History of Mathematics - Classical algebra: equation solving 1800 BC - AD 1800. 3rd Year Lecture

Note: this is a lecture from a wider course. You can access the full course notes explaining the context of the course and covering other aspects of the subject including contributions from across the world (for example, China, India and Japan): https://courses.maths.ox.ac.uk/course/view.php?id=5516 The kind of mathematical problem solving that we now label as 'algebra' has been going on for at least 4000 years, beginning with the solution of quadratic equations in ancient Babylon. Over the following millennia, methods for solving other types of equations were gradually added to the mathematician's toolkit. In this lecture and the next one from Chris Hollings’ History of Mathematics’ course, we survey the history of algebra, starting from those ancient times, looking at how algebra eventually shifted away from the solution of individual problems towards a broader 'theory of equations'. We take the story up to the early twentieth century, when an altogether more abstract and structural type of algebra began to emerge.