8th of the 23

After everything that was said and done, what will be the future of mathematics? With almost everything being discovered, how could this language be strengthened when everything is about to be defined by mathematical symbols as well as representations? What will keep this language alive and be further studied? To infinity and beyond, the fourth installment of The Story of Maths revolved around certain people, of any race and gender, who spent most of their lives solving the most important mathematical problems of all times which then gives us the hint to the possible future that mathematics may take.

            In Paris, the greatest congress led by David Hilbert became memorable for almost all the mathematicians who have been able to witness the settling out of the 23 most important problems in mathematics which became the bridge on redefining mathematics of the modern age.

            In Halle, East Germany, there was this known mathematician who spent his life studying mathematics and became the first person to really understand the concepts of infinity, George Cantor. He bagged his way to the top through proving the infinity of the whole numbers, fractions as well as decimals. He was never worried of knowing the exact end of infinity unlike other mathematicians because he believed that the abstract of infinity is not in the hands of mathematicians, but of God. He continued his study in the clinic because he suffered from his mental illness triggered by the kind of math he was dealing with. Then there comes a storm, continuum hypothesis, he doesn’t know how to solve this problem. This problem talks about locating the infinity between the smaller infinity of all the whole numbers and the larger of all the decimals.

            Another European mathematician is taking the spotlight out of the other mathematicians, Henri Poincare. As Paris progresses to become the central for world mathematics, Poincare became the sought-out mathematician to lead the others mathematicians. Algebra, geometry, analysis and different fields of Math, he covered everything. He was even given the recognition for studying the positions of the planets in the solar system as well as the orbits which became significant to what we know as chaos theory. He even pointed out that in order to foresee the outcome of all the studies done through mathematics; we should study the past and connect it to the present discoveries of science.

            In Kaliningrad in Russia, a famous 7 bridges started out as a puzzle where mathematicians try to find out if they can cross each of the seven bridges once. Leonhard Euler proved it to become impossible, not by getting the distances between the bridges but by looking through how those bridges were connected with each other. This connection as well as positions in geometrical terms called topology or bendy geometry.

            Back to David Hilbert, he showed that an infinite number of equations can be divided up to become a finite set. For him, he does not care whatever you are (a penguin, an ox, a man of different color) as long as you discovered something relevant to mathematics. He believed that math as a universal language could unlock all the secrets of mathematics, even his 23 mathematical problems. But his belief came to an end as Kurt Godel tried to solve his second problem. He proved the opposite of what was about to be discovered on Hilbert’s problem. He called his discovery the incompleteness theorem. He pointed out that there are statements, mathematical statements, which are true but are hardly proven.

            During World War II, when Nazis came to overpower almost all the countries in Europe, Math became a dying language. With almost all mathematicians suffering and dying, some decided to leave their country to transfer to America where bigger, better opportunities await. As time comes, American youngsters became more interested in living a stress-free lifestyle than involving themselves in mathematical works. But there’s this one guy who stood out, Paul Cohen. Being a mathematical whiz, he studied about Cantor’s unresolved continuum hypothesis. He was able to justify and give proof to the hypothesis which gave him the fame, riches and everything nice. He even decided to study Hilbert’s eighth problem, Riemann’s hypothesis for 40 years until he died.

            This installment of Story of Maths also covered the women who made big in the field of mathematics like Sofia Kovalevskaya, Emmy Noether and Julia Robinson, the first woman to be elected president of the American Mathematical Society. She was really interested in learning mathematics and wanted to go to places where there were mathematicians. She went to Berkeley to find her luck with the hopes of being a mathematician. She met Raphael Robinson, a number theorist, and discovered that they have more in common than just the love for mathematics. Together, they settled down and looked for ways to solve Hilbert’s tenth problem in search for a method that would identify if a certain equation could have a whole number solution or not. This problem was solved by the Russian Mathematician, Yuri Matiyasevich, who used Robinson’s former discoveries and works.

            Many mathematicians have been given credit to their contributions to math like Andre Well, to the anonymous mathematicians who used an alias like Nicolus Borbaki and many more. But as years go by, the controversial Riemann’s hypothesis still become unsolvable. Not everything in mathematics has been given proof that’s why continuous study and research is needed, going back through the Egyptians and Ancient mathematicians’ contributions, up to the discovery of the greatest concepts of math including zero and the theorems that made math interesting up to the present times.

            With this installment, including the first three installments that I saw, it gave me a great background on the different concepts of Math. The more difficult a concept of math is, the more it becomes applicable to the real world. Many mathematicians sacrificed their social lives in search for something that will be relevant to studying the natural world and become more aware of the connections of math with everything we see. There might be these unresolved problems of math, but there was this quote of Hilbert that gave us the guarantee that everything is bound for discovery that “We must know, we will know.” I see math as a great way for a better understanding and better view of the universe because to every problem, there will always be a solution no matter how long proving might take.