Mathematician of the week

Leonhard Euler

1707 – 1783

Where to begin with this gentleman? Well he was born in Basel and when Euler was still young his father trained him in some elementary mathematics (his father had been friends with another mathematician known as Mr Bernoulli). His father actually wanted him to follow him into the church and so he sent the still young Euler to Basel University where he began a general education. However (luckily for us) he was far more interested in mathematics and with the help of that Mr Bernoulli he managed to change courses and purely study mathematics.

Now towards the end of 1720’s (he was around about 19!) Euler completed his studies at the university and he applied for a position in the physics department at Basel. However he was unsuccessful and so off he went to St Petersburg. During his time in St Petersburg Euler served in the Russian navy. He managed to leave the navy due to his rise to professor of physics (well done to him).

Euler worked in St Petersburg until around 1750 and then he left for Berlin (Russia wasn’t the best place for a foreigner at this moment in time). He stayed in Berlin for around a decade under the employment of the Academy there. He did return to St Petersburg after this and this is when he lost his eyesight and he was totally blind by the 1770’s. This did not stop his exceptional output as he published half of his overall work when blind! (You can’t even imagine this!) Euler eventually died in 1783 although the Academy in St Petersburg continued to publish his work for the next 50 years.

His body of work is massive no other mathematician has come close to this. He developed: mathematical analysis made contributions to number theory and he solved the Basel problem (what is the exact solution of the following sum? ∑ (1/n²) ). He also made contributions to calculus and geometry. He investigated planetary motion and the three body problem. He introduced i for the square root of -1, f(x) to represent a function, e for the base of natural logs, π for pi and ∑ for summation and even more notation!

I could easily go into more detail and list more topics and notations but this would take me half a lifetime!

I can say I have not given this man the justice he deserves in this post. (I would end up writing a book and I don’t want to!) He was one of the greatest mathematicians ever. Well done Mr Euler what a lad!

Again I apologise if I have missed any obvious achievements or made any glaring mistakes.

Problem 1

Problem 1: A little sailing trip! (answers on a postcard)

You are sailing due south on the sea. You see two lighthouses and you are perpendicular to the first lighthouse. The second lighthouse is 10km due south form the first lighthouse (you find this distance from your chart). You then decide to measure a bearing from your current location to the second lighthouse and find it to be 214⁰. Sometime later you pass the second lighthouse and again you measure the bearing from your new location to the second lighthouse and it is now 283⁰.

Assuming you have travelled in a straight line, what distance have you travelled between the two measurements?

Mathematician of the week.

Augustin Louis Cauchy

1798 – 1857

Cauchy was born in Paris. However due to a certain historical event (the French revolution) his father decided to move to a more quiet place called Arcueil.

They swiftly returned to Paris (obviously Arcueil was to quiet). His father then began to tutor him and two gentlemen named Mr Laplace and Mr Lagrange visited from time to time, which was nice of them!

When the young Cauchy grew up he worked for Napoleon on engineering projects. This did not stop him from entering into mathematical research of polygons. This research was probably a reflection of his current situation. He returned to Paris due to an illness. People are of the opinion that this was a mental illness. On returning to Paris he rested and he then produced work on functions.

Cauchy was Catholic (not that being Catholic is a bad thing) and it seems that his views on Catholicism and his manner with his colleagues might have annoyed them.  One example of this is when a colleague approached Cauchy to ask him a question. In response to this Cauchy just pointed him in the direction of his new book and then walked off! I don’t know about you but sometimes I would love to do that. He also worked for Charles X (In Prague) tutoring his grandson. Apparently in his frustration with the prince he would scream at him. It does seem however that his manner did cause him to be passed over for many academic positions. 

Moving back to the mathematics Cauchy produced a vast amount of work during his life well over 700 papers. His major works were into analysis, divergence of infinite series and differential equations (apologise if I have missed anything).

He also researched the theory of light in which he developed new mathematical techniques. (I think it was Fourier transforms?)

Some terms in mathematics that bear his name are:

·         Cauchy integral theorem

·         Cauchy - Riemann equations

·         Cauchy sequences

This is just a very short account of Cauchy so apologies for any mistakes, inaccuracies or omissions. He was a genius and a bit of a character which can only be a good thing and for some reason I do like him even though he probably wouldn’t have liked me.

Welcome

I have always liked maths and have studied it for a number of years. I figured I would start this blog as a portal for my love of the subject. Book reviews, great reference papers and just general maths chat. I may also throw in some exciting aspects of my life along the way.