Infinitely, Possibly

Mathematics has been, still is and will be the answer to many of the problems that people faced yesterday, today and plausibly, tomorrow. It has allowed people to view the world and understand it in a whole new paradigm. The title “To Infinity and Beyond” rightfully fits this final episode of the Story Maths as it details what lies beyond the Infinity. Now the infinity detailed here refers to the first of Hilbert’s problems. There are twenty three unsolved problems, some of which became the foundation of 20^th century mathematics, presented by David Hilbert on the Second International Congress on August 8, 1900. It details the works of mathematicians who challenged these problems and made an impression upon history itself.

Cantor’s problem, the first problem, questions whether a separate infinity lies between the larger infinity of fractions and the smaller infinity of whole numbers. George Cantor thinks that there is no such set of numbers that lies between these two. This is known as the Continuum Hypothesis. Later proven and disproven by Paul Cohen by the stating that in one universe such a set exists and in another equally true universe it doesn’t.

Shapes that have the same topology can be moulded or morphed into the shape of one another. Henri Poincare identifies all the possible two-dimensional topological surfaces. However, Poincare could not identify all the possible topological figures in for three-dimensional objects. Grigori Perelman solved this problem by looking at how things can flow over the figure.

Kurt Godel proves that there are things that are definitely true, but cannot be proven. He proposed the Incompleteness theorem based on Hilbert’s second problem.

The host details works of some mathematicians who have conducted a chain reaction in the history of mathematics. One of which is Julia Robinsons work on the Hilbert’s tenth problem. She then formulated the Robinson’s Hypothesis based on this. It states that there is no solution or method to tell if an equation had whole number solutions or not. Her work then became a stepping stone for Yuri Matiyasevich.

The challenge now comes to the newer generations to solve more of Hilbert’s problems. Like his eight problem now worth a million dollars to the genius who gives an answer to it, an excellent challenge to go further and further, to go more than infinity yet stay within the realms of reality. Math really is the key and language of the universe and as it stands, with Hilbert’s problems not even fully solved, it just shows that there are still uncertainties pertaining to the truths of this universe. What we know with math right now were spurred by questions asked by a man a hundred years ago. For all we know, the next set of problems may be infinitesimally harder than Hilbert’s. This really requires the next generations to go to the Infinity and Beyond.