# Andrew Hodges

Dr Andrew Hodges Emeritus Fellow in Mathematics, Wadham College

# Dr Andrew Hodges Emeritus Fellow in Mathematics

Dr Andrew Hodges has taught mathematics at Wadham College since 1986. He is tutor for a wide range of courses in pure and applied mathematics, both in the College and for inter-collegiate classes, and gives University lectures in Calculus of Variations and Classical Mechanics. He became an Emeritus Fellow in October 2016.

Contact Andrew Maths at WadhamTwistor geometry involves a radical new description of space and time, and has the potential to transform our understanding of the universe as radically as Einstein did a century ago.

Andrew's main research interest is in the mathematics of fundamental physics. Since the 1970s he has contributed to the twistor programme for physics initiated by Roger Penrose (an Emeritus Fellow of Wadham College).

Andrew’s work involves studying certain large-dimensional complex contour integrals, called twistor diagrams, which give a completely new description of how elementary particles interact.

Interest in the British mathematician Alan Turing (1912-1954), the founder of modern computer science and the chief scientific figure in Second World War code-breaking, has inspired Andrew’s work. He wrote Alan Turing: the enigma (1983) which has been translated into several languages, most recently Chinese, and was dramatised (as Breaking the Code) for stage and television.

My work shows how the historical roots of modern technology lie in mathematical discovery.

Starting with a short book about Alan Turing in a series on The Great Philosophers (1997), Andrew has written further papers on the history and philosophy of computation.

Andrew was elected a Fellow at Wadham in 2007 and appointed Dean in 2011. In 2012 he became a Senior Research Fellow in the Mathematical Institute, with CUF status. He is a member of the Mathematical Physics group at Oxford.

# Selected publications

Eliminating spurious poles from gauge theoretic amplitudes (2009)

The box integrals in momentum-twistor geometry (2010)

(With N. Arkani-Hamed, J. Bourjaily, F. Cachazo and J. Trnka) A note on polytopes for scattering amplitudes (2010)

New expressions for gravitational scattering amplitudes (2011).

A simple formula for gravitational MHV amplitudes (2012).

The Essential Turing, *Notices of the American Mathematical Society*, 53, 1190 (2006), also in Chinese: Mathematical Advances in Translation, 27 (2008).

Alan Turing: the logical and physical basis of computing, for *British Computer Society* symposium (2008)

Alan Turing, Logical and Physical, opening essay in *New Computational Paradigms*, eds. S. B. Cooper, B. Löwe, A. Sorbi (Springer, 2008)

What did Alan Turing mean by 'machine', in *The Mechanical Mind in History*, eds. P. Husbands, O. Holland and M. Wheeler (MIT Press, 2008)

In retrospect: Gödel's Proof, *Nature* 454, 829 (2008)

Alan Turing: entry in the *Princeton Companion to Mathematics* (2008)

Fair play for machines, *Kybernetes* 39, 441 (2010)

(With C. V. Sukumar) Bernoulli, Euler, permutations and quantum algebras, *Proc. Roy. Soc.* 463, 2401-2414 (2007). See my on-line introduction.

(With C. V. Sukumar) Quantum algebras and parity-dependent spectra, *Proc. Roy. Soc.* 463, 2415-2427 (2007)*One to Nine*, Short Books (2007)

# Contact

Andrew Hodges

andrew.hodges@wadh.ox.ac.uk