September 12, 1894 - February 11, 1976

Dorothy Wrinch was a mathematician who made contributions to the areas of mathematics, philosophy, physics, and biochemistry. She was born in Rosario, Argentina, where her British parents were temporarily located while her father, an engineer, worked for a British firm. Dorothy was raised in England, and in 1913 began her studies in mathematics and philosophy at Girton College, Cambridge University. She was the only Girton woman Wrangler in the Mathematical Tripos in 1916, earning a First Class degree. In 1917 she took Part II of the Moral Sciences (Philosophy) Tripos so that she could study symbolic logic with Bertrand Russell whom she had met during her first year. She remained at Girton as a research scholar during the academic year 1917-1918, continuing to correspond with Russell who had moved to London. In 1918 she won Girton's prestigious Gamble Prize (given to distinguished alumnae) for her work on transfinite numbers. The prize had been awarded to Grace Chisholm Young three years earlier.

In 1918 Wrinch began teaching algebra, trigonometry, calculus, and solid geometry to first- and second-year mathematical honor students at University College, London. While teaching at University College she also earned M.S. (1920) and D.Sc. degrees (1922). She returned to Girton College in 1921 with a research fellowship. The next year she married John William Nicholson, the director of studies in mathematics and physics at Oxford College. Wrinch remained at Cambridge during the first year of their marriage, but in 1923 she moved to Oxford to become a part-time mathematics tutor and lecturer at one of Oxford's women college, Lady Margaret Hall. She also gave lectures at the other women's colleges on a per-term basis. Her status changed in 1927, however, when she received a three-year appointment from Lady Margaret Hall as a lecturer in mathematics. She also became the first woman to qualify for a university lectureship in mathematics at Oxford which meant that her lectures were open to male students.

Russell's influence had led Wrinch towards a mathematical interest in logic and epistemology, but neither of these subjects were popular among the general population of English mathematicians and philosophers, especially after Russell abandoned his academic pursuits in 1921. By 1929 she had published 42 papers in pure mathematics, mathematical physics, and philosophy of science, including six papers in probability theory and the theory of the scientific method written with Harold Jeffreys between 1919 and 1923. One of Wrinch's early papers in 1923 covered the topic of mediate cardinals from Russell's *Principia Mathematica* [Abstract]. Wrinch wrote two papers with her husband, including a 1925 paper on Laplace's equation and surfaces of revolution [Abstract]. An example of one of her papers in complex analysis is the 1928 paper on the asymptotic evaluation of functions defined by contour integrals [Abstract]. Fifteen of her papers were submitted in 1929 as a basis for a D.Sc. degree from Oxford, the first such degree to be awarded to a woman by that university. All of her papers were published under her maiden name. As Abir-Am writes, "Her insistence on her own professional identity stemmed both from her Girton education, which promoted female scholarly independence, and from the socialist and feminist beliefs she had absorbed in Russell's circles" [1].

Wrinch and Nicholson had a daughter in 1928. By 1930, however, her husband's excessive drinking had caused a nervous breakdown and the two separated that year (the marriage was dissolved in 1938). Wrinch also published a book in 1930, using the pseudonym of Jean Ayling, called *The Retreat from Parenthood* that tried to illustrate the difficulties of professional women in combining careers with parenthood, using examples no doubt based on her own life and those of her friends. Her utopian ideals of childcare stressed the need for professional women to have freedom from both domestic and financial anxieties through the establishment of Child Rearing Services.

In 1931 Wrinch began shifting her research focus to molecular biology. With a leave from Oxford and with the help of several research fellowships, she spent the years 1931 to 1934 in Vienna, Paris, London, and Berlin, visiting various universities and laboratories and studying the biological applications of the mathematical theory of potential theory in explaining the mechanics of chromosomes and the structure of proteins. During the summer of 1932 she became a founding member of the Theoretical Biology Club, a group of scientists who shared the vision that philosophy, mathematics, physics, chemistry and biology could all contribute to the understanding and investigation of the complexity of living organisms. She published her first paper on proteins, "Chromosome behavior in terms of protein pattern," in *Nature* in 1934. In 1935 Wrinch received a five-year research fellowship from the Rockefeller Foundation to support her work in mathematical applications to biological problems. It was during this time that she developed her controversial model of the structure of proteins. She presented the first architectural plan of protein molecules at the 1937 meeting of the British Association for the Advancement of Science. Abir-Am describes her theory [2]:

This theory combined certain ideas of mathematical symmetry with the notion of a relatively rare type of chemical bond, called the cyclol bond. It suggested that the two-dimensional cyclol bond was the main link between the proteins' building blocks, the amino acids. In Wrinch's theory, the spatial structure of proteins (known to be the source of their functional versatility) was built of fabrics instead of the chains that then current chemical theory assumed to exist on the basis of inferences from the results of analytic protein chemistry.

Wrinch's theory, promoted in part by a lecturing tour in the United States in 1937, created great interest among those scientists concerned with the molecular viewpoint of proteins as it could explain qualitatively much of what was currently known about the behavior of proteins. Niels Bohr wrote in 1939: "Dr. Wrinch's work is indeed a most striking illustration of the fruitfulness of the application of mathematical argumentation to problems of natural science" [8]. The New York Times reported on her talk at the spring 1940 meeting of the American Philosophical Society:

Dr. Wrinch presented a model of the building blocks of living things in the form of a hollow cage, a truncated tetrahedron in shape.The metal model, two four-sided pyramids base to base, was stamped with holes showing the fundamental hexagonal ring structure of proteins. The patterns, running over the surface of the cage, comprised many of these six-sided rings, all interconnected.

Dr. Wrinch took diagrams of the structures of related chemical and biological substances and fitted them into the "template" of living matter; that is, the geometric surface pattern of the atoms in her ultimate life unit. These included the sterobs, from which bile acids can be built up; hormones, vitamins, cancer-causing substances and heart-stimulating drugs.

Offering an explanation of how viruses reproduce, she said that a protein unit gave birth to another by having a second layer form on its surface in exactly the same pattern, with the first splitting and flattening.

Although protein cages are "hollow" they are filled with substances the nature of which, it was stated, might determine differences between proteins which are similar in their molecular structure.

Wrinch's cyclol bond theory also came under attack, however, by a group of British protein X-ray crystallographers who argued that her model was not supported by X-ray data, despite her claims to the contrary. In the United States, Linus Pauling calculated that the cyclol bond was too thermodynamically unstable to exist in nature or the laboratory, leading to an ongoing confrontation between the two strong-willed scientists carried out publicly and in the pages of the *Journal of the American Chemical Society*. The dispute even led Wrinch's 13-year old daughter, Pamela, to write to Pauling complaining that "Your attacks on my mother have been made rather too frequently. If you both think each other is wrong, it is best to prove it instead of writing disagreeable things about each other in papers. I think it would be best to have it out and see which one of you is really right" [7]. Actually, in the end, neither were. Pauling's claims and calculations were refuted in 1952 when the cyclol bond was indeed discovered by a Swiss chemist in the ergot (a parasitic fungus) alkaloids. By that time, however, improved experimental techniques had led most scientists to believe proteins did not have the cyclol structure and molecular biologists had shifted their attention to the study of DNA rather than proteins as the "secret of life." Nevertheless, Wrinch's hypothesis produced so much interest in the structure of proteins that biologists eventually discovered over 100 such structures by 1980.

Partially because of Pauling's attacks, Wrinch had a difficult time finding a full-time position after emigrating to America in 1939. After a one-year visiting position in the chemistry department at Johns Hopkins University where she taught a course on the mathematics connected with organic structural chemistry, she accepted in 1941 a joint visiting research professorship at Amherst, Smith, and Mount Holyoke Colleges. This arrangement was engineered by Otto Glaser, a biologist and vice-president of Amherst College, who had been corresponding with Wrinch for three years and was a strong supporter of her cyclol theory. The two married that same year in the unusual setting of the Marine Biological Laboratory at Woods Hole, Massachusetts. An announcement of the wedding in the New York Times mentioned that "her work on protein molecules started a controversy among the leading chemists, physicists and biologists of this country and Europe." The next year she was appointed as a special research professor of physics at Smith College where she worked with graduate students, lectured, and continued her research. She and her husband spent their summers at Woods Hole. Wrinch became an United States citizen in 1943. Upon her husband's death in February 1951 she moved to a residence on the Smith College campus, remaining at Smith until her retirement in 1971.

Wrinch's research during the 1940s focused on mathematical techniques for interpreting X-ray data of complicated crystal structures. The basic steps in finding a structure of proteins by X-ray crystallography are to form a high quality crystal from a sample
of protein, place the crystal in an X-ray beam and measure the
intensities of the diffraction spots, then compute the structure from the diffraction intensities using Fourier analysis. In 1946 Wrinch published a monograph on *Fourier Transforms and Structure Factors* that was an important contribution to this use of Fourier series in representing and determining the periodic structure of crystals. When the cyclol bond was found in nature and then synthesized in a laboratory during the 1950s, Wrinch felt vindicated and spent much of her remaining professional life working on her mathematical theory of protein structure. Her two books, *Chemical Aspects of the Structure of Small Peptides, An Introduction* published in 1960, and the sequel, *Chemical Aspects of Polypeptide Chain Structures and the Cyclol Theory* published in 1965, were meant to be the culmination of her thirty years of developing and defending her study of proteins. Wrinch's list of publications eventually included 192 papers and books. A complete bibliography is given in [7]. In the same volume, Carolyn Cohen, professor of biology at Brandeis University, describes Wrinch's influence in molecular biology:

...Dorothy Wrinch began her creative work as a mathematician and philosopher, and in the 1930s turned her attention to Biology. She became a member of a small remarkable group at Cambridge University—the Theoretical Biology Club. Joseph Needham's classic book,Order and Life(1936), was, to a large extent, generated form their discussions. It is dedicated to members of that club; among them are J.D. Bernal, J.H. Woodger, C.H. Waddington; Dorothy Needham and Dorothy Wrinch. The full story of this group is not yet known, but they were primarily concerned with the analysis of biological form–both its philosophical and physical basis. And their common belief was in the vital importance of proteins as the key structures in Biology. Dorothy Wrinch's life's work centered on this problem, and she influenced many, including Joseph Needham in England and, in America, Ross Harrison, the great embryologist at Yale, and Irving Langmuir, the physical chemist. I believe that her influence has been vastly underestimated.

Wrinch moved to Woods Hole after her retirement from Smith in 1971. Her daughter, Pamela, had become one of the first women to earn a Ph.D. in international relations when she received her degree from Yale University in 1954. Pamela died tragically in a fire in November 1975. Dorothy Wrinch died 10 weeks later. In [7], Marjorie Senechal writes:

During her years with us [at Smith], she was an inspired teacher, a severe critic, an example of dedication and courage. We will always be grateful to her for the guidance and encouragement she showed to students and junior colleagues, and for the uncompromisingly high standards she set for herself and for others. We share her concern that the great questions of science be studied in their whole as well as in their parts.

- Abir-Am, Phina G. "Synergy or Clash: Disciplinary and Marital Strategies in the Career of Mathematical Biologist Dorothy Wrinch," in
*Uneasy Careers and Intimate Lives: Women in Science 1789-1979*, Phina G. Abir-Am and Dorinda Outram, Editors, Rutgers University Press, 1987, 239-280. - Abir-Am, Phina G. "Dorothy Maud Wrinch (1894-1976)," in
*Women in Chemistry and Physics: A Biobibliographic Sourcebook*, edited by Louise S. Grinstein, Rose K. Rose, and Miriam H. Rafailovich, Greenwood Press, 1993, 605-612. - Carey, Charles W. "Dorothy Maud Wrinch," in
*American National Biography*, Vol. 24, Oxford University Press, 1999, 69-71. - "Dorothy Maud Wrinch".
*A to Z of Women in Science and Math*, Lisa Yount (Editor), Facts on File, Inc., 1999. - Julian, Maureen M. "Women in Crystallography," in
*Women of Science-Righting the Record*, G. Kass-Simon and Patricia Farnes, Editors, Indiana University Press, 1990, 364-368. - Hodgkin, Dorothy Crowfoot and Harold Jeffreys. "Obituary - Dorothy Wrinch," Nature, Vol. 260 (April 8, 1976), 564.
*Structures of Matter and Patterns in Science, inspired by the work and life of Dorothy Wrinch, 1894-1976*," The Proceedings of a Symposium held at Smith College, Northampton, Massachusetts September 28-30, 1977, and Selected papers of Dorothy Wrinch, from the Sophia Smith Collection. Marjorie Senechal, editor. Schenkman Publishing Company, 1980.- Senechal, Marjorie. "A Prophet without Honor: Dorothy Wrinch, Scientist, 1894-1976," Smith Alumnae Quarterly, Vol. 68 (1977), 18-23.
- Senechal, Marjorie. "Hardy as Mentor," Mathematical Intelligencer, Vol. 29, No. 1 (2007), 16-23. Describes the time from when Wrinch entered Girton College through her early years as a professional mathematician, and the role G. H. Hardy played as her mentor.
- Howie, David.
*Interpreting Probability, Controversies and Developments in the Early Twentieth Century,*Cambridge University Press, 2002. [Contains a description of Dorothy Wrinch's work with Harold Jeffries in probability theory and the scientific method.] - "Protein Units Put in Graphic 'Cage'," New York Times, April 19, 1940, p14.
- "Dr. O. C. Glaser Weds Dr. Dorothy Wrinch," New York Times, August 21, 1941, p20.
- "Waffle-Iron Theory of Proteins," New York Times, February 2, 1947, pE9.
- Obituary, New York Times, February 15, 1976, p67.
- Author Profile at zbMath
- Biography at the MacTutor History of Mathematics Archive.

Note: The papers, letters, diaries, and notebooks of Dorothy Wrinch are part of the Sophia Smith Collection at Smith College.