The Strangest Man

When I was in Edinburgh I picked up a copy of Graham Farmelo’s new biography of Dirac. It’s entitled The Strangest Man: The Hidden Life of Paul Dirac, Quantum Genius, and is not yet available in the US. I read the book on the plane trip back to New York and very much enjoyed it. While I’ve read a large number of treatments of the history and personalities involved in the birth of quantum mechanics, this one is definitely the best in terms of detail and insight into the remarkable character of Paul Dirac. I gather that Farmelo had access to many of Dirac’s personal papers, and he uses these well to provide a sensitive, in-depth portrait of a man who often is reduced to a bit of a caricature.

The book is less of a scientific biography than the other book about Dirac I know of, Helge Kragh’s 1990 Dirac, A Scientific Biography, and emphasizes more the development of Dirac’s personality and the story of his relations with others, especially with his father, his mother, and his wife (who was Wigner’s sister). I learned quite a lot about Dirac that I’d never known before, including for instance the story of his work on the atomic bomb project during WWII.

Dirac is responsible for several of the great breakthroughs in 20th century physics. At the age of 23, while still a graduate student, he took Heisenberg’s ideas and found the fundamental insight into what it means to “quantize” a classical mechanical system: functions on phase space become operators, with the Poisson bracket becoming the commutator. This remains at the basis of our understanding of quantum mechanics, and Dirac’s textbook on the subject remains a rigorously clear explanation of the fundamental ideas of quantum theory. Two years later he found the correct relativistic generalization of the Schrodinger equation, the Dirac equation, which to this day is at the basis of our modern understanding of particle physics. This equation also turns out to play a fundamental role in mathematics, linking analysis, geometry and topology through the Atiyah-Singer index theorem. Around the same time, Dirac was one of the people responsible for developing quantum field theory and quantum electrodynamics, as well as coming up with an understanding of the role of magnetic monopoles in electromagnetism.

The period of Dirac’s most impressive work was relatively short, ending around 1933. By 1937, the year he married, Farmelo reports Bohr’s reaction to reading Dirac’s latest paper (on the “large numbers hypothesis”):

Look what happens to people when they get married

Farmelo discusses a bit the question of why Dirac never later achieved the same sort of success after the dramatic initial period of his career. There may be a variety of reasons: the open problems got a lot more difficult, marriage and celebrity changed the way he lived and work, the war intervened, etc. For the rest of his career, Dirac took the attitude that there was something fundamentally wrong with QFT, and this may be why he stopped making fundamental contributions to it. He believed that a different sort of dynamics was needed, one that would get rid of the problems of infinities. He never was happy with renormalization, either in the form used to do calculations in QED after the war, or the more sophisticated modern point of view of Wilson and the renormalization group.

Unfortunately, some of the later parts of Farmelo’s book are marred by an attempt to enlist Dirac in the cause of string theory. This starts with the claim that Dirac’s work on “strings” during the fifties should be seen as a precursor of present-day string theory. These “strings” occur in the context of QED and magnetic monopoles, where they are unphysical artifacts of a choice of gauge, and have very little to do with the modern-day interest in physical strings as a basis for a unified theory.

Farmelo sees string theory as a resolution of the problem of infinities that Dirac would have approved of:

What would surely have impressed Dirac is that modern string theory has none of the infinities he abhorred.

I don’t see any reason at all to believe that Dirac would have been impressed with the idea of resolving the problems of QFT that bothered him by replacing it with a 10-dimensional theory that, despite the endless hype, has its own consistency problems (its perturbation expansion diverges, just like that of QFTs, and, unlike QFT, a 4d non-perturbative theory remains unknown). String theory was around for at least a dozen years before Dirac’s death, I’m sure he had heard about it, and there is no evidence he took any interest in the idea. Farmelo reports the reaction Pierre Ramond got from Dirac in 1983 when he tried to sell him on the idea of replacing 4d QFT with a higher-dimensional theory:

So he asked Dirac directly whether it would be a good idea to explore high-dimensional field theories, like the ones he had presented in his lecture. Ramond braced himself for a long pause, but Dirac shot back with an emphatic ‘No!’ and stared anxiously into the distance

The book ends with long discussion of Dirac and string theory that I think is seriously misguided, but it does include a mention of the fact that many physicists are unconvinced by the idea of string theory unification. Veltman is quoted, and the last footnote in the book refers the reader to Not Even Wrong.

Dirac is famous among physicists for his views on the importance of the criterion of mathematical beauty in fundamental physical law, once writing:

if one is working from the point of view of getting beauty in one’s equation, and if one has really sound insights, one is on a sure line of progress.

Farmelo believes that Dirac “would have revelled in the mathematical beauty” of string theory, but this is based on an uncritical acceptance of the hype surrounding the question of the “beauty” of string theory. “String theory” is a huge subject, and one can point to some mathematically beautiful discoveries associated with it, but the attempts to use it to unify physics have led not to anything at all beautiful, but instead to the landscape and its monstrously complex and ugly constructions of “string vacua” that are supposed to give the Standard Model at low energies.

I very much share Dirac’s belief that fundamental physics laws and mathematical beauty go hand in hand, seeing this as a lesson one learns both from history and from any sustained study of mathematics and physics and how the subjects are intertwined. As it become harder and harder to get experimental data relevant to the questions we want to answer, the guiding principle of pursuing mathematical beauty becomes more important. It’s quite unfortunate that this kind of pursuit is becoming discredited by string theory, with its claims of seeing “mathematical beauty” when what is really there is mathematical ugliness and scientific failure.

Ignoring the last few pages, Farmelo’s book is quite wonderful, by far the best thing written about Dirac as a person and scientist, and it’s likely to remain so for quite a while. Definitely a recommended read for anyone interested in the history of the subject, or some insight into the personality of one of the greatest physicists of all time.

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27 Responses to The Strangest Man

  1. Shantanu says:

    Peter, thanks for pointing to this. Also in this post, you forgot to
    mention Dirac’s contributions to GR. There is a good exposition on that
    in here
    Does this book discuss Dirac’s contributions to GR?

  2. Peter Woit says:


    Yes, the book does discuss a bit his contributions to GR. What I wrote is by no means intended as a comprehensive list. Dirac did significant work on many topics, but I think the general notion of quantization and the Dirac equation are the two that are both of greatest importance, and cases where the insight is purely his, no one else was doing the same thing around the same time.

  3. Chris Oakley says:

    I have to applaud Farmelo for having the courage to point out that Dirac was weird and probably mildly autistic – people normally just try to make excuses for his odd behaviour.

    I have only skimmed the book so far (tho’ it is near the top of my reading list) and am disappointed to read here that the author has tried to enlist Dirac in the String Theory Roll of Honour. I do not blame him for that in itself (I am just as guilty as any in claiming “support” by the great man): it is just that I did not expect that Farmelo, as an adjunct physics professor not obviously attached to any String program, would have a horse in that particular race.

  4. I must disagree that Dirac slowed down after 1933. For me, his most precious (and, unfortunately, underappreciated) work is P. A. M. Dirac, “Forms of relativistic dynamics”, Rev. Mod. Phys. 21 (1949), 392.

  5. Jules Moulin says:

    A strange story about Dirac’s equation is told by Thomas Racey, who with Battey-Pratt deduced the Dirac equation from a slightly expanded version of Dirac’s belt trick: see E.P.Battey-Pratt; T.J.Racey, Geometric model for fundamental particles, International Journal of Theoretical Physics, 19:437-475, 1980. They deduced all the details of Dirac’s equation from a few simple topological ideas. They then sent a copy of the paper to Dirac, but unfortunately, Dirac never answered.

    Racey then turned to other research topics. Only a few scattered people are trying to revive interest in the approach.


  6. Thomas R Love says:

    I thought some of Dirac’s best work was his 1951 Letter to Nature:”Is there and Ether” and his idea that the velocities of the ether provide potentials. Thanks Jules, I’ve thought for a long time that “Geometric Models” one of the most important papers that never developed a following.

    Dirac presented his last talk at the 2nd New Orleans Conference on Quantum theory and Gravitation in 1983. I went up to him carrying his book on General Relativity and asked for an autograph. He refused saying “I don’t do that”.

  7. MathPhys says:

    Many scientists and artists are probably slightly autistic.

  8. Made me laugh: ‘…string theory as a resolution of the problem of infinities that Dirac would have approved of…’. I don’t have the right to claim the opposite but it’s fun to see how these days anything and everything is used to defend string theory. Like many, I reckon he would have liked the mathematical integrity/beauty of string theory but that doesn’t make it a physical theory.
    Soon there will be a book about Boltzmann who anticipated string theory, a book about Wolfram’s NKS which proves the statistical advantages of the landscape…?
    I love you blog, keep writing, you’re my hero.

  9. cynic says:

    ‘As it become harder and harder to get experimental data relevant to the questions we want to answer, the guiding principle of pursuing mathematical beauty becomes more important. It’s quite unfortunate that this kind of pursuit is becoming discredited by string theory, with its claims of seeing “mathematical beauty” when what is really there is mathematical ugliness and scientific failure.’

    In 1930 he wrote:

    ‘The only object of theoretical physics is to calculate results that can be compared with experiment.’

    – Dirac, The Principles of Quantum Mechanics, 1930, page 7.

    But he changed slightly in his later years and on 7 May 1963 Dirac actually told Thomas Kuhn during an interview:

    ‘It is more important to have beauty in one’s equations, than to have them fit experiment.’

    – Dirac, ‘The Evolution of the Physicist’s Picture of Nature’, Scientific American, May 1963, 208, 47

    Other guys stuck to their guns:

    ‘… nature has a simplicity and therefore a great beauty.’

    – Richard P. Feynman (The Character of Physical law, p. 173)

    ‘The beauty in the laws of physics is the fantastic simplicity that they have … What is the ultimate mathematical machinery behind it all? That’s surely the most beautiful of all.’

    – John A. Wheeler (quoted by Paul Buckley and F. David Peat, Glimpsing Reality, 1971, p. 60)

    ‘If nature leads us to mathematical forms of great simplicity and beauty … we cannot help thinking they are true, that they reveal a genuine feature of nature.’

    – Werner Heisenberg (page 2 here)

    ‘A theory is the more impressive the greater the simplicity of its premises is. The more different kinds of things it relates, and the more extended is its area of applicability.’

    – Albert Einstein (in Paul Arthur Schilpp’s Albert Einstein: Autobiographical Notes, p. 31)

    ‘My work always tried to unite the true with the beautiful; but when I had to choose one or the other, I usually chose the beautiful.’

    – Hermann Weyl (page 2 here)

  10. Lowell Brown says:

    I once asked Dirac how he invented the Dirac Equation. He said:

    I found that a times sigma sub x plus b times sigma sub y plus c times sigma sub z — quantity squared — was a squared plus b squared plus c squared, and I marveled at the beauty of this result.

  11. Thomas Larsson says:

    The circle is the most beautiful geometrical shape. Hence planets must move in circles, or in circles around circles.

    A misguided concept of beauty held progress back for 1500 years. Something to ponder when arguing for beauty.

  12. Chris Oakley says:


    This version of WordPress seems to allow you to write that in HTML, or the generalisation:


    I feel a piece about “the square root of the Klein-Gordon equation” coming on. But don’t worry – I’ll put it on my web site and not here.

  13. publius says:

    While it seems clear that Dirac was not seduced by the idea of extra dimensions, as shown by his answer to Ramond, and it also seems to be no evidence of interest from him on string theory during his last years, he was certainly one of the firt researchers (if no the first) to consider fundamental relativistic extended objects in physics, introducing a relativistic brane, motivated partly by the hope to get rid of just those troubling infinities in particle theory. I believe the reference is
    Proc. R. Soc. London A 268(1962)57
    This reference is quite more pertinent than Dirac’s string to make a connection between Dirac and string theory (which possibly Dirac himself would have rejected…) It would be surprising if the author of the book does not mention it.

  14. Chris Oakley says:

    Forget that – it did the <sub>…</sub> in the preview, but not in the final result.

  15. Peter Woit says:


    Farmelo does mention the 1962 paper in this context. In it Dirac was trying to interpret the electron as a charged conducting surface, with the muon an excited state. The connection to current ideas about branes seems rather slim….

  16. none says:

    The Dirac-Born-Infeld action, a nonlinear modification of the Maxwell action, shows up in string theory as part of the effective action for a D-brane.

  17. Carl says:


    the smarter physicists used “beauty” in physics to mean “simplicity” (see the citations above) which is the real thing to achieve. Beauty is maybe misguided, simplicity is not. Over the years, the description of physics has become simpler and simpler. Maybe also more beautiful, but most of all, simpler.

  18. dir says:

    mentioning infinities in qft, i once read a small book by yukawa who also tried to use extended objects to replace point-particles. maybe this trend had an influence to japanese theoretical physicists, including nambu?

  19. davetweed says:

    With regards to Chris Oakley’s comments, it is rather strange that people insist on ascribing medical conditions to people where they cannot possibly know enough details to make a meaningful medical diagnosis, rejecting the idea that many people can be weird without some having some medical condition to explain it. (Autism is a relatively precise medical diagnosis, and someone not acting with the general societal level of gregariousness and following of social conventions doesn’t automatically imply they have some degree of autism.)

    Note that I’m not arguing either that Dirac would or wouldn’t have been diagnosed as autistic by a specialist had he been examined by one, but rather about the cavalier “well those anecdotes sound vaguely like they fit with autism, so he must have been mildly autistic” approach.

  20. D R Lunsford says:

    I have to disagree as well that Dirac was spent in the 30s. “Forms..” as mentioned is an extremely important work. His book on GR remains the most concise exposition imaginable. His attempts to rid classical EM of inconsistencies were heroically motivated and fascinating to follow. The LNH remains an extraordinary idea. He was the first person to rigorously explore anti-deSitter space (early 60s) (“A Remarkable Representation of the 3+2 deSitter Group”). Very late in life he was working on infinite dimensional representations of the Lorentz group. Like Beethoven, he knew only one direction, forward.

    I agree that connecting the “Dirac string” as it came to be called with string theory, is analogous to connecting General Relativity with General DeGaulle.


  21. D R Lunsford says:

    T R Love,

    This work behind this article in Nature was no doubt his “New Classical Theory of Electrons” which appeared in the Royal Society Proceedings in three papers – early 50s. Basically he posited an equation of state such that the current was proportional to the potential,

    J = -k A

    so one has a sort of superconducting vacuum in the London sense. It’s an extremely interesting series if only as a demonstration of how to think physically, and how intractable is the problem of the electric charge.


  22. Thomas Larsson says:


    A circle is simpler than an ellipse. Thus Ptolemy was right. And since we remember him after 2000 years, I bet he was really smart, too 🙂

    The problem with simplicity or beauty is that it lies in the eyes of the beholder. Beauty is an important motivation and inspiration, but eventually it must be up to experiments to decide whether Nature agrees with your subjective notion of beauty. E.g., it really doesn’t matter how fearful a symmetry that SUSY might be; if the Tevatron finds no light Higgs and the LHC finds no sparticles, SUSY is dead nontheless.

    One of my favorite models is the CFT with c = 1/2, which describes the 2D Ising model at criticality. It consists of three fields, belonging to three separate Virasoro representations (with h = 0, 1/16 and 1/2). This model is thus not unified in the sense that all fields belong to the same multiplet of the relevant symmetry, but it is unified in the weaker sense that the representations are connected by fusion rules. If this is the way that things will work out in Nature (and it does for the 2D Ising model), then the idea of GUTS (putting everything in the same multiplet) may be fundamentally misguided. And so may SUSY, since fusion rules of a purely bosonic symmetry can connect both bosonic and fermionic fields.

  23. Greg Sivco says:

    Dirac was the way he was because of an extremely strict father. Read the Wiki entry and it explains that precisely. I look forward to reading the book, P.A.M. Dirac is one of our all-time favorites. The list of his accomplishments (right hand side, Wiki again) is so amazingly large. Is there anyone who did more? I often debate with myself if either he or Max Born loved Mathematics more. Shrug, I’ll never know, but they’re up there amongst the Early Titans of 20th Century Physics.

    Thank you, Peter for your excellent review, we have been looking forward to this book for a long time, and I will most assuredly skip the last “string section” on purpose. That New Scientist article is depressing enough … I see no reason to add to the masochism. 🙂

  24. Carl says:


    beauty might lie in the eye of the beholder, simplicity does not.
    The inverse square law is simpler than epicircles.

    A single QED Feynman diagram is simpler than Maxwell’s equations.

    The issue now is how to continue this…


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  27. Georges Melki says:

    I would like to add to the list of quotes by Cynic regarding the importance Dirac assigned to the “beauty” of a physical theory. My quote is taken from a very good book :”Paul Dirac-The Man and his Work”, Peter Goddard,Ed.(Cambridge UP), page 89:
    “In 1977, he explained his attitude in a particularly vivid way when describing his affinity with Erwin Schrœdinger(with whom he shared the Nobel Prize:
    …Schrœdinger and I both had a very strong appreciation of mathematical beauty, and this appreciation of mathematical beauty dominated all our work.It was a sort of act of faith with us that any equations which describe fundamental laws of Nature must have great mathematical beauty in them. It was like a religion with us. It was a very profitable religion to hold, and can be considered the basis of all our success.
    It has to be admitted that in most hands and at some times in the development of science this approach can be dangerous.”
    I believe this to be as clear and concise as possible…
    On the other hand Peter, I prefer your review of the book to that of the New York Times!

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