The Quest in Finding the Answers

"The great unsolved problems are what makes math really alive"

                  From the early budding of numbers to the application of geometry in the field of architecture in many ancient structures and the discovery of many wonderful theorems and equations, it is undeniably true that mathematics has already gone a long way to its maturity. It has evolved from a simple science of counting into a more complex series of computations, both of applied and pure mathematics. It doesn’t just end there because now at present, mathematics has defined the status of our modern world. Its development symbolizes the fast advancements of technology in our time. As a matter of fact, it is the cornerstone of the machines we currently depend upon since math is, if I’m not mistaken, the language used in making codes.

                   In the fourth and last installment of ‘The Story of Maths’ entitled To Infinity and Beyond, the discovery of the infinity was unleashed and some great unsolved problems were tackled, along with the persons behind those problems.

                    One gigantic date in the history of Mathematics occurred on August 8, 1900 in Paris. A man named David Hilbert, presented in the International Congress of Mathematicians the 23 then unsolved problems which he believed to be worthy of focus and attention. He first presented Hilbert’s first problem.

                    The first person who understood infinity was Georg Cantor. He proved that infinity of fractions is much bigger than the infinity of whole numbers. He was very eager in his work and found out that the infinity of fractions is vaster than the infinity of the whole numbers. He even matched fractions with whole numbers by arranging fractions in an infinite grid and saw that the infinities of both the fraction and whole numbers are of the same size. And since the emergence of the discovery of infinity, the counting was never the same again. An entirely new math was born.                  

                    

                 But somehow in the middle of his reign in the Mathematical field, he came very troubled on his endeavor in fully understanding infinities. He was unable to solve and fathom if there is an existing set between smaller infinities of fractions and the larger infinities of the decimals. He believed that there is no such set, and it is now known as the Continuum Hypothesis. He became very obsessed with it, so then he decided to retreat himself in a mental center of some kind. I don’t clearly get what happened to him afterwards because of the British accent of the host which is slightly hard to comprehend. Anyway, so this was the first problem listed by Hilbert.

              Okay. Next stop, Henri Poincare’, who got a splash of his inspiration while riding a bus. It was when King Oscar II of Sweden and Norway back in 1885, offered a prize of 2500 crowns (or rings, not sure though haha), to whoever can establish mathematically whether the solar system going to continue turning like a clock or suddenly fall apart. So he worked on it but along his approximation, a problem was detected. His work was work but it gave rise to another theory called the Chaos theory. It can be best represented by butterflies’ wings can cause changes in the atmosphere that could eventually cause a tornado in the other side in the world.

               

               Have you heard the 7 bridges of Konigsberg? Yes, and it has something to do with Math. It’s a place which lies between Poland and Lithuania. In 1735, Leonard Euler became famous in his work of the Graph theory and he also had a problem concerning topology. It is finding a route along 7 bridges where you only have to pass once in each bridge. From there, he said that the connection is much important than the distance.

               Back to Poincare’, shapes can be changed by topology, that a piece of donut can be a soccer ball. However, in 1904, there was a problem he couldn’t solve. One century later, it was solved by Grigori Perelman. In order to solve this problem, he even linked it to another area of mathematics that even mathematicians find it hard to comprehend. Perelman looked at the dynamics of the way things can flow over the shape. This enabled him to find all the ways that 3D space could be wrapped up in higher dimensions. Just a trivia, Perelman is still alive at this moment, but he doesn’t entertain any interviewers. How sad.

                 Back to 1900’s, Hilbert also studied on the Number theory. His love and zeal for math was indeed burning like a fire. He even stated “We must know. We will know”, referring to the solutions he is after. Talk about passion.  

                   Kurt Godel, a fellow from Vienna formulated the Incompleteness Theorem based on his study of Hilbert's second problem. He said that there are things that are true yet cannot be proved. Same as Cantor, he became obsessed with his works because of the crisis that maybe the false things can be mistaken as true. He got depressed but then he was saved by his lover. During this time, mathematics was in hiatus and everyone was feeling that it was about to die. In the opening of the new German regime in 1930, the Nazis allowed to remove all kinds of civil service including those in the academe. The mathematicians on this time suffered the most. Fourteen of them even committed suicide. One man tried to stay. It was David Hilbert, but eventually he became silent. He died in 1943 and only ten people attended in his funeral. This marked the end of the 500-year crowning reign of Europe in the field of Mathematics. It was the time to hand it down to Europe.

          In state of New Jersey in the United States, in Princeton University, mathematicians attempted to revive the collegiate atmosphere via the Institute of the Advance Studies. Kurt Godel migrated in there and he met lots of great mathematicians including German Vile, Game theory, and John Neumann who pioneered Computer Science. He also met the great Albert Einstein. Wow. But sadly, Godel became depressed and got lost in track.

                   In 1950’s, American mathematician Paul Cohen took up the challenge of Cantor's Continuum Hypothesis which asks "is there is or isn't there an infinite set of number bigger than the set of whole numbers but smaller than the set of all decimals". Cohen found that there existed two equally consistent mathematical worlds. In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set. Cohen would subsequently work on Hilbert's eighth problem, the Riemann hypothesis, although without the success of his earlier work.

          Three female mathematicians were also rise in the field of Mathematics including Sophia Kovalevski, Emmy Noether and Julia Robinson. Julia Robinson was the first female of American Society. She worked on Hilbert tenth problem was insanely passionate about it. She also created the Robinson Hypothesis which stated that to show that there was no such method all you had to do was cook up one equation whose solutions were a very specific set of numbers: The set of numbers needed to grow exponentially yet still be captured by the equations at the heart of Hilbert's problem.  Robinson was unable to find this set. This part of the solution fell to Yuri Matiyasevich from St. Petersburg who saw how to capture the Fibonacci sequence using the equations at the heart of Hilbert's tenth. In 1985, Julia Robinson died.

  

                      Back in Paris on May 29, 1832, Evariste Galois stated that math is not just the study of numbers and shapes, but of structure. Almost one century later, Andrei Weil discovered the Algebraic geometry which was considered to be the greatest achievement in modern mathematics. Another great mathematics was Alexander Grothendiek but he turned back in mathematics to enter the political world.

                    Lastly, it was stated there that the Riemann’s hypothesis was the Holy Grail of mathematics. Moreover, it was said that mathematicians are pattern searchers. For them, finding solutions is not just for the sake of riches and application, they say, but the glory of knowing the answer.

                To be honest, this was the first time I made a movie review wherein I summarized all the things that was discussed in the film. I don’t have any comments about this film really. It’s their thing you know. I appreciate their zeal and passion for solving solutions, but it’s just not me. But I’m glad and thankful of their existence though, because they are, without doubt, greatly influenced how the world works at present. Kudos, mathematicians! :)