The Remarkable Lady J

Life Fellow Ruth Williams recalls the eminent Girton mathematician Bertha Jeffreys

In 1903 in Northampton, a couple with the unusual surname of Swirles, but otherwise quite ordinary, had a baby daughter whom they called Bertha. Little did they suspect that her life would be far from ordinary and that she would be involved in one of the most important scientific revolutions of the twentieth century. Her father, a leather salesman, died while she was still a toddler. Her mother was a schoolteacher, as were seven of her nine aunts, which perhaps gives a hint of her future path. A photograph of her in her pram wearing glasses makes her look suitably studious.

Her mother taught at Bertha’s primary school and her Aunt Bertha was headmistress. She escaped from the family’s clutches when she moved to the newly-established Northampton School for Girls, where she was taught mathematics by three Cambridge women graduates. Her mother subscribed to Scientific American for her and, looking back at that time, she wrote ‘As I was brought up almost entirely by women, it did not occur to me that there was anything strange in wanting to become a mathematician or physicist.’ It was no great surprise when she was awarded a scholarship at Girton to read mathematics.

Bertha and Harold in their garden at 160 Huntingdon Road, after apple picking, in 1984 (Girton College Archive GCPH 6/2/94/5)

John Davies

Bertha flourished in Cambridge, and found time to play the organ as well as the piano. At that time the Girton organ was hand-blown and she had to bribe one of her friends to blow it for her. She graduated with a first in 1924, then spent the next year reading Part II Physics. The practical classes were rather disastrous as she was quite clumsy, perhaps feeling conspicuous as the only woman in the class, and her practical notebook was never the same after she, her bicycle and it ended up in a ditch on the way back to Girton one evening.

What she read about the Bohr theory of atomic spectra caught Bertha’s imagination, and, having found financial support for research from Girton and a government grant, she was sent to see the distinguished physicist and Nobel laureate (in chemistry) Rutherford, who said ‘They tell me that you are not much good at experiments; you had better go and see Fowler.’ In 1925 she did indeed become a research student of Fowler, joining a distinguished company of students that included Nobel prize winners such as Dirac and Chandrasekhar. Soon she became involved in research in the new and very exciting field of quantum mechanics, which describes the properties of matter at the very smallest scale, and is the basis for much of what we now take for granted, like televisions, computers and mobile phones. Bertha encountered many eminent visitors from abroad, but it was difficult to meet and talk informally with them and with other students as the relevant societies, which met in the evenings, were not open to women.

In contrast, when she spent the winter of 1927–28 in Germany, at Göttingen, the epicentre of the new theory, she interacted with many of its originators, like Born and Heisenberg, from whom she would have learned about the uncertainty inherent in the theory. Its fundamental entity, the wave function, encodes the probability of observing the system in a particular state. Furthermore, knowing the position of a particle very accurately necessarily limits how accurately its speed can be known, and vice versa. It was not just over physics that Bertha spent time with the researchers: as one of the few women in those circles, she played a pivotal role in dancing classes for physicists.

After completing her PhD in 1929, Bertha moved to Manchester as an Assistant Lecturer. It was here that she did some of her most innovative research; she worked on extending calculations of electron interactions to the relativistic case, which was necessary since tiny particles can move very fast, with speeds near that of light. She also included superpositions of wave functions, a crucial conceptual development in quantum mechanics. An example of superposition is the famous thought experiment of Schrödinger’s cat. In a quantum mechanical world, the cat exists in a mixture or superposition of states of being alive or dead, and only when the cat is observed does it jump into a definite state of life or death. The calculational methods Bertha was instrumental in developing have led to tabulations of wave functions for many multi-electron atoms, and these tables are still used today by atomic physicists and theoretical chemists.

Appointments followed at Bristol and at Imperial College, London, then after a further spell at Manchester, Bertha returned to Cambridge in 1938 to an Official Fellowship and Lectureship in Mathematics at Girton. She was to remain here for the rest of her career and taught many generations of women mathematics students, who have gone on to propagate her influence to ever-widening circles.

Bertha was a gifted musician and played the cello in the CUMS orchestra. Amongst the tenors in the CUMS chorus was Harold Jeffreys, a distinguished mathematician and geophysicist, a Fellow of St John’s. They had met earlier at a conference, and, chatting after rehearsals, they cemented their friendship and eventually married in 1940. (She was heard to say ‘It took a war to get us together!’) Harold was knighted in 1953 for services to science and Bertha became Lady Jeffreys or Lady J as she was known affectionately by her students.

After marriage, Bertha continued her research in quantum theory but for a while her major focus was on writing a book with Harold. Methods of Mathematical Physics, first published in 1946, is an extremely comprehensive account of the techniques which form the essential mathematical equipment of a theoretical physicist or applied mathematician. It is written in a very clear and scholarly way, with the innovation that, at the start of each chapter, there are appropriate and amusing quotations taken from sources ranging from Ibsen to Lewis Carroll. The authors were making the point that studying mathematical methods can be fun. The book has instructed generations of students and is still a recommended text at universities all over the world.

When not involved in academic work, Bertha could often be found selecting birthday gifts for the children and grandchildren of her former students, or indulging her passion for music. She had kept up her piano playing and in her nineties still played piano duets with a nonagenarian friend. She was still writing letters to colleagues who, when they saw her handwriting on a re-used envelope, realised with dismay that there must be another mistake in their book or paper. Bertha was an avid re-cycler before it was fashionable: she always wrote on the back of old examination scripts in supervisions.

Bertha’s mother and one of her aunts had lived in the Jeffreys household in their nineties, and she was determined to live longer than they had, although not bothered about living longer than Harold who had died in 1989 aged 98. She was also very sure that she did not want to see in the Millennium, with the predictions of cataclysmic (but eventually unrealised) events. She was not one to be defeated, and succeeded on both counts, dying of natural causes at the age of 96 in December 1999. Hers was a remarkable life of innovation in research in a field where there were very few women, and in teaching, stretching over almost the entire twentieth century. Formidable but warm and approachable, she was a memorable Girton figure.

Some of the many editions of Methods of Mathematical Physics

John Davies