It's time for a chick to hold the Lucasian Chair

The Lucasian Professorship in Mathematics at the University of Cambridge has become not only one of the most prestigious professorships in science but indeed of all academia. The Chair is now vacant, following the announced retirement of its current incumbent Stephen Hawking.

The University of Cambridge has put a call out for applicants, looking especially for theoretical physicists.

The position was created by Henry Lucas, hence the Lucasian Professorship, in 1663. Holders of the chair include a who's who of some of history's greatest thinkers, who have done so much to shape not only our understanding of nature, but of the modern world. The first incumbent was Isaac Barrow who played a very important role in the early development of calculus, the gateway to higher mathematics, an essential tool for understanding natural and social processes.

The most well known fictional holder of the Lucasian chair was Data from Star Trek: The Next Generation as depicted in the final episode “All Good Things ...” That I remember the relevant scene with such fondness, alas, may well tell a little bit too much about me.

The fact that the chair is a Cambridge chair very much helped to cement the University of Cambridge as the science university in comparison to its rival the University of Oxford, more noted for educating the political elite not only of the United Kingdom but of a good part of the Anglo-Saxon world.

Of course, the most well known holder of the Lucasian chair has been Isaac Newton, who gave us classical mechanics, the inverse square law of gravitation and, together with Gottfried Leibniz, the calculus. Much of Newton's work was presented in perhaps the greatest text of all time his Philosophiae Naturalis Principia Mathematica. The influence that Newton has had on the development of the modern world-view has been immense.

Newton's bitter and fierce feud with Leibniz on priority for the development of the calculus has gone down in history as one of the greatest intellectual bust ups of all time. The fact that Newton held the Lucasian chair accounts for much of its overall mystique.

Other noted holders of the Lucasian professorship include Charles Babbage and Paul Dirac. Babbage played a very important role in the development of the modern computer, further developing some work of Leibniz. He proposed the development of an automatic computational machine, what he called the analytical engine, which he was not actually able to build given the technological limitations of his era. However, his vision of developing such a machine helped to inspire others such as Alan Turing and John von Neumann who went on to play seminal roles in ushering in the computer revolution that, as any reader of this website would be well aware, has done so much to shape modern life.

Paul Dirac was one of the most fascinating characters in all of physics, where there has existed no appreciable shortage of curious characters. Dirac is most well known for his key contributions to the development of quantum mechanics, especially the Dirac equation. It was the Dirac equation that predicted a new particle, essentially an opposite charged companion of the electron, known as the positron. It was the positron and the Dirac equation that lead to our discovery of anti-matter.

Dirac was an incredibly quiet and logical person. Although he was very taciturn, this merely hid strongly held opinions. His views have been re-told in Crease and Mann's delightful The Second Creation: "Dirac had violently colored political views; with passionately lofty detachment, he told his Continental colleagues that there was no reason for the poor to suffer, that he saw little purpose in rewarding the greedy with wealth, and that organized religion was a ludicrous sham."

It was indeed fortuitous that Dirac did not hold a professorship at the University of Oxford.

The most obvious candidate to succeed Stephen Hawking would be Ed Witten, currently at the Institute for Advanced Study at Princeton University.

Witten is the leading figure in the superstring approach to quantum gravity, which seeks to unite the two main theories of physics, general relativity and quantum field theory, into one all encompassing theoretical structure. In the Principia Newton discovered a property of gravity that holds for weak gravitational fields famously stating of the ultimate nature of gravity, hypotheses non fingo, that he frames no hypothesis. It was Albert Einstein who developed great insight into the nature of gravitation with general relativity, but the ultimate nature of gravity is still unknown given the incompleteness of Einstein's theory hence the search for quantum gravity.

Witten, whose brother is a writer for the TV show House, is especially noted for the power of his mathematical thinking, himself making important new discoveries in the mathematics underlying string theory in such esoteric aspects of algebraic topology as K-theory and the like.

There would be some irony in Witten taking the chair. Hawking's inaugural lecture provocatively posed the question, "is the end in sight for theoretical physics?" His pessimism for the future of theoretical physics was based on his optimism that N=8 supergravity (where N refers to the number of space-time dimensions the universe has according to the theory) would lead to a consistent theory of quantum gravity. Not a word is devoted to superstring theory, but not long after Hawking spoke the first superstring revolution erupted and supergravity became a back water.

It was Witten who showed that supergravity and superstrings, in the second superstring revolution that he unleashed during the 1990s, were intimately related. However, it was N=11 not N=8 supergravity that was the relevant approach. There would be some neat irony therefore if Witten were to take the chair.

Another candidate is the French mathematician Alain Connes, one of the world's leading mathematicians. He is most well known for his non-commutative geometry and is currently using his insights to develop a rival conception of quantum gravity to superstring theory. But, hey, could you imagine the University of Cambridge handing the Lucasian chair to a Frenchman?

One thing about the Lucasian professorship stands out. It has never been held by a woman throughout its long history. Perhaps now is the time for a woman to occupy this most venerable of scientific chairs. There are some candidates who do readily come to mind.

One possible candidate could well be Fotini Markopolou-Kalamara, a noted researcher in the most well known rival approach to quantum gravity, that being loop quantum gravity. This approach is more favoured by those who have more of a background in general relativity than high energy particle physics or quantum field theory, and given that superstring theory is currently stuck in a morass of universes each with their own laws of physics, might just well be the correct approach, although we should not neglect the more revolutionary twister theory favoured by Hawking's long time colleague Roger Penrose.

The leading female candidate, however, would undoubtedly be Lisa Randall, who currently holds a chair in theoretical physics at Harvard, America's version of Oxford.

Randall has written some of the most widely cited physics papers of recent times, which deal with some of the niceties of string theory such as p-branes and brane-worlds.

There would be a neat symmetry in Randall holding the Lucasian chair.

She is most well known for her work on higher dimensional spaces and string theory, invoking brane-worlds (other universes) to explain the relative weakness of the big G, Newton’s universal constant of gravitation. Although the big G plays a very important role in the large-scale structure of the universe, now we cannot neglect "dark energy" an unknown form of anti-gravity, its small value has always been a source of great mystery.

A female Lucasian chair would be a good way of breaking a hitherto male monopolised professorship in science and may well be a good way to encourage more girls to enter into mathematics and the physical sciences, currently seen as a pursuit for geeky males.

If the TV reality series Beauty and the Geek is any guide this would be what a game theorist would, like, call a win-win outcome or a Nash equilibrium if you will.