Hardy: A Mathematician’s Apology

Hardy: A Mathematician’s Apology

You rarely get an insight into the workings of a mathematician mind. However in, A Mathematician’s Apology G.H Hardy gives an excellent account of what mathematics is. Its usefulness (or lack of) and how it is more than just a science it is a creative art!

The apology was written as his powers as a mathematician were on the decline. This detail offers the reader an insight into how Hardy viewed his career as a mathematician and how he viewed some of his contemporaries. He mentions his work with Littlewood, his discovery of Ramanujam and his time at Oxford and Cambridge.

Hardy gives a brilliantly composed account of ‘real’ mathematics and this comes from his background in pure mathematics. He was known as ‘a real mathematician’ and this style of thinking comes across in the well-constructed, eloquent argument he proposes for his subject. His dislike of war and the lack of involvement that mathematics has had upon it is displayed in the book. He acknowledges the use of applied mathematics on ballistics however he hardly ranks them as ‘real’. He further states that the mathematics involved are “indeed repulsively ugly and intolerably dull.” You can’t help but like the language he uses.

This book is a must for anyone (not just mathematicians) as it is not only fantastically written but it offers an insight into one of the finest mathematical minds of the twentieth century.          

Maths LoL

Problem 3

Problem 3: You find a body! (Well that's your story to the police anyway)

A body is found at midnight, on a night when the air temperature is 16 degrees C. Its
temperature is 32 degrees, and after another hour, its temperature has gone down to 30.5
degrees. Estimate the time of death.

All problems are also found on the problem page (maths problems not people problems)

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!