a fact came from a critical mind wanting to search for truth and to become more acquainted with the secrets of the world. These processes of formulating, gathering evidences and even analysis of data do not just occur in a single snap with a single person doing the entire job. Improvement says it all. Sometimes, an idea needs to be rewritten, restudied and re-evaluated in order to ensure that we are getting the right information from the data we gathered from numerous findings and experimentations. Also, these processes are continuous. Continuous in the sense that change is constant and the world is experiencing a rapid advancement in technology giving us the opportunity to explore everything deeply, resulting to the discovery of new knowledge and ideas. And with the observed trend, more and more people become interested in finding the real solutions to problems with the fact that it would give them the opportunity to be remembered and to finally see their names in books and have a statue built for them like Isaac Newton.
                How a mathematical idea (like calculus, geometry, and algebra) changed the whole course of living and how it became significant to the lives of the experimenters are the highlights of the third installment of BBC: The Story of Maths. How they were remembered and how their lives were re-lived by their relatives and their enthusiasts were also tackled as well as how a single, complex problem involved so many mathematicians, from so different races, in becoming more interested in determining the mysteries of everything through mathematical representations and symbols.
                The Story of Maths: Frontiers of Space elaborated the evolutions in mathematics that changed the subject as a whole. It all started with Piero dela Francesca where he became popular for using perspective to study Math, perspective leading to Mathematical revolution in which we view the world in a different way, more specifically, in a mathematical way. Rene Descartes had a different approach. He used philosophy to study the concepts of Math and used his knowledge to observe the relationship of both aspects and realized that numbers, in its most important function, can hinder the possibilities of uncertainty. Henk Bos’ contributions to mathematics also become significant in understanding the concepts that are hardly understood in Math. With equations combined and theorems further studied, he managed to merge geometry and algebra.
                Many mathematicians from the time of Descartes viewed math and science as the evidence of God’s existence, like Marin Mersenne. He became a Descartes’ fan urging people to read the journals written by Descartes. He also became Pierre de Fermat’s pathway for discovery. Pierre de Fermat’s greatest contribution to mathematics includes the invention of modern number theory. He created his own theorems and assumption about numbers and focused on the wonders of prime numbers. He enjoyed playing with numbers in his time. The greatest application for his theorem, “The Little Theorem”, includes the codes that protected our own credit cards on the internet.
                And on the 17th century, Britain became the world power where Isaac Newton, one of my favorite scientists who I never thought to be a mathematician, existed. Most people knew Isaac Newton because of his discoveries in physics, like acceleration. New theory of light, gravitation and calculus were his greatest contributions to the world. Because of his formulated equations, he helped us to evaluate the exact speed and distance travelled at any moment in time. Gottfried Leibniz also became interested about calculus, focusing on the concepts about differential calculus and integral calculus. He even invented a practical calculating machine that worked on the binary system. And then a problem arises, Newton never wanted to share credits with whatever Leibniz discovered. But since Leibniz captured the real essence of using the right language to capture a new idea, his notations were used more than the clumsy and hard-to-use notations of Newton. Bernoulli also became a great mathematician for developing the calculus in solving classic problems. He used calculus in problems like profits, energy use and even construction optimization. Euler studied topology and analysis, numbers like e and i and the use of pi. He even applied his skills to topics like prime numbers, optics and astronomy.
                In France, revolution emphasized the usefulness of mathematics. Mathematicians like Wilhelm Von Humboldt and Joseph Fourier showed significant contributions to math, most especially on their mathematical services for the military including the making of the best weapons and armors. But the one who really top them all is no other than Carl Friedrich Gauss, the Prince of Mathematics. By the age of 12, he already censured Euclid’s geometry. At 15, he discovered new patterns in prime numbers and at 19, discovered the construction of a 17-sided figure which nobody had known in their time. And then, we have Bernhard Riemann, the mathematician who lectured the foundations of geometry.
                This installment, for me, showed two very opposing concepts. 1.) People (relatively close to the mathematicians and their fans) still acknowledge the contributions of our mathematicians. If keeping their journals, naming an entire supermarket and a village for them, having a classroom project focusing on their lives, works and contributions and putting up a statue for them is not enough, then I don’t think that wouldn’t inspire other people to put their A-game in discovering and formulating new theories and ideas that change the notion that we already know. 2.) Despite their great contributions, the knowledge of people, in today’s generation, about the mathematicians seems to be so shallow that they hardly even knew the significance of their discovery in our daily living. People tend to forget the great people behind everything that we are studying in schools today, and the people who gave us the idea about certain concepts explained through mathematics. This installation gave me a really good background on the less familiar aspects of the life and career of our mathematicians, as well as their successes and their downfalls. It taught me a lot about the concepts of mathematics and deepened my knowledge and ideas about the mathematicians that I just read on books. Because of this installment, those unrecognized mathematicians were given the opportunity to showcase what they have done and what they have achieved in making mathematics a concept worthy to be called one of the foundations of the world. I hope the contributions made by our mathematicians will still be remembered and will be given importance, not just kept on books and on their museums. 

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