Anymore Questions?

Life is full of questions. We can’t stop our minds from wondering and so we spend our lives finding out the answers. There has never been a time when I had no questions in my mind. And when it comes to math, I have about a hundred.

In this episode, Marcus du Sautoy sheds light on David Hilbert’s 23 major mathematical problems. No, these are not the ordinary math questions we have in our minds like ‘what is the value of x?’ rather; these are much deeper and have boggled the minds of mathematicians in the 20^th century. 

 

Infinity. We often associate that term in cheesy lines (sorry hipsters) describing something with no limit. But if it wasn’t for Georg Cantor, we wouldn’t be able to understand the concept of infinity at all. He considered the infinite set of whole numbers and paired it with a bigger set to denote that these numbers had the same size. He did the same for fractions and was still able to pair them up with whole numbers. But he then discovered that different infinities had different sizes when he reached the infinite set of decimal numbers. A problem he was unable to solve, Continuum Hypothesis, became Hilbert’s first problem. This was solved by Paul Cohen though who also worked on the 8th problem but was unsuccessful. 

Henri Poincare came up with the Poincare Conjecture which he himself was unable to solve. While trying to solve one of the problems, he committed a mistake which resulted in the Chaos Theory.

Kurt Godel formulated the Incompleteness Theorem rooted from Hilbert’s second problem which was proving the consistency of the axioms of arithmetic. His theorem states that not all mathematical statements that are true can be proved. 

The tenth problem which asks ‘if there was some universal method that could tell whether any equation had any whole number equations or not’ was attempted by Julia Robinson who came up with the Robinson Hypothesis. Unfortunately she was not able to find the very specific set of numbers that could exponentially grow. This part of the solution was discovered by Yuri Matiyasevich who also worked on the Reimann Hypothesis. 

Sautoy concludes the episode with a brief coverage of algebraic geometry developed by Andre Weil. He also introduced Alexander Grothendieck who is the figure behind the establishment of the modern theory of algebraic geometry.

 
In this last episode, Marcus du Sautoy leaves us with problems; not to burden us, but to awaken the mathematicians in each one of us. I don’t mean mathematicians who come up with theorems and formulate new equations, but simply, people who appreciate math and understand its role in our lives.