Emeritus Rouse Ball Professor of Mathematics.

What are you working on today?
My new ideas on cosmology.

What do you regard as the most important idea of your career?
Before thinking of my cosmological scheme, I would undoubtedly have said "twistor theory". This is a different way of looking at space and time, translating these familiar notions into a different geometrical picture based on the mathematics of complex numbers. The cosmological idea is slightly easier to explain, although a little mind-blowing. I am claiming that the Big Bang was not actually the beginning but that there was a previous aeon very much like our own, and so on. To make sense of this idea, you have to get used to the notion that time measurement ultimately loses its meaning in the very remote future of each aeon, which can then be reinterpreted as the big bang of the next one.

Why does it matter?
These things are all part of our attempts to better understand the universe around us. More specifically, since 2003 there has been a renewed interest in twistor theory in the high-energy community – twistors have become a valuable tool in calculations anticipating results from the Large Hadron Collider in Geneva. This understanding is important, whether or not it leads to specific scientific advances such as curing cancer (an area that has indeed benefited from radioactive isotopes produced by high-energy accelerators).

What has been your most controversial idea?
My claim that conscious thinking is something quite different from the action of a computing machine. What people baulk at is my proposal that non-computational activity can come about through processes acting in accordance with strict physical laws, involving principles that physicists have not yet discovered. My claim is that our present-day theory of quantum mechanics is fundamentally incomplete. New concepts, equations, etc. will be needed for the formulation of a fundamentally new scheme in which the quantum mechanics of small-scale phenomena somehow merge into large-scale classical physics. The thought that is alarming to people is that action of a conscious brain would have to depend upon this modification of current physics. This would imply that large-scale coherent quantum behaviour is actually taking place in brains – a shocking proposal both to many physicists and certainly to most biologists. However, recent experimental observations do seem to lend some critical support to the proposal. We shall have to wait and see how all this develops.

Is mathematics more or less important than 500 years ago?
If people like Cardano, Galileo and Kepler had not begun to show a new importance for mathematical ideas in the way things work, then science might not have had such a profound impact on our lives by now. On the other hand, the volume of mathematics that is being applied now is utterly vast in comparison with what these ancient pioneers were doing around five centuries ago.

Interview by Josie Dixon

The life work of Sir Roger Penrose is collected in six volumes by OUP and his book Cycles of Time is published by Bodley Head.