Mathematics into pictures – Infinity and perspective (1978)

Christopher Zeeman

What does a race with a tortoise, renaissance art and a barbershop have to do with mathematics? Christopher Zeeman explores these questions and more as he devotes his third lecture to the concept of infinity.

Watch time: 01:00:11
Christopher Zeeman writing equations using a projector in the Ri theatre
Credit: Royal Institution

Lecture 3 – Infinity and perspective

Although its use in common language is often vague, infinity is very important to mathematics and is used very precisely within a variety of contexts, from Greek paradoxes to the development of perspective in renaissance art.

Its usage is therefore dependent upon the context in which it is used. Zeeman outlines three typical examples: Zeno's Paradox of Achilles and the tortoise, The vanishing point of perspective painting and the theory of infinite sets.

Zeeman demonstrates the importance of infinity not only to mathematics but also to the world of art, where its use in perspective is integral to conveying three-dimensional spaces in two-dimensional artworks. 


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.