Tuesday, October 14, 2008

Gauss, Lagrange and the others: who were they?

As economists we need to make use of mathematics in our work. We use equations to represent relationships between economic variables. We draw graphs to illustrate the nature of these relationships. We use algebraic methods to solve systems of demand and equations to find the equilibrium price of a good. We differentiate a total cost function to obtain an expression for marginal cost. We check necessary and sufficient conditions to ensure that we have located the optimal combination of consumption of various goods for a consumer aiming to maximize her utility subject to a budget constraint. We use matrix algebra to represent and manipulate equations linking final demand and intermediate demand for goods and services between different industries.

Sometimes the mathematical (and statistical) tools and methods that we use have the names of famous mathematicians of the past associated with them. Here are just a few of the names that students taking the course in Statistics and Mathematics for Economics at Portsmouth will come across - in no particular order: Cramer, Gauss, Lagrange, Fisher, Kuhn and Tucker. Perhaps you may wonder who these people were and what is was that prompted them to develop the mathematical tools and methods linked to their names.

Today, by making use of the Internet and a search tool like Google, it is easy to find out. For example a seach for "Lagrange" can lead you to the website at St Andrews Univesrity in Scotland at MacTutor History of Maths where you can read that Lagrange is alleged to have said "If I had been rich, I probably would not have devoted myself to mathematics." which refelects the fact that economics is often the impetus for the development of new mathematics.

Of course there are many excellent books available that give some historical background on the development of mathematics and statistics. One of my favourite books on the history of statistical methods is David Salsburg's The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century

If you would prefer to watch a video or a TV programme rather than reading a book or a text based web site I have good news for you. You can find a lot of useful maths and stats video clips on YouTube (although a search for Lagrange will lead you mostly to clips of ZZ Top!). But right now there is an excellent programme on TV called The Story of Maths: The Language of the Universe. It's a four part series presented by Oxford professor Marcus de Sautoy and covers important developments in mathematics from ancient Egypt, Mesoptamia and Greece up to more recent times. A joint production with the Open University, you can find more about the series on the open2.net website. Mind you, I am extremely envious of Professor du Sautoy. In making the programme he got to travel to Greece, Egypt, Syria, Italy, India, Morocco and several other places where important developments occurred in the history of mathematics; including Göttingen in Germany to find out about Gauss and his contribution.


At 4:16 pm, Blogger Alistair Windsor said...

I hope that you mention William Karush too. He actually came up with the Kuhn-Tucker conditions before the work of Kuhn and Tucker. The conditions were in his Masters thesis but had gained no attention. These conditions are now popularly known as the Karush-Kuhn-Tucker conditions.


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