But perhaps you will hear more about those in some of the other lectures taking place during this meeting. Moreover there is no point in trying to give just a list of theorems or even a list of famous mathematicians over the last hundred years. That would be rather a dull exercise. So instead I am going to try and pick out some themes that I think run across the board in many ways and underline what has happened. Let me first make a general remark.
Centuries are crude numbers.
We do not really believe that, after a hundred years something suddenly stops and starts again. So when I describe the mathematics of the 20 th century, I am going to be rather cavalier about dates. If something started in the 1890's and moved into the 1900's - I shall ignore such detail. I will behave like an astronomer and work in rather approximate numbers. In fact many things started in the 19 th century and only came to fruition in the 20 th century.