Something Beyond Mathematics

“Mathematics as a universal language that is powerful enough to reveal all the truths and unravel all the problems there is.” This is what David Hilbert believed for a very long time.

The final installment tackled about the greatest problems that remain unsolved and served as challenge to the mathematicians of this century. David Hilbert is a mathematician who set different unsolved problems for the 20^th century mathematicians.

            Marcus first discussed the problem imposed by Cantor about the concept of infinity. He was able to unearth a lot of fact about infinity and yet one day, Cantor came up with a question he was not able to answer, “Is there an infinity sitting between the smaller infinity of all the fractions and the larger infinity of the decimals?” Henri Poincare's discipline of the ‘Bendy geometry’ was the next one that Marcus discussed. This work of his states that if two shapes can be molded to each other’s shape, then they must have the same topology. But, like with Cantor, he was not able to answer the question, “What possible shapes are there in a 3-dimensional universe”. Aside from these problems, Hilbert discussed 21 more problems emphasizing those famous ones.

            These unsolved problems contradicted Hilbert’s belief. This belief was also shattered by Kurt Godel’s Incompleteness theorem. But still, it was said that these problems were not unsolvable, they are just waiting for the right person to crack them.

            The final part of the installment briefly discussed about algebraic geometry. Evariste Galois had a different way of defining mathematics. Galois said that mathematics should not be the study of number and shapes, instead, it should be the study of structure. This concept was used by Andre Weil to build a whole new language of mathematics, the Algebraic Geometry. His work was then connected to geometry, algebra, number theory and even topology.

            Like infinity, mathematic is limitless. If mathematics is infinite, do we expect something beyond math?  I think that is the notion that the installment wants imply. It is said that there are still problems that the mathematics we know can’t solve. So, what can? Maybe the thing that is needed to solve it is the something beyond mathematics. We never know.