# Dorothy Maud Wrinch

### Quick Info

Born
12 September 1894
Rosario, Argentina
Died
11 February 1976
Falmouth, Massachusetts, USA

Summary
Dorothy Maud Wrinch was an Argentinian-English-American mathematician and biochemist famous for her use of mathematical techniques to deduce protein structure.

### Biography

Dorothy Wrinch's parents were Ada Minnie Souter (1867-1933) and Hugh Edward Hart Wrinch (1866-1934), who was an engineer. Although Dorothy was born in Argentina, Ada and Hugh were British and they returned to Surbiton, which is 19 km southwest of central London, where Dorothy was brought up. Let us give some details of Dorothy's parents to understand how she came to be born in Argentina.

Hugh Wrinch was born in Woodbridge, Suffolk, attended Woodbridge Grammar School, then worked for the firm of Whitmore & Binyon who made steam engines and mills of all different types. He showed considerable abilities and in 1890 he decided to go abroad to take a leading position in an engineering firm. There was much British investment in railways and water works in Argentina so he decided to go there. He was soon the pumping manager in the Consolidated Water Works Company in Rosario, Argentina. When he went to Argentina in 1890 he had a fiancé, Ada Minnie Souter, who had been born in Harleston, Norfolk. Ada's father was a station master for the Great Eastern Railway, and the family lived in a number of different towns as she was growing up. She became a school teacher and then headmistress before deciding to travel alone to Argentina to meet up with Hugh; she arrived in September 1893. They were married in St Bartholomew's Anglican Church in Rosario on 11 November 1893 and their first child, Dorothy Wrinch, the subject of this biography, was born in the following year.

Rosario benefitted greatly from Hugh Wrinch's work in heading a project to provide running water to the houses of the town. The Consolidated Water Works Company showed their appreciation for his excellent work but, for health reasons which are rather unclear, he decided to return to England in 1897. He quickly got a job with the Chelsea Waterworks Company and the family lived at 1 Milford Place, Maple Road, Surbiton. On 14 July 1899 Dorothy's sister, Muriel Louise Wrinch, was born.

Dorothy Wrinch began her education at Surbiton High School in January 1899. The school was run by Alice Procter assisted by her sister Zoë Procter. Wrinch gained certificates in History, English, Mechanics, French, Latin, Mathematics (elementary) and Mathematics (advanced). She wanted to learn more mathematics than the school could provide, so she attended mathematics courses at the University of London. She won a scholarship to attend Girton College, Cambridge University, and was accepted for entry in 1912. She decided, however, to defer entry for a year and matriculated at Girton in 1913. There she studied mathematics and philosophy, in particular studying the Mathematical Tripos. In her first year she joined the Musical Society, the Mathematical Club, and the Society for the Study of Little-Known Literature. She also played tennis for the Girton College team. She took the examinations for Part I of the Mathematical Tripos in 1914 after one year at Cambridge. Many students took two years before taking these examinations and Wrinch might have been better to have followed that route. She was graded Second Class in the examinations, something which greatly disappointed her. She determined to do better in Part II, and was now advised by Neville Watson.

She was much influenced by Bertrand Russell's work and she studied this on her own, sometimes corresponding with Russell who had been appointed as a lecturer at Cambridge three years before Wrinch began to study there. Also at Cambridge she attended lectures by William Ernest Johnson on logic. She took Part II of the Mathematical Tripos and graduated in 1916 as a Wrangler, meaning that she had achieved a First Class degree [22]:-
Dot Wrinch was Girton's only Wrangler in 1916. The 'Manchester Guardian' published the names of all the Wranglers, hers included, but biographies only of the men.
Russell's ideas on mathematical logic were a major influence on Wrinch and she also strongly supported his anti-war beliefs. In June 1916 Wrinch met Russell for the first time. She was looking for a scholarship to allow her to undertake research on mathematical logic. Russell agreed to advise her, she arranged a part-time job to support herself and Girton College awarded her a scholarship to study the Moral Sciences Tripos. These plans, however, all fell apart almost immediately since Russell's lectureship was cancelled because of his anti-war stance. All was not lost since he invited Wrinch and three other students to study privately with him in London. After a while G H Hardy agreed to become Wrinch's official research supervisor, although Russell would continue to unofficially advise her, and Hardy persuaded Girton College to award Wrinch a stipend to cover her expenses for a year of research. In 1917 she published three papers: Mr Russell's Lowell Lectures in Mind, Bernard Bolzano (1781-1848) in The Monist, and On the summation of pleasures in the Proceedings of the Aristotelian Society.

For more information on these papers and other papers published by Wrinch between 1917 and 1927, see THIS LINK.

In 1917 Wrinch also wrote the essay Transfinite types which was considered for Girton College's Gamble Prize. Russell wrote to Girton in March 1918:-
Miss Wrinch's notes consist in the main of an interesting development of certain ideas suggested by Hausdorff. They deal with the investigation of series constructed by the 'principle of first differences.' There are a number of new results, and the method employed is obviously a fruitful one, giving possibilities of very important theorems. it points the way to a whole field of new research.
Two months after writing this recommendation, Russell was in Brixton prison beginning a six-month sentence for an anti-war leaflet he had written. Wrinch was awarded the Gamble Prize. She remained at Cambridge undertaking research in mathematics until 1918 when she moved to University College in London. She lectured in mathematics at University College while working for her M.Sc. and then D.Sc. in mathematics advised by John Nicholson (1881-1955). The master's degree was awarded in 1920, the year in which she returned to Girton to take up the Yarrow Research Fellowship in mathematics; this funded her for the next four years. She was awarded her D.Sc. by University College while undertaking research at Girton.

During this time, as well as undertaking research for her doctorate, Wrinch was working closely with Harold Jeffreys. They [22]:-
... were constant companions, writing papers together, singing in the Philharmonic Chorus, and planning - with a small group of Cambridge scientists - the post-war organisation that became the National Union of Scientific Workers. [Wrinch's] name appears next to Harold's in a guest list for a reception for Einstein. Harold grew close to the Wrinch family; his photographs are the only ones we have of them in those years. Not surprisingly, some observers thought they were engaged.
Three joint papers they wrote on probability over these years were On Some Aspects of the Theory of Probability (1919), On Certain Fundamental Principles of Scientific Inquiry (1921) and On Certain Fundamental Principles of Scientific Inquiry (1923). In their views of probability they were influenced by William Ernest Johnson, whose lectures Wrinch had attended, and John Maynard Keynes. For more information about these papers, see THIS LINK.

Jeffreys continued to work on these topics and always acknowledged that it was built on his joint work with Wrinch. For example, you can see the Preface to Jeffreys' book Scientific Inference (1931) at THIS LINK.

Also while working for her doctorate, in 1921 Wrinch joined the British Committee on Mathematical Tables. Some of the work she carried out for the Committee was done in collaboration with her father Hugh E H Wrinch. Some papers in this areas are: (with Hugh E H Wrinch), Tables of the Bessel function $I_{n}(x)$ (1923), Some approximations to hypergeometric functions (1923), (with Hugh E H Wrinch), Tables of Bessel functions (1924), (with Hugh E H Wrinch), The roots of hypergeometric functions with a numerator and four denominators (1926).

On 1 August 1922 she married John William Nicholson in St Mark's Church, Surbiton. John Nicholson was the director of mathematics and physics at Balliol College, Oxford and had been her thesis advisor; they had one child, a daughter Pamela born on 20 March 1927 in Oxford. After her marriage Wrinch moved to Oxford where she taught mathematics at different women's colleges. In 1927 she was appointed as a lecturer at Lady Margaret Hall, Oxford. Despite already having an M.Sc. and a D.Sc. from London, she worked at Oxford for these degrees again, and was awarded her second M.Sc. in 1924 and her second D.Sc. in 1929. This was the first Oxford award of a D.Sc. to a woman.

A measure of her research activity during this period is that from 1918 to 1932 Wrinch published twenty papers on pure and applied mathematics, and sixteen papers on scientific methodology and the philosophy of science. In addition she published a large number of reviews of books and also eight papers giving overviews of ongoing work in pure mathematics, applied mathematics and logic. Sadly Wrinch's marriage became a difficult one as her husband turned increasingly towards alcohol. By 1930 things reached such a state that Wrinch and her husband separated and she brought up their child Pamela. In the same year she published the book The Retreat from Parenthood which appeared under the pseudonym "Jean Ayling." She writes in the Preface:-
In the earlier pages of this book, the author has permitted herself the liberty of making an exposé of certain typical "happy" homes of England. These private places, though an unexpectedly rich mine of information with regard to present-day ideas and tendencies, and an undoubtedly intriguing subject to the anthropologists of to-day and the historian of to-morrow, were not the prime objective. They presented themselves for investigation in answer to a question which faces the student of current events: Why is it that, during the last twenty or thirty years, doctors and lawyers, scientists and civil servants, engineers and educationalists, artists and architects, and all the rest of the men and women who earn their living in professional fields, have so severely curtailed their fertility?
In the book, she argued for a Child Rearing Service and wrote that:-
... children's interests are seriously damaged by the fact that so many women are presented with the choice between career and cradle; and that the insistence on a sterility qualification for women who undertake professional work is as prejudicial as the insistence on whole-time motherhood for those that breed.
Between 1931 and 1934 she was awarded a number of fellowships which enabled her to broaden her scientific knowledge by studying physics, chemistry and biology at a number of the leading European universities. In particular she spent time at the universities in Vienna, Paris, Prague and Leiden. D'Arcy Thompson had encouraged her to apply her mathematical skills to biology and [5]:-
Wrinch became a founding member of the Biotheoretical Gathering. Among the particular interests of this group of Cambridge biochemists and crystallographers was the structure of proteins and chromosomes; the possibility of linear sequences of amino acids or nucleic acids being involved in the genetic process was already being considered.
She began to publish papers on the application of mathematical techniques to biology. In particular she wrote five papers on chromosomes between 1934 and 1936 to which she applied potential theory. These are: Chromosome behavior in terms of protein pattern (1934), The contractile factors of the chromosome micelle (1935), The chromosome micelle and the banded structure of chromosomes in the salivary gland (1935), Chromosomes and molecular aggregates (1935), and On the molecular structure of chromosomes (1936). The fourth of these papers begins with a review of the earlier papers:-
In a recent communication (Nature, 134, 978, 1934) the present writer has put forward a molecular model of a chromosome, based upon the present state of knowledge in protein and physical chemistry, which provides a simple and obvious explanation and interpretation of the banded structure of the giant chromosomes belonging to the salivary glands of Drosophila, Chironomus, Sciara ... which has been the subject of a large number of recent researches in Europe and America.

In this model, homologous protamine molecules lie helically along a quasi-cylindrical surface, and the chromosome is specified in terms of the side chains belonging to the peptide linked amino acid residues which constitute these molecules. The hypothesis is in fact that the genetic nature of a chromosome resides in a characteristic arrangement of amino acid residues of various types. There is a consensus of opinion that the amino acids which occur in protamines are for the most pact highly basic. Given the arrangement of the residues, the arrangement of the molecules of nucleic acid is largely determined. Where there are arginine or other basic residues, there will also be molecules of nucleic acid, but where there are non-basic residues nucleic acid molecules will be absent. Thus the model implies the existence of rings of nucleic molecules at various positions along the length of the chromosome micelle.

I would therefore interpret the "dark bands" on the chromosomes of the salivary gland as regions of high nucleic acid density. The salivary chromosome is. of course, a compound structure consisting of homologous chromosomes lying side by side. Dark bands simply indicate regions of the constituent chromosomes where there is a high density of basic amino acid residues.
This remarkable work led to Wrinch being awarded a Rockefeller Foundation fellowship to support her study of the application of mathematics to biological molecular structures. This fellowship allowed her to undertake a lecturing tour of universities in the United States where she put forward her theories, including a controversial idea of cyclol protein structure. This theory was based on ideas of mathematical symmetry. Although it was later shown to be incorrect for proteins, her theories were found to apply to chemical bonds which occur in some alkaloids. Wrinch's [12]:-
... theory hinged on the existence of cyclol bonds between the amino acids that make up proteins. Although the theory was attractive for the mathematical symmetry that it possessed and its ability to explain many properties of proteins, it came under attack almost immediately by British X-ray crystallographers, who asserted that the theory did not conform to their experimental data. In addition, American chemist Linus Pauling calculated that cyclol bonds were too unstable to persist for any length of time. Pauling and Wrinch engaged in an increasingly acrimonious debate through the pages of the Journal of the American Chemical Society. Eventually, both were proved wrong: cyclol bonds were found to exist in ergot (a fungal disease of cereal grasses), and amino acids were found to combine in DNA chains. Wrinch blamed Pauling for her difficulty in finding an academic position in the United States after immigrating there in 1939.
By 1939 the world was moving towards war and Wrinch offered to work for the British war effort. Her offer, however, was rejected and this led to her deciding to emigrate to the United States where she was appointed as a visiting lecturer in chemistry at Johns Hopkins University.

By the time that Wrinch had emigrated to the United States her marriage had been dissolved (this happened in 1938). While she was a visiting lecturer at Johns Hopkins she met Otto Charles Glaser (1880-1951), a biologist who was vice president of Amherst College for men in Amhurst, Massachusetts. In 1941 she was appointed visiting professor at Amherst College and also at Smith College for women in Northampton, Massachusetts, and Mount Hoylake College for women in South Hadley Massachusetts. On 20 August of the same year she married Glaser. Two years later, in 1943, she was appointed as research professor of physics at Smith College where, in 1965, she was awarded a Sophia Smith Fellowship. The Fellowship was named after Sophia Smith who was an heiress who left her fortune to establish Smith College, which was founded in 1871 and opened in 1875. Wrinch held the Fellowship until she retired in 1971 when she went to Woods Hole, Massachusetts.

After emigrating to the United States, Wrinch focused on the application of mathematical principles to the interpretation of X-ray crystallographic data of complex crystal structures. This work was set out in detail in her text Fourier Transforms and Structure Factors which was published in 1946. An interesting episode is related in [27]. Von Neumann wrote in a letter to Norbert Wiener, which is discussed in [27], that he would consult with Irving Langmuir and Wrinch regarding the possibility of using electronic computers to determine protein structure via X-ray crystallographic analysis. A meeting between von Neumann, Langmuir, Wrinch and A D Booth did indeed take place in Schenectady on Wednesday 16 April 1947. After discussions they decided (correctly it turned out) that computers would not give an immediate solution because of the difficult problem of determining phases.

Mary Creese paints a picture of Wrinch's last years [5]:-
A controversial figure in early research in molecular biology, bright, ambitious, hardworking, and adventurous, Dorothy Wrinch was for much of her life a restless outsider, something of an exile in her American environment, who took up difficult problems in a field in which she, a mathematician by training, had insufficient background. Possessing a sharp wit and a dynamic, forceful personality, she was not always easy to get along with. Nevertheless, she was also an attractive woman and an inspired teacher who set high standards. After Otto Glaser's death she lived on the Smith College campus, moving to Wood's Hole, Massachusetts, on her retirement in 1971. She died in Falmouth Hospital, Falmouth, Massachusetts, of pneumonia, on 11 February 1976 and was cremated two days later at Forest Hills crematory, Boston. Her ashes were taken to Wood's Hole.
In fact the end of Wrinch's life was much sadder than this quote tells us and we should relate the tragic circumstances. Wrinch's daughter Pamela was awarded a B.A. and an M.A. by Michigan University, then a Ph.D. in international relations by Yale. She wrote the monograph The Military Strategy of Winston Churchill (1961), then taught in several institutions including Wellesley College, Boston University and West Virginia University. She married the publisher Alfred S Schenkman in Falmouth, Massachusetts in 1966. In the autumn of 1975 Pamela moved her mother from her home in Wood's Hole to a nursing home. She was not happy there and Pamela moved her mother back to Wood's Hole and organised 24 hour care for her. On 4 December 1975 Pamela was in her summer house in Gardiner Road, Wood's Hole, not far from her mother's home. The summer house caught fire and Pamela died. Dorothy Wrinch was devastated to lose her daughter and died around two months later.

Carey sums up Wrinch's contribution in [4]:-
By advancing a theory of protein structure that reached beyond the boundaries of classical biology to encompass chemistry, physics, mathematics, and philosophy, she contributed to the development of molecular biology by inspiring other scientists to take a multidisciplinary approach to the study of life.

### References (show)

1. P G Abir-Am, Synergy or Clash: Disciplinary and Marital Strategies in the Career of Mathematical Biologist Dorothy Wrinch, in P G Abir-Am and D Outram, (eds.), Uneasy Careers and Intimate Lives, Women in Science 1789-1979 (Rutgers University Press, New Brunswick, NJ, 1987)
2. P G Abir-Am, Dorothy Maud Wrinch (1894-1976), in L S Grinstein, R K Rose and M H Rafailovich (eds.), Women in Chemistry and Physics : A Biobibliographic Sourcebook (Greenwood Press, Westport, CT, 1993), 605-612.
3. W Aspray, The origins of John von Neumann's theory of automata, in The legacy of John von Neumann, Hempstead, NY, 1988 (Amer. Math. Soc., Providence, RI, 1990)
4. C W Carey Jr, Dorothy Maud Wrinch, American National Biography 24 (Oxford, 1999), 69-71.
5. M R S Creese, Wrinch [married names Nicholson, Glaser], Dorothy Maud, Oxford Dictionary of National Biography (2004).
6. Dorothy Maud Wrinch, in Lisa Yount (ed.), A to Z of Women in Science and Math (Facts on File, Inc., 1999).
7. Dorothy Maud Wrinch, Obituary, New York Times (15 February 1976), 67.
8. Dorothy Maud Wrinch, Obituary, The Times (8 March 1976).
9. L Else, The forgotten life of Dorothy Wrinch, New Scientist 216 (2893) (2012), 45.
10. G Felappi, "It is quite conceivable that judgment is a very complicated phenomenon": Dorothy Wrinch, nonsense and the multiple relation theory of judgement, British Journal for the History of Philosophy (2021).
https://www.tandfonline.com/doi/epub/10.1080/09608788.2021.1888694?needAccess=true
11. D C Hodgkin and Harold Jeffreys, Obituary - Dorothy Wrinch, Nature 260 (8 April 1976), 564.
12. W L Hosch, Dorothy Maud Wrinch. British-American mathematician and biochemist, britannica.com.
https://www.britannica.com/biography/Dorothy-Maud-Wrinch
13. D Howie, Interpreting Probability, Controversies and Developments in the Early Twentieth Century (Cambridge University Press, 2002).
14. M M Julian, Women in Crystallography, in G Kass-Simon and P Farnes (eds.), Women of Science: Righting the Record (Indiana University Press, Bloomington, 1990), 354; 364-368.
15. M M Julian, Dorothy Wrinch and a search for the structure of proteins, Journal of Chemical Education 61 (10) (1984), 890-892.
16. R B Martin, Dorothy Wrinch and the structure of proteins, Journal of Chemical Education 64 (12) (1987), 1069.
17. T Miyake, Scientific Inference and the Earth's Interior: Dorothy Wrinch and Harold Jeffreys at Cambridge, Integrated History and Philosophy of Science (2017), 81-91.
18. L Pauling, Dorothy Wrinch and the structure of proteins, Journal of Chemical Education 64 (3) (1987), 286.
19. J C Poggendorff, Biographisch-literarisches Handwörterbuch der exakten Naturwissenschaften. Band VIIb. Teil 9. Lieferung 4 (Akademie Verlag, Berlin, 1992), 6081-6144.
20. M Rayner-Canham and G Rayner-Canham, Dorothy Maud Wrinch (1894-1976), in Women in Chemistry: Their Changing Roles from Alchemical Times to the Mid-Twentieth Century (American Chemical Society and the Chemical Heritage Foundation: Washington, DC, 1998), 159-160.
21. L Riddle, Dorothy Maud Wrinch. September 12, 1894 - February 11, 1976, Biographies of Women Mathematicians, Agnes Scott College (25 February 2016).
https://www.agnesscott.edu/lriddle/women/wrinch.htm
22. M Senechal, I Died for Beauty: A Biography of Dorothy Wrinch (Oxford University Press, Oxford, 2012).
23. M Senechal, A Prophet without Honor: Dorothy Wrinch, Scientist, 1894-1976, Smith Alumnae Quarterly 68 (1977), 18-23.
24. M Senechal, Hardy as Mentor, Mathematical Intelligencer 29 (1) (2007), 16-23.
25. M Senechal, Dorothy Wrinch, 1894-1976, in E Kaufholz-Soldat and N Oswald (eds.), Against All Odds. Women in the History of Philosophy and Sciences 6 (Springer, 2020), 231-248.
26. M Senechal, D'Arcy Thompson and Dorothy Wrench: A friendship, 1918-1948, in Ellen K Levy and Charissa N Terranova (eds.), D'Arcy Wentworth Thompson's Generative Influences in Art, Design, and Architecture: From Forces to Forms (Bloomsbury Publishing, 2021).
27. J von Neumann, The cybernetical movement: von Neumann's letter to Norbert Wiener, 1946, Kybernetes 21 (4) (1992), 7-10.

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Written by J J O'Connor and E F Robertson
Last Update December 2021