Born in 1900, Wolfgang Pauli’s debut as a physicist came in 1921 with the publication of a review paper on relativity so thorough and incisive that Einstein wrote of it “No one studying this mature, grandly conceived work would believe the author is a man of twenty-one”. Three years later, Pauli formulated the exclusion principle that bears his name, and that forms the basis of atomic and molecular structure; this work earned him the 1945 Nobel Prize for Physics. In 1930 he introduced the concept of the neutrino, which is central to modern elementary particle physics. By then, he had already become the key arbiter in the year-long discussions held in Copenhagen between Werner Heisenberg and Niels Bohr that had led to the modern formulation of quantum mechanics. He was also the holder of a prestigious professorship in Zurich, Switzerland, where young physicists from around the world – including Felix Bloch, Max Delbruck, Lev Landau, J Robert Oppenheimer, Rudolf Peierls and Victor Weisskopf – were flocking to work with him. Hence, by the age of just 30, Pauli had already established himself as one of the 20th century’s great physicists.

And yet all was far from well. Although Pauli continued to flourish professionally, his personal life was a shambles. His father, a talented scientist but also a womanizer, had fallen in love with a sculptor who was Pauli’s age and had left his wife, Pauli’s mother. In a fit of despondency, she committed suicide in November 1927. Pauli – never a picture of health and athleticism – began drinking and smoking more heavily. He had always been a night owl, a frequenter of bars and cabarets, and these tendencies also increased. In 1929 he married a dancer, but their union lasted less than a year; his wife left him for another man.

In crisis, Pauli decided to consult a psychiatrist. In 1930s Zurich the obvious choice was Carl Gustav Jung, a pioneer in psychiatry and its broad ramifications in other areas, including religion and mythology. What happened next is the subject of Arthur I Miller’s Deciphering the Cosmic Number, which charts the unexpected friendship that developed between the troubled young physicist and the eminent psychiatrist.

The Pauli–Jung friendship is an ideal subject for Miller, who trained as a physicist but has had a long-time interest in the boundary between science and art, particularly in imagery and questions of creativity. He has explored these topics in previous works, including a joint study of Einstein and Picasso. In this book, he first introduces Pauli, then Jung before beginning to weave their story together. He focuses in particular on Jung’s analysis of Pauli’s dreams – several of which Jung later published along with their interpretation, but without identifying their source other than as “a distinguished scientist”. It makes for a fascinating and an unlikely story, one that Miller follows exceedingly well through its twists and turns. His style is both brisk and accessible, making the book exciting to read as well as informative.

In 1930 Jung had already become an icon in 20th-century intellectual thought. Some 25 years older than Pauli, he placed great emphasis on integrating the analytical, scientific mind with the emotional and the unconscious self. He wrote voluminously, but also had an extended clinical practice. Though interested in Pauli’s condition, he initially felt that his new patient’s analysis would be more successful if he did not carry it out himself. Instead he directed Pauli to Erna Rosenbaum, a young woman whom Jung had trained, feeling that her presence would not threaten or intimidate Pauli in any way. She would act as a conduit, encouraging Pauli to record his dreams and free his unconscious.

Two years later, Pauli began consulting Jung directly, gradually forming an association that had elements of simple friendship and collaboration in addition to the expected doctor–patient relationship. By 1934 Pauli felt himself cured of his neurosis. He remarried, this time happily. His scientific productivity continued unabated, but he seldom mentioned his explorations of the unconscious to his colleagues, although such topics continued to interest him. Indeed, the connection between Pauli and Jung lasted for nearly 25 years, ending only with Pauli’s early death from cancer in 1958. During this period, Pauli sent Jung more than a thousand dreams, transcribed for his own benefit and for Jung to study. The two also carried on a voluminous correspondence, much of which has been published; see, for example, C A Meier’s Atom and Archetype: The Pauli–Jung Letters (1992, Princeton University Press).

The relationship clearly stretched both men and must have been strained at times. Jung’s pursuits of phenomena such as extrasensory perception, unidentified flying objects and astrology were not to Pauli’s liking. However, their bond continued unabated, focusing on issues such as synchronicity and the potential deeper meaning of numbers. In exploring such issues, Pauli also began to study the works of Kepler and his contemporaries, looking for the origins of the so-called scientific mind and what may have been lost in its adaptation to a modern world – both topics of great interest to Jung.

In exploring all these aspects of Pauli and Jung’s relationship, this book also includes a number of visual illustrations that clarify the questions being discussed. Among the most interesting of these are a series of drawings that represent graphic interpretations of important Pauli dreams. The book concludes with a chapter on Pauli and Jung’s interest in the significance of the fine-structure constant, which specifies the coupling of charged particles to the electromagnetic field. Was it really equal to 1/137 and, if so, what did that mean? Was there some deep explanation for that value? As of 2009 the answer is no; the latest value for the inverse of the fine-structure constant is 137.035999070. Nevertheless, the ideas of both Pauli and Jung remain very much part of our intellectual heritage, even if they do not apply to the fine-structure constant as we understand it today. The interaction between the two men, very well told in this book, remains one of the 20th century’s most interesting links between two thinkers who were apparently so different.