Content: Mathematicians seek answers to questions, problems, and challenges of various kinds. They have at their disposal methods that may or may not work, and they get answers that may or may not be any use. This is clearest in mathematical physics (e.g. when a power series converges too slowly to be any help) but it can also be true in pure mathematics. This is a historical course about getting good answers to good problems in mathematics.

Aims: The module aims to:

• consider topics in the history of ordinary and partial differential equations from their introduction in the 17th century to the early 20th century;
• discuss what was taken to be so important about them.

Objectives:

• To develop a critical sense of what was, and even what is, important and exciting about mathematics and its evolution.
• To raise questions about the rigour in mathematics and its relation to problem solving.

Books: A full set of Lecture Notes will be provided. There is no book on the topic, and in that sense the course will present the result of ongoing historical research. There are some specialist treatments of individual topics, and these will be pointed out as and when they are relevant.