Mary Elizabeth Layne Boas
Quick Info
Prosser, Washington, USA
Seattle, Washington, USA
Biography
Mary L Boas was the daughter of Felix Festus Layne (1877-1976) and his wife Lucy Annie Goff (1873-1963). Felix Layne had been born in Surry, North Carolina on 8 December 1877 to Pascal Clayborn Layne and Elizabeth Jane Greenwood. He obtained a marriage license with Annie Goff in Benton County, Washington and they were married on 14 September 1911. Annie Goff had been born in Henry, Missouri on 23 November 1873 to William Walker Goff and Mary Temperance Cock; she became a school teacher. Felix and Annie Layne had one child, a daughter Mary Elizabeth Layne (the subject of this biography), born on 10 March 1917 in Prosser, Benton County. The town of Prosser had only been incorporated in 1899 and in 1908 a high school was built there.Although born in Prosser, Mary Layne was brought up on a poultry and fruit farm near Monroe, Washington where her father farmed. It was a wonderful area with fertile river valleys, many working farms, and dense evergreen forests set against the scenic foothills of the Cascade Mountains. After schooling in Monroe, Mary went to what was her local university, namely the University of Washington in Seattle. There she studied mathematics and graduated with a Bachelor's degree in 1938. At this time the head of mathematics was Robert Edouard Moritz (1868-1940) who had held the post since 1904. He had broad mathematical interests especially analysis, number theory, geometry and economics. The only female member of staff was Mary E Haller who joined the faculty following the award of her Ph.D. by the University of Washington in 1934. Students called her "The Doc" and she was widely regarded as one of the best lecturers in the Department. Another highly effective lecturer was Lee Horace McFarlan (1895-1964). He served as the Secretary-Treasurer of the Pacific Northwest Section of the Mathematical Association of America for many years. He published papers on the calculus of variations and differential equations.
After the award of her Bachelor's degree in 1938, Mary Layne remained at the University of Washington where she studied for a Master's Degree in mathematics. She was awarded the degree in 1940. Continuing her studies, but now also being employed as a mathematics instructor, she went to Duke University in Durham, North Carolina. In spring 1940 she met another young mathematics instructor, Ralph Philip Boas Jr. They became engaged in the spring of 1941 and, having made certain that Mary could keep her job if they married, they married on 12 June 1941 in Orleans, Massachusetts. Paul Erdős sent them the following message for their wedding (see [28]):
Here's to Boas, Ralph and Mary,
Who no longer solitary
Constitute a form binary.
This occasion celebratory
Brings this wire felicitary
From the house of Pondiczery.
Ralph and Mary Boas had three children: Ralph Layne Boas (born 1948), Anne Louise Boas and Harold Philip Boas (born in Evanston, Illinois on 26 June 1954). Let us note at this point that H P Boas received his A.B. and S.M. degrees in applied mathematics from Harvard University in 1976 and his Ph.D. in mathematics from the Massachusetts Institute of Technology in 1980. After being J F Ritt Assistant Professor at Columbia University (1980-1984) he became a professor of mathematics at Texas A&M University. He was awarded the Stefan Bergman Prize by the American Mathematical Society in 1995.
Who no longer solitary
Constitute a form binary.
This occasion celebratory
Brings this wire felicitary
From the house of Pondiczery.
Mary Boas' first publication (co-authored with her husband Ralph Boas and with Norman Levinson) was The growth of solutions of a differential equation published by the Duke Mathematical Journal. Both Mary and Ralph Boas give their address as Duke University on this paper (see [10]).
In 1942, the United States having entered World War II, Ralph Boas applied to work at the Navy Pre-Flight School at Chapel Hill. After a few months the Navy decided they did not want non-military teachers at the Pre-Flight School and Ralph Boas was recruited to teach in the military training programme at Harvard. Once there he taught courses in the military training program and also some regular Harvard courses. While her husband was teaching at Harvard, Mary taught at Tufts University in Boston until 1945.
Ralph Boas was the Executive Editor of Mathematical Reviews during 1945-1950 and a lecturer at the Massachusetts Institute of Technology during 1948-1949. Mary Boas began studying at the Massachusetts Institute of Technology for a PhD. in Physics in 1945 and in 1948 was awarded the degree having written the thesis The Photodisintegration of the Triton. Photodisintegration is a nuclear process where an atomic nucleus absorbs a high-energy gamma-ray photon and breaks apart into its constituent nucleons. Triton is the atomic nucleus (with one proton and two neutrons) of a tritium atom, a radioactive isotope of hydrogen. In 1950 the family moved to Evanston, Illinois when Ralph Boas became Professor of Mathematics at Northwestern University.
In 1950 Mary Boas, her husband Ralph Boas and her two children Anne Louise Boas and Ralph Layne Boas all attended the International Congress of Mathematicians held Cambridge Massachusetts. In 1953 Mary Boas published the paper Nomograms Used in Analysis of Data in the Reaction which has the following Abstract [7]:-
Several nomograms and similar computational devices have been found useful in the analysis and interpretation of data from the reaction in photographic emulsions. Three of these are discussed here: (1) a slide rule to determine from measurements on a track with the triton in a small forward cone, what the track length would have been if the triton had gone exactly forward; (2) a nomogram to determine the true alpha‐triton angle from its measured projection in the plane of the emulsion; (3) a device for determining, from measurements on a track, the angle between the emulsion and the incident neutron giving rise to the track.A couple of years after the birth of her son Harold Philip Boas, Mary Boas looked to have a part-time lecturing position. Northwestern University was not an option since they had an anti-nepotism policy officially titled the "Employment or Evaluation of Relatives" policy which prevented Mary Boas working there since her husband was head of mathematics. Fortunately DePaul University in Chicago was close and in 1957 she was able to obtain a part-time position in physics there. In April the DePaulia published the following [14]:-
Dr Mary Boas: A career in instructing others was inherited from the school teacher mother of this DePaul physics professor. A further influence was a liking for all types of mathematics and the application of principles; this eventually caused Dr Boas to choose physics as her major field. Dr Boas has been teaching part-time for twenty years, combining marriage and raising a family with a career. This is her first year at DePaul.Mary Boas continued to work at DePaul University for the rest of her career. Derek Potts writes in [26]:-
... in addition to teaching, Mary was active with the "newly-established DePaul chapter of Sigma Pi Sigma in 1973 … a branch of the only national physics honour society in the U.S." In the 1973 DePaulian group photo, Sigma Pi Sigma members including Boas are identified as "attempting to popularise physics on campus by sponsoring speakers, discussion groups, and informal get-togethers with faculty." Mary Boas taught physics at DePaul until her retirement in 1987.She is best known through her book Mathematical Methods in the Physical Sciences first published in 1966. F J Milford writes [21]:-
Boas has adopted one of a number of possible views as to how undergraduates majoring in the physical sciences should learn mathematics. This viewpoint is that such students need a utilitarian knowledge of a variety of material concerning analysis, special functions, vector analysis, and so on in order to pursue their studies of the physical sciences and that furthermore, this material should be presented in a single course.G D J Phillies writes [24]:-
For self-study by students at the intended level, this is clearly the best-written text I have ever seen.For detailed information about the three editions of this book (1966, 1984, 2005), see THIS LINK.
The high praise given to this book led to Mary Boas receiving invitations to talk on teaching mathematics to physics students. For example she addressed a 'Symposium on Mathematics in the Undergraduate Program in the Sciences' run by the American Association for the Advancement of Science on 28 December 1970. She gave the talk Mathematics for the Undergraduate Physics Major. Here is a summary of the lecture as given in [3]:-
It has been traditional to have a course for graduate students in mathematical methods of physics. A similar course at the undergraduate (say sophomore-junior) level has never become very customary and I think this is too bad. At the present time the usual physics major "picks up" much of his knowledge of mathematical techniques in his physics courses. The few mathematics courses he does take go into much greater detail than he finds either interesting or useful. Meanwhile the topics not studied in mathematics classes must be mastered from sketchy introductions in the physics textbooks. If the student is not overwhelmed by the new physical ideas he is trying to master, he is likely to be by the combination of new physics and a new mathematical technique presented simultaneously.For a version of the full lecture, see THIS LINK.
The physics teacher's counter argument here is that the motivation of the immediate use of a technique is very important and that for this reason the mathematics should not be taught separately. Years of experience have convinced me otherwise. It is quite possible in a mathematical physics course to tell the students enough about some of the simpler applications of the topic at hand to keep up interest.
Mathematics teachers may argue that the science major should study mathematics with as much detailed proof as mathematics majors. My only objection to this is lack of time to cover so many courses. What alternative is there?
After about ten years' experience with a course at DePaul University and writing a book (Mathematical Methods in the Physical Sciences, Wiley, New York, 1966), which we now use as our text, I think I am in a position to say that a mathematical physics course of about one year's length covering the needed topics can be given. How? First, such a course must be taught as a scientist's methods course and not as a mathematicians' theory course. This does not have to mean careless or incorrect teaching. I make a strong point of never teaching anything a student will ever have to unlearn. However, generality can be sacrificed with little loss at this stage. The special cases of theorems that are going to be needed are quite sufficient. Second, long and detailed proofs can be omitted; careful statements of the theorems can be substituted. With these two methods of condensation (limited generality and few proofs), we cover in one year the following topics: probability, infinite series, complex numbers, determinants and matrices, partial differentiation, multiple integrals, vector algebra and calculus, Fourier series, calculus of variations, transformation theory, diagonalization of matrices and applications, tensors, complex variables, special functions, Laplace and Fourier transforms, and partial differential equations.
Mary Boas published a number of papers reviewed in Mathematical Reviews, for example [5], [6], [8], [9]. On the whole these useful papers give simpler proofs or different approaches to known results. In [5] she gives a simpler proof than the one given by C C MacDuffee that a geodesic in Minkowski space is a path of maximum length. Note MacDuffee's paper was published in 1959 and Boas' simpler proof was received on 29 June 1959. In [6] Boas simplifies results of Roger Penrose on the difference between the measured Lorentz contracted shape of an object moving at relativistic speed and the shape as seen by a single observer. The paper [9], a joint publication by Mary and Ralph Boas, has the following abstract:-
Many physical problems lead to integrals that can be evaluated by contour integration, and sometimes there are poles on the contour. In practice, it usually is appropriate in such cases to express the result as a principal-value integral. Most textbooks treat each problem involving principal values individually by considering an indented contour and taking limits. We want to call the attention of users of the calculus of residues to a theorem which, although known, seems not to be well-known.We obtain a fascinating look at Mary Boas' interests other than mathematics or physics in the paper by her son Harold P Boas [11]:-
My mother, Mary L Boas, was a professor of physics at DePaul University in Chicago. My father, Ralph P Boas, was a professor of mathematics at Northwestern University and a prominent researcher, teacher, writer, editor, and translator; he was active in the affairs of both the American Mathematical Society and the Mathematical Association of America. With such parents, had I not a predetermined future? I think not, for my two siblings showed no inclination to pursue a scientific or an academic career.After she retired in 1987, Mary Boas and her husband went to live in the Seattle area in the same part of the country where Mary had been brought up. Ralph Boas died in July 1992 but Mary continued to live near Seattle, worked on the third edition of her book and enjoyed her hobbies such as gardening. In 2008 she established the Mary L Boas Endowed Scholarship at the University of Washington. It was first awarded in 2009 [20]:-
Certainly all three of us children were profoundly influenced by our parents' passion for teaching and learning. We absorbed by osmosis the conviction that every craft can be mastered through diligence. For instance, we observed that when our parents took up photography, they went so far as to convert the utility closet into a home darkroom to develop their own film; their gardening activities expanded to include forcing bulbs under lights in the basement, building window boxes, and constructing cold frames in the backyard; they taught themselves how to work with fibreglass in order to maintain a succession of small sailboats. ... my mother knew how to sew her own clothes, to make peach-plum jelly, and to wring a chicken's neck.
After her illustrious career, Dr Boas is happy to be able to offer a small repayment to the department where she got her start and encourage other women to be theoretical physicists. ... This is the first year the Boas Scholarship has been awarded. The scholarship recognises undergraduate women students in the Department of Physics for outstanding academic achievements.Following her death in 2010 Martha Clatterbaugh wrote [13]:-
I met Mary at the Lake Forest Park Garden Club and it is through that organisation that I have known her. When I first met her she was in her eighties and still actively engaged in her profession. She "complained" that the work on the third revision of her textbook was not going as fast as she would like. ... Mary was an inspiration to me and many of those around her. She was older than most in the garden club but was among the most technically knowledgeable. She kept the email list for the club and preferred to receive communications electronically. Mary was a very knowledgeable gardener and gave a presentation to the Lake Forest Park Garden Club last year on growing amaryllis. She grew tomato starts for the garden club plant sale every year and patiently explained the intricacies of growing them to new gardeners. She was generous with plants and information. She served on the garden club board of directors up until her death and was at the last Lake Forest Park Garden Club meeting, complete with oxygen tank and just a little help from friends.
References (show)
- M L Boas, Photodisintegration of Triton, American Doctoral Dissertation (Massachusetts Institute of Technology, 1948).
- M L Boas, Mathematics for the Undergraduate Physics Major, The Two-Year College Mathematics Journal 2 (1) (1971), 49-52.
- M L Boas, Mathematics for the Undergraduate Physics Major, American Mathematical Monthly 78 (7) (1971), 788-789.
- M L Boas, Mathematical Methods in the Physical Sciences (3rd edition) (John Wiley & Sons, 2006).
- M L Boas, The Clock Paradox, Science 130 (1959), 1471-1472.
- M L Boas, Apparent shape of large objects at relativistic speeds, American Journal of Physics 29 (1961), 283-286.
- M L Boas, Nomograms Used in Analysis of Data in the Reaction , Review of Scientific Instruments 24 (5) (1953), 356-359.
- M L Boas and R P Boas Jr., A new use for an old counterexample, American Mathematical Monthly 82 (1975), 481-486.
- M L Boas and R P Boas, A remark on principal‐value integrals, American Journal of Physics 52 (1984), 276.
- M L Boas, R P Boas and N Levinson, The growth of solutions of a differential equation, Duke Mathematical Journal 9 (1942), 847-853.
- H P Boas, Why I became a Mathematician: A Personal Account, in Peter Casazza, Steven G Krantz and Randi D Ruden (eds.), I, Mathematician (Mathematical Association of America, 2015), 255-256.
- B V Bonk, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, American Scientist 55 (1) (1967), 118A.
- M Clatterbaugh, Mary Boas, gardener, legacy.com (20 February 2010).
- Dr Mary Boas, DePaulia (25 April 1958).
- R Howes and C L Herzenberg, After the war: women in physics in the United States (Morgan & Claypool Publishers, SanRagael, 2015).
- J J Hupert, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, IEEE Spectrum 4 (7) (1967), 166-167.
- Marriage: Felix Layne and Annie Goff, The Spokesman-Review (19 September 1911).
- Mary Boas Obituary, legacy.com (20 February 2010).
https://www.legacy.com/us/obituaries/seattletimes/name/mary-boas-obituary?id=28161437 - Mary Boas Obituary, The Seattle Times (20 February 2010).
- Mary L Boas Endowed Scholarship, Department of Physics, University of Washington (2026).
https://web.archive.org/web/20120428055447/http://www.phys.washington.edu/awards.htm - F J Milford, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, Science, New Series 155 (3769) (1967), 1530-1531.
- W J Moore, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, Journal of Chemical Education 44 (4) (1967), 246; A352.
- A A Mullin, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, American Journal of Physics 36 (7) (1968), 644-645.
- G D J Phillies, Review: Mathematical Methods in the Physical Sciences (2nd edition), by Mary L Boas, Journal of the American Chemical Society 106 (17) (1984), 5046.
- L A Pipes, Review: Mathematical Methods in the Physical Sciences, by Mary L Boas, The American Mathematical Monthly 74 (8) (1967), 1024-1025.
- D Potts, Women's History at DePaul, DePaul University Library (2 March 2016).
- F Smithies, H P Boas, D T Haimo and P J Davis, Reminiscences, in Ralph Philip Boas Jr., Lion hunting & other mathematical pursuits (Mathematical Association of America, Washington, DC, 1995), 25-39.
- D Spector, Review: Mathematical Methods in the Physical Sciences (2nd edition), by Mary L Boas, American Journal of Physics 67 (1999), 165.
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Written by J J O'Connor and E F Robertson
Last Update October 2026
Last Update October 2026