Andrew Hodges
Main Page
Me in New York, 2001
In New York City, 29 January 2002
Email: andrew(AT)

University of Oxford page
Wikipedia page

Seeing the world in a different light

Since 1972 I have worked with Roger Penrose in developing the theory of twistors which he originated.

This work has brought me to the Mathematical Institute at Oxford University.

A fast track to reality?

Twistor theory gives a new way of describing space and time. It treats light rays, rather than points, as the most primitive objects of physical existence.

This is a radical reformulation of physics. According to Roger Penrose's twistor programme, this reformulation is not just a mathematical technique, but a clue to the ultimate basis of reality. It is hoped that the outstanding problems of physics, for instance that of making quantum theory consistent with gravity, will be resolved within some form of twistor geometry.

Professor Sir Roger Penrose, FRS, OM
My own work has developed the theory of twistor diagrams which Roger Penrose started around 1970.
Twistor diagrams give a new description of how elementary particles interact through the elementary forces of Nature.

A waste of space-time?

This has not been a fast track to fame or fortune. For thirty years, super-string theory dominated the attempts to find a more fundamental level to physical reality, and twistor theory received very little attention.

But in 2003, new ideas from the physicist Edward Witten showed a twistor-string connection. I saw that this shed quite new light on twistor diagrams and showed them to be highly relevant to fundamental physics. Now they take a central place.

See my twistor diagram site for my recent work in this field.

A twistor diagram
for eight gluons

I am a Senior Research Fellow in the Mathematical Institute, and give University lecture courses.

As a Fellow of Wadham College, I also give student tutorials covering a wide range of mathematical topics.

But I have not followed a conventional academic career. I have put a high value on the freedom to cultiver mon jardin. Back in the 1970s, before I came to Oxford, this led me into a quite different line of enquiry.

Alan Turing: the enigma

Alan Turing in 1931
The British mathematician Alan Turing (1912-1954)
  • founded computer science (1936)
  • cracked the German U-boat Enigma cipher (1939-40)
  • led the world in computer plans (1945-47)
  • started the Artificial Intelligence programme (1946-50)
  • and non-linear dynamics in biology (1950-54)
(amongst other things).
In 1972 I learned from some unusual sources that there was a dramatic human and historical story lying behind these scientific and technical achievements and his early death in 1954. Alan Turing was a gay man, at a time when homosexuality was completely criminal. In 1952 he had suffered arrest, humiliating treatment with hormones, and surveillance.

This was the background to his death in 1954. He died of cyanide poisoning, in a scenario involving a partly eaten apple.

The whole story was wrapped up in great secrecy. In 1977 I felt impelled to do justice to him, so I conducted substantial research into all aspects of Alan Turing's life and work and wrote the book Alan Turing: the enigma, published in 1983.

This has brought him fully into the light. The book has been republished in many editions and translations over the last thirty years.

Over the rainbow

The book has also been the basis for many artistic and other public developments. In 1986, the dramatist Hugh Whitemore wrote Breaking the Code, starring Derek Jacobi on the stage in London and New York, and later on the television screen.

The statement of the Prime Minister in 2009, and Turing's centenary in 2012, stimulated the demand for an extraordinary Royal Pardon in 2013. In July 2014 the Pet Shop Boys performed an equally extraordinary new concert piece, A Man from the Future, using text from my book.

Only connect

Alan Turing was a free-thinker in all ways, and his crime was one of associating too freely. He would have been the first in line to exploit the freedom of the Web, which in turn exploits the concept of the universal machine that he discovered in 1936.

In 1995 I began a website to support the book. This stimulated new thoughts about Alan Turing and his work. Another influence in the 1990s was the Roger Penrose's theory of computability and physics. See my Publications page.

There is a greater unity to my aspirations that I could have seen in the 1970s. Alan Turing was thinking about space-time and quantum mechanics shortly before he died in 1954, and the radicalism of twistor theory is close in spirit to his own.

Wondrous  Light  . . . some of Alan Turing's last words, and part of my own inspiration.


My projects have taken forty years to make their impact. I haven't quite forgotten their origin in the radical 1970s.

My short book One to Nine (2007) brought all this together, and also foretold my favourite synthesis of them all: working with the Pet Shop Boys.

cool maths

gay rights

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