To Infinity and Beyond

“To Infinity and Beyond” is the fourth and last installment of our journey through the story of maths. In this part of the series, Professor Marcus du Sautoy takes us to a whole new level of mathematics where we would be able to decode some of David Hilbert’s 23 most important mathematical problems for mathematicians to crack which would eventually define the mathematics of the modern age. And also this documentary would not be entitled to infinity and beyond if it would not tackle the term infinity.

It is said that Georg Cantor from East Germany was the first to have a clear understanding of infinity and give it a mathematical precision. According to him, there are infinitely many infinities and he also proved that the set 1-10 and 2-20 have the same size of infinity by comparing them up. However, Cantor encountered one problem which he considers as his greatest problem, the continuum hypothesis. The continuum hypothesis is trying to answer the question whether there is an infinity between the smaller infinity of all the whole numbers and the larger infinity of decimals. With this, the most famous and respected mathematician of France, Bertrand Russell, helped him.

In 1885, King Oscar II promised a prize to the person who could solve whether the solar system would continue turning like a clockwork. Henri Poincare solved this problem however before publishing his paper he realized that he made a mistake and this led to the Chaos Theory.

David Hilbert has inspired many mathematicians to solve his 23 mathematical problems and here are the problems tackled in the story of maths:

Problem Number 1: The Continuum Hypothesis.

This is solved by a teenager named Paul Cohen.

Problem Number 2: Prove that axioms of arithmetic are consistent.

Kurt Godel, an active member of the highly influential group of philosophers and scientists called Vienna Circle, formulated the Incompleteness Theorem however this is the opposite of what Hilbert is looking for. The incompleteness theorem states that there are mathematical statements that are true but cannot be proven.

Problem Number 10: Is there is a universal method that could tell whether any equation had whole number solutions or not?

This problem was first encountered by Julia Robinson however she was not able to solve it. But with the help of her initial study on the 10^th problem, another bright young mathematician was able to solve it. It was Yari Matiyasevich who is currently working on the Reimann Hypothesis which is Hilbert’s 8^th problem and is considered as the Holy Grail of Mathematics.

Through this documentary I learned that for you to be successful or in order for you to achieve your dream you must make sacrifices and always have discipline like what Henri Poincare did. He allotted 2 hours in the morning and afternoon to do his work and therefore he was able to achieve his goal. I also earned that the harder mathematics is the more is its application.

Therefore, the story of maths would be a good way to reach out to the masses and be able to encourage them to be interested in math for with the different mathematical ideas presented from all over the world from different eras it would leave them wanting more.

BY: DAISIC DE ASIS BELLO