Mathematician of the week August Möbius

August Möbius

1790 – 1868

August Möbius was born in Saxony (now more commonly known as a part of Germany). He was an only child and an interesting fact to mention straight away is that his mother was a decedent of one Martin Luther!

Möbius was home schooled until he went to college. Once he had completed his studies at college he entered Leipzig University in 1809. At university his family wanted him to study law (and here comes the but.......) but Möbius found greater pleasure in mathematics (obvious), astronomy and physics and so he changed courses. Moving to 1813 Möbius studied under Gauss who was working at an observatory in Göttingen. So Gauss was able to coach Möbius in astronomy but being the greatest mathematician of his day Gauss was able to give Möbius an excellent mathematical education as well.

The Prussian army tried to draft Möbius to which Möbius was extremely annoyed. I am sure there’s a quote from him in response to being drafted saying something similar to, “no one will be safe from my dagger if they suggest such a thing”. He managed to avoid being drafted and he was given the chair of mathematics at Leipzig University. Apparently he wasn’t a good lecturer (we can’t be perfect all the time) but he was an excellent researcher which led to a promotion to a full professorship.

Der barycentrische Calcul was a classic piece of work on analytical geometry where he introduced the idea of a Möbius net. His name is also attached to the objects Möbius function and Möbius inverse formula these two terms came in later works.

Möbius was also interested in topological ideas and an illustration of this was a problem he posed about five sons to a king.

The problem is as follows:

A king has 5 sons each of which will be given a part of the kingdom when he dies. Can the kingdom be divided in such a way that each region has a common border with the other four?

I will leave you to work it out!

He is also known for the Möbius strip which is a two dimensional surface with only one side. You can make one taking a strip of paper twisting it by 180 degrees and then joining the two ends together. You can then dazzle your friends with your amazing piece of paper!