# Sir Roger Penrose : A man of extraordinary vision

News, Student news, Alumni newsEmeritus Fellow and Nobel Prize winner Sir Roger Penrose joined Wadham in 1973 and it was not long before his colleagues realised the extraordinary breadth of Roger’s vision.

The ‘polymath’ label does not do justice to the coherence of his scientific outlook and to his extraordinary facility for seeing connections between seemingly diverse fields.

Wadham Emeritus Fellow Nick Woodhouse, reflects on Roger’s career and achievements, from black holes, programming language and twistor theory to lively Friday lunchtime discussion groups.

Roger Penrose moved to Oxford in 1973 to take up the Rouse Ball Chair of Mathematics together with a Professorial Fellowship at Wadham. Eight years earlier he had published a remarkable three-page paper with the title *Gravitational Collapse and Space–Time Singularities*. It had not passed unnoticed. He was elected to a Royal Society Fellowship in 1972, and he received many prizes for the work that he, and later Stephen Hawking, built on its foundation.

Finally, more than fifty years after publication, the paper was cited by the Nobel Prize Committee in awarding Roger half of the 2020 Prize in Physics for ‘The discovery that black hole formation is a robust prediction of the general theory of relativity’.

A remarkable paper and a remarkable story. The long gap and the fact black holes are not mentioned explicitly in the paper may be puzzling, but the explanation lies in the context of his work and in the fact that the Physics Prize cannot be awarded for a theoretical discovery, however brilliant, until it has been confirmed by observation or experiment.

Roger’s paper opens with a reference to the discovery of ‘quasistellar radio sources’ (quasars). It had been suggested in 1964 that the source of a quasar’s enormous energy might be matter falling into a massive black hole in the centre of a galaxy. But it was still a highly controversial idea that black holes might actually exist. Moreover it was not even clear in 1964 that general relativity would allow black holes to form under reasonable physical assumptions. There were models of gravitational collapse that produced black holes, but only from highly symmetric initial conditions and with highly unrealistic assumptions about the gravitating matter. It was widely thought that the collapse of a real astronomical body would require impossible compression. It was this theoretical problem that Roger’s paper solved.

The remarkable observational work of his co-laureates, Reinhard Genzel and Andrea Ghez, has now demonstrated that our own galaxy does indeed have a black hole at its centre with a mass some four million times that of the sun, thus opening the door for the award of the Nobel Prize for Roger’s theoretical discovery and for their observational verification.

It was widely thought that the collapse of a real astronomical body would require impossible compression. It was this theoretical problem that Roger’s paper solved

Roger is often described as a ‘polymath’, with his scientific and mathematical contributions spread over many fields. That is certainly true, but the ‘polymath’ label does not do justice to the coherence of his scientific outlook and to his extraordinary facility for seeing connections between seemingly diverse fields. His 1965 paper is a remarkable exploitation of one of the key ideas that runs through many of his contributions to geometry and theoretical physics, namely the central roles of conformal structure and null geodesics (photon trajectories).

When Roger arrived in Oxford, he was exploring through his ‘twistor theory’ a related circle of connections between conformal geometry, null geodeiscs, and the way in which complex numbers enter relativity theory and quantum mechanics. The role of complex numbers in quantum theory was familiar, but Roger was struck by the fact that they also enter relativity through the natural identification of the celestial sphere with the Riemann sphere—natural in the sense that it is independent of the motion of the observer. Twistor theory was motivated originally by the need to reconcile general relativity with quantum field theory, but it soon became apparent that the ideas had much wider application, notably through discussions in Oxford about four-dimensional geometry with Michael Atiyah and Nigel Hitchin.

Roger quickly built up a large and very lively group of graduate students, postdocs, and visitors. Every Friday, the group gathered in his office for a ‘lunchtime’ meeting that often lasted into early evening. The meetings started with a question and answer session, Roger usually providing the answers with impromptu lectures on a huge range of topics. One in particular stands out in my memory, on Church’s λ-calculus (lambda-calculus). I did not know until later that Roger had played a key part in the importation of the λ-calculus into the design of programming languages, when he worked for Christopher Strachey in the 1950s.

Several from the group went on to achieve great distinction in areas that at first sight have little connection with the central motivation of twistor theory, but where a little digging shows the extraordinary breadth of Roger’s vision at work. It was a wonderful and inspiring era. Today Roger is still working on these ideas, not least in the context of his ‘cyclic cosmology’, where conformal geometry is again centre stage.

Professor Nick Woodhouse, Emeritus Fellow Wadham College

Roger quickly built up a large and very lively group of graduate students, postdocs, and visitors. Every Friday, the group gathered in his office for a ‘lunchtime’ meeting that often lasted into early evening

# Penrose Paving

In front of Wadham’s Bowra building in Webb Quad is a small terrace with an intriguing pattern. In 1974 Roger Penrose (then Rouse Ball Professor of Mathematics and Fellow of Wadham) discovered that it was possible to construct a curious pattern from just two different shapes, each of them a rhombus with angles which are multiples of 36 degrees; the pattern achieves fivefold symmetry and, most remarkably, can be extended to infinity without repeating itself. Extraordinarily, ten years later, chemists discovered a new class of metallic alloys with similar fivefold symmetry, in defiance of the previously accepted laws of crystallography.

The paving at the entrance to Oxford’s Mathematical Institute which opened in 2013 is also Penrose, constructed from just two different diamond-shaped granite tiles, each adorned identically with stainless steel circular arcs. There are various ways of covering the infinite plane with them, matching the arcs. But every such pattern is non-repetitive and contains infinitely many exact copies of what you see along the entrance flooring.

# Black hole research today

Interestingly, our own Lindemann Fellow and tutor in Physics Martin Bureau spends most of his research time measuring the masses of the supermassive black holes that lurk at galaxy centres. While this relies primarily on Newtonian physics, Roger’s work provides the basis/evidence that what Martin is measuring are indeed black holes (rather than some other form of extremely dense and dark matter). A whole swathe of present-day astrophysics (including the work of many past Wadham graduate students) is in fact concerned with understanding how these black holes influence the evolution of galaxies, and thus ultimately us!

Professor Martin Bureau# Watch Roger’s Nobel Prize Lecture

# Sir Roger Penrose, in conversation with the Warden

Wadham alumni are invited to join the Warden of Wadham College, Ken Macdonald QC in conversation with Sir Roger Penrose on Thursday 18 February, followed by the opportunity to watch a recorded conversation and Q&A with Sir Roger and alumnus Melvyn Bragg (Modern History, 1964).

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