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

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. I am also a Fellow of Wadham College.

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

My uneconomic base
I am a Senior Research Fellow in the Mathematical Institute, and give University lecture courses. I also give a lot of tutorials for first and second-year work, and classes for the third and fourth-year options.
The timelessness of mathematics always keeps me going. But I have not followed any conventional career structure, taking a rather independent attitude, and I have valued the freedom to cultiver mon jardin.

This unusual way of carrying on has led me to a second line, a second string, of unconventional mathematical enquiry:

Alan Turing in 1931

This is

Alan Turing


who (amongst other things)

  • 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)

The book

During the 1970s I learned from some unusual sources that there was a dramatic human and historical story lying behind the scientific and technical achievement and the 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 dramatic background 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 been a successful book, bringing him fully into the light.

The next stage — and screen

The dramatist Hugh Whitemore used my book as the basis of his play Breaking the Code (1986). Alan Turing was played by Derek Jacobi in London and New York. A cut-down version of the play was filmed for television, also starring Derek Jacobi, and first broadcast in 1997.

The somewhat ironic result is that I have earned much of my income from show business, and that this has allowed me to pursue scientific research rather independently of current fashion. Eventually, this has paid off.

After 1995 I started an Alan Turing website, and this has allowed me to extend and update the original work, as well as to reach a new readership.

Alan Turing was a free-thinker in all ways, and his crime was one of associating too freely. I'm sure 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.

Where the rainbow ends?

The website stimulated new thoughts about Alan Turing and his work, and set in motion many invitations to speak at conferences and write new articles. Another influence in the 1990s was the Roger Penrose's theory of computability and physics. A climax came in 2012, the Turing centenary year. See my Publications page.

From my present perspective, there is a greater unity to my aspirations that I realised 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.


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

More syntheses: continue to...

fundamental physics
Alan Turing:
fundamental computing
A short book One to Nine
brought together logic, physics,
arts and science, light side and dark side.

See my Cool Maths site.

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Big Oxford Computer Company Ltd.