The Secrets of Mathematics

These two video sessions explore the development of Sir Roger Penrose's thought over more than 60 years, ending with his most recent theories and predictions. In the first session, Roger Penrose explains the impact of his time at Cambridge in the 1950s. The interview brings out his highly unconventional choice of subjects for deep study, which completely ignored the boundary between 'pure' and 'applied' mathematics. Those familiar with his world-leading development of relativity theory in the 1960s may be surprised to learn how much he was influenced by quantum theory in the 1950s, and also by the early origin of his new ideas.

Roger Penrose explains the influence of Dirac, Sciama and other leading figures of the 1950s, and goes on to characterise the emergence of twistor theory. Non-experts will be interested to hear how the ideas of his best-known work, The Emperor's New Mind, also had an origin in this early period. Roger Penrose also adds fascinating detail about the psychology of mathematical discovery, explaining how he was very slow at school, needing extra time to think issues through for himself. The mystery of time, in physics and human consciousness, runs through the entire conversation, and lights up even the most technical aspects of the discussion.

These two video sessions explore the development of Sir Roger Penrose’s thought over more than 60 years, ending with his most recent theories and predictions. In the second session, the emphasis shifts to the recent developments in Roger Penrose's thought. He gives a very clear outline of his argument for Conformal Cyclic Cosmology as the correct description of the Big Bang. However, the conversation turns once again to the precursors of these ideas in the 1950s, with new anecdotes about Dirac and the origin of Roger Penrose’s geometrical innovations. Bringing the discussion up to the present moment, Roger Penrose describes the impact of recent observations of primordial magnetic fields and also addresses the significance of his own predictions for the form of dark matter.

In a closing segment, the discussion turns to the current discoveries in neurology and biophysics relevant to Roger Penrose’s theory of microtubules as advanced in Shadows of the Mind. The discussion ends tantalisingly with renewed speculation on the foundations of quantum mechanics and its relation to general relativity. Non-experts will relish Sir Roger Penrose’s comment that 'To me eternity is not such a long time'.

In conversation with Paul Tod on the occasion of Sir Michael's 85th birthday conference. A portrait of the contribution that Sir Michael Atiyah has made to mathematics over his career together with his recollections of formative people and events. Interview by Professor Paul Tod.

Jim Murray is one of the leading mathematical biologists of our times. In this wide-ranging interview Jim talks about his career, the range of his work, his successes and failures and his hopes and expectations for the future of mathematical biology.

Professor James D Murray, Professor Emeritus of Mathematical Biology, University of Oxford and Senior Scholar, Applied and Computational Mathematics, Princeton University, gives the annual Hooke Lecture. Understanding the generation and control of pattern and form is still a challenging and major problem in the biomedical sciences. I shall describe three very different problems.

First I shall briefly describe the development and application of the mechanical theory of morphogenesis and the discovery of morphogenetic laws in limb development and how it was used to move evolution backwards. I shall then describe a surprisingly informative model, now used clinically, for quantifying the growth of brain tumours, enhancing imaging techniques and quantifying individual patient treatment protocols prior to their use. Among other things, it is used to estimate patient life expectancy and explain why some patients live longer than others with the same treatment protocols.

Finally I shall describe an example from the social sciences which quantifies marital interaction that is used to predict marital stability and divorce. From a large study of newly married couples it had a 94 percent accuracy. I shall show how it has helped design a new scientific marital therapy which is currently used in clinical practice.

A portrait of the contribution that Bryce McLeod has made to mathematics over his career together with his recollections of formative people and events. Interview by Professor Sir John Ball FRS, FRSE , Sedleian Professor of Natural Philosophy.

Professor Gui-Qiang G. Chen presents in his inaugural lecture several examples to illustrate the origins, developments, and roles of partial differential equations in our changing world. While calculus is a mathematical theory concerned with change, differential equations are the mathematician's foremost aid for describing change. In the simplest case, a process depends on one variable alone, for example time. More complex phenomena depend on several variables - perhaps time and, in addition, one, two or three space variables. Such processes require the use of partial differential equations. The behaviour of every material object in nature, with timescales ranging from picoseconds to millennia and length scales ranging from sub-atomic to astronomical, can be modeled by nonlinear partial differential equations or by equations with similar features. The roles of partial differential equations within mathematics and in the other sciences become increasingly significant. The mathematical theory of partial differential equations has a long history. In the recent decades, the subject has experienced a vigorous growth, and research is marching on at a brisk pace.

Dr Richard Earl of the Mathematical Institute, Oxford presents a talk about prime numbers. What they are and their role in internet security.

Stephen Wolfram, creator of Mathematica and Wolfram Alpha, gives a talk about the future of mathematics and computation.

Professor Marcus du Sautoy (New College), Charles Simonyi Chair in the Public Understanding of Science, author and broadcaster gives a talk about how much we can understand of the world through maths