Mathematics into pictures – Numbers and geometry (1978)

Christopher Zeeman

Christopher Zeeman presents the second Christmas Lecture from his groundbreaking 1978 series.

Watch time: 59:54
Christopher Zeeman speaking to a child at the Ri theatre
Credit: Royal Institution

Lecture 2 - Numbers and geometry

As mathematics has developed down the centuries, our concept of numbers has grown more sophisticated to include many different types of numbers.

From rational and irrational numbers used for measuring the real world to complex numbers used for solving equations, Zeeman outlines the historical development of maths and explains why it happened. 

It's not as complex as it sounds. Through demonstrations and simple proofs, we are introduced to the contributions of Greek mathematicians during the fifth century B.C. through to 1799 when Gauss proved the famous theorem that with complex numbers all equations can be solved. 

Plus, watch out for the giant calculator!


Professor Christopher Zeeman presents the 1978 CHRISTMAS LECTURES on one of the oldest and most splendid endeavours of mankind.

As he explains in his original introduction to the series maths is at its core a paradoxical subject: "We are never quite sure whether it is an art or a science, whether we invent it or discover it, whether it is a man-made toy or a truth so universal that it is independent of the universe."

True to the tradition of the CHRISTMAS LECTURES, Zeeman places practical demonstrations at the heart of his presentations, using diagrams and pictures to reveal the nature and beauty of mathematical theorems and illustrating different types of mathematical modelling.

The first three lectures start with a pure point of view to ask 'What is the nature of mathematics?' before shifting to an applied point of view to explore the mathematics of nature.

These were the first CHRISTMAS LECTURES in its then 149-year history to be presented on the subject of mathematics and the series is still lauded as inspiring a new generation of mathematicians. Amongst the live audience was a budding young mathematician called Marcus du Sautoy who went on to present the Lectures in 2006 entitled ‘The num8er my5teries’.

Furthermore, the enthusiasm generated by the series led Professor Zeeman to establish the Ri’s Mathematics Masterclasses programme in 1981. They continue to enable thousands of young people across the UK to participate in the hands-on and inspired learning that is the hallmark of the CHRISTMAS LECTURES.