## Some books and papers by Marjorie Senechal

**Patterns of Symmetry (L, P) (1977), by Marjorie Senechal and George Fleck (eds.).****1.1. Review by: Thomas J Brieske.**

*The Mathematics Teacher***71**(9) (1978), 787.How is it that mathematics can be at once so extraordinarily useful in its application and so fertile in its internal structure? Why are so many works of mathematics rightly described as beautiful and so many works of beauty aptly described as mathematical? The answers to these questions, if indeed they are answerable, must include elements of symmetry. Many of the patterns of symmetry that inhabit the worlds we live in and create are described in this interesting book. The book is a collection of essays, some of which were written for an interdisciplinary symmetry festival held at Smith College in 1973. ... final essay by Marjorie Senechal explains the mathematical structure of some of the patterns of symmetry that appear in the other essays.

**Shaping Space: A Polyhedral Approach (P, L) (1988), by Marjorie Senechal and George Fleck (eds.).****2.1. Review by: Donovan R Lichtenberg.**

*The Mathematics Teacher***81**(9) (1988), 757.In April 1984, Smith College was the site of a Shaping Space Conference. Many of the world's leading geometers participated. Also in attendance were students of all ages, teachers, artists, scientists, engineers, architects, and others. I wish I could have been there. This fascinating book was inspired by that conference. The topics in the book range from directions for making polyhedron models to some rather abstract polyhedral theory and unsolved problems. Other topics include the history of polyhedra and the role of polyhedra in science. (It should be noted that the editors are a mathematician and a chemist.) With more than 350 figures, many of which are photographs, the book is profusely illustrated. Many pictures show students making models, and others illustrate examples of polyhedra in the world around us. In the last chapter the editors express their dismay that "virtually none of the topics in this book is included anywhere in our present school curriculum." They conclude by recommending a re structured geometry curriculum in which the study of three dimensional forms would play a central role. Any teacher who wishes to move in such a direction will find this book a valuable resource.

**Crystalline Symmetries: An Informal Mathematical Introduction (1990), by Marjorie Senechal.****3.1. Review by: Doris Schattschneider.**

*SIAM Review***35**(2) (1993), 335-336.This slim volume is advertised as "a guided tour through the maze of mathematical models and classifications that are used today to describe the symmetries of crystals." Its author, Marjorie Senechal, is a professor of mathematics who has a deep interest and broad experience in the many fields that mathematical crystallography draws from: symmetry, polytopes, geometry of numbers, tilings and packings, lattices, and discrete groups. She also writes with the critical knowledge and scepticism of a historian of science, a missing ingredient in most texts on the subject. The result is a book that succeeds marvellously in providing not only the essential mathematical ideas that underlie mathematical crystallography, but also the background and historical milestones that have shaped the subject and also influence its future development. ... [This] is a delightful book, written with the clarity of someone who knows the field well, yet has the good sense to know how to say just enough to inform the outsider but not to overwhelm with detail. This is the only book to recommend as an introduction to the subject of mathematical crystallography for a beginner or someone outside the field. ... Senechal's closing remarks in the last chapter point to the need for new techniques to try to encompass in the theory of crystalline order the newest discoveries that do not fit the model of lattices and crystallographic groups. "Understanding the relation between local and global order is the pre-eminent challenge for mathematical crystallography today; it is the newest chapter in the problem of structure and form. ... Group theory, geometry, graph theory, number theory, tiling theory, Fourier analysis and techniques yet to be developed will all be needed to understand the fascinating new patterns we are discovering in the world of crystals."

**3.2. Review by: Rolf L E Schwarzenberger.**

*Mathematical Reviews*MR1100479**(92c:20092).**This monograph is the best introduction to mathematical crystallography available and is unlikely to be surpassed for a very long time. Unusual features, in comparison with other texts, include historical accuracy and clear precise definitions. It deals with dual lattices and diffraction patterns but avoids complicated matrix algebra. It is very readable but at no point sacrifices precision. It does not make exaggerated claims for any particular approach, and at several points draws attention to the need for new, and perhaps radically different, theories. ... The author has included a number of particularly important and illuminating results with a full and totally understandable proof: the enumeration by Klein of the finite rotation groups of the sphere, the classification by Fedorov (as simplified by Delone) of the five types of parallelohedra, and the construction by de Bruijn of Penrose tilings by means of pentagrids. This choice of material is so well handled that the reader ends up regretting the defensive modesty of the subtitle (the treatment may be informal but it meets the highest mathematical standards of clarity and precision) and the brevity of the book (a few more chapters in the same style could save many hours of decoding more "formal'' texts).

**Quasicrystals and Geometry (1995), by Marjorie Senechal.****4.1. Review by: John W Cahn.**

*Science, New Series***270**(5237) (1995), 839-840.Exploring the consequences of altering the fundamental axioms and definitions of a field can be a very rewarding enterprise for mathematicians. At its best, this is a quest for abstractions with wide-ranging implications that is both a cerebral and an aesthetic joy. On occasion this activity is triggered by a physical observation. Such was the effect of the report in November 1984 of the discovery of quasiperiodic crystals - quasicrystals for short. The discovery raised many mathematical questions and sparked intense activities in many aspects of geometry: what constitutes an orderly spatial arrangement of points or subdivision of space, and what the definition of a crystal should be. This ferment is still going on. In this excellent monograph Marjorie Senechal, a mathematics professor at Smith College, gives us insight into what occurred when established ideas had to be re-examined, modified, or overturned. There were, and still are, many alternative routes, different axioms and definitions, to be explored. Because the development of each is logical and rigorous, none is wrong; each has different implications, and some have more interesting consequences than others. The choice of which route to take is clearly subjective and aesthetic; the logical arguments and the rigorous mathematics follow from such choices. Senechal's book alternates between raising new possibilities and subjective questions and presenting dry and logical mathematical developments that are all the more fascinating because the author lets us understand the goals. This is unusual for a mathematics book; before each mathematical section there is a glimpse of the goals and then a telling of what has been achieved.

**4.2. Review by: Brian Hayes.**

*American Scientist***84**(4) (1996), 404-405.Senechal offers an engrossing introduction to the geometric questions raised by the discovery of aperiodic patterns and structures. As she is quick to point out, the questions still outnumber the answers, but that in itself is an intriguing development in a branch of mathematics that has repeatedly been written off as a closed, senescent field of study - and then repeatedly rejuvenated. The level of discourse herein will not bore the mathematical sophisticate, but most of the exposition is well within reach of the determined amateur. Senechal's enthusiasm for the subject shines through everywhere. This is a little gem of a book with a quasicrystalline elegance to it.

**4.3. Review by: Richard Kenyon.**

*Mathematical Reviews*MR1340198**(96c:52038).**This book is an introduction to the young science of (mathematical) quasicrystallography. The book starts with a brief history of the subject of crystallography, up to the discovery in 1984 of non-periodic "crystalline'' materials and the subsequent coining of the term "quasicrystal''. The term crystal has been recently redefined to be a substance whose X-ray diffraction spectrum has Bragg peaks (i.e. bright spots: these correspond mathematically to delta functions in the intensity). Such a phenomenon implies the existence of some sort of "long-range order'' in the substance. A quasicrystal is a crystal whose diffraction pattern in addition has symmetries forbidden by periodic crystals. As yet no one has a universally-accepted proposal for how the atoms in a quasicrystal (or other non-periodic crystals) are arranged. Certain mathematical models have been proposed, however, and this book introduces us to some of them.

**4.4. Review by: Charles Radin.**

*Notices Amer. Math. Soc.***43**(4) (1996), 416-421.Penrose tilings are beautiful. They also suggest significant new mathematics, so it is about time someone wrote a book about them which is readable (in fact, eminently readable) by mathematicians. The book,

*Quasicrystals and geometry*, by Marjorie Senechal, has an even broader goal: to present certain developments in crystallography from the past decade. The developments were generated in the wake of two profound discoveries. The first was the mathematics discovery in 1966 of aperiodic tilings, the origin of Penrose's 1977 examples. The more recent one was the physics discovery [8] in 1984 of quasicrystals. These two discoveries have led to a large volume of interdisciplinary research - among the fields of crystallography, physics, and mathematics, and also between subfields of mathematics, especially discrete geometry and ergodic theory. The interaction of the viewpoints of the different fields has been enormously beneficial to the mathematics which is emerging. We begin with an overview of the terrain, strongly emphasizing those aspects of relevance to mathematics. ... In summary, *Quasicrystals and geometry*is concerned with a variety of phenomena which are expressed equivalently in terms of configurations or tilings. The main characteristics of these structures which are studied are order properties and symmetry properties, both separately and as they affect one another. The book is aimed at a very broad scientific audience, and the level of mathematics is kept low accordingly. There is, however, significant mathematics coming out of this area. Those wanting to pursue this would need to hunt a bit in more specialized literature. However, there is a large number of appealing examples - well described, illustrated, and referenced - which should fire the imagination and entice new blood into related research.**4.5. Review by: Istvin Hargittai.**

*Adv. Mater.***9**(12) (1997), 994-995.Quasicrystals are truly advanced materials. They have outstanding tribological properties. Some of them have been found to outperform Teflon. Since these materials have excellent high-temperature, friction, and wear properties, many more applications are anticipated. ... Marjorie Senechal, Professor of Mathematics at Smith College (Northampton, MA) and well-known researcher in mathematical crystallography, has been a player in this drama. Among other, she has participated in the formation of the new definition, according to which "a crystal is a solid with an essentially discrete diffraction diagram." Quasicrystals are a special case of aperiodic crystals. This book deals with one of the new directions brought about by the quasicrystal discovery, the exciting development of the related geometry. It focuses on the relationship of the geometry of discrete point sets to the diffraction patterns of functions associated with them. It deals also with the relevant theory of periodic tilings. The author introduces her topic with great care, showing the historical and scientific context. She stresses that the book is not about real crystals but, rather, about mathematical concepts. She makes a conscious and much appreciated effort to keep the level of the discussion accessible to non-mathematicians, without loss of rigour. ... The book is most enthusiastically recommended to a broad readership of graduate students and researchers in mathematics, physics, material science, and ctrystallography.

**Mathematics and Narrative at Mykonos (2006), by Marjorie Senechal.****5.1. Review by: Philip D Straffin.**

*The College Mathematics Journal***38**(1) (2007), 68-69.Senechal reports on a 2005 conference on Mathematics and Narrative sponsored by a group of Greek mathematicians called "Thales and Friends." The papers presented were wide-ranging, discussing mathematical fiction, mathematical exposition, the path of mathematical research as a story, and analogies between mathematical proofs and stories. For example, "both narratives and proofs are stratified and self-similar, with rich local structure and many levels. And the points of linkage between the levels in a narrative or in the levels of a proof play the same role: they are the elements of causality." We can have productive conversations with our colleagues in the humanities.

**Hardy as Mentor (2007), by Marjorie Senechal.****6.1. Review by: Cecil Rousseau.**

*The College Mathematics Journal***38**(4) (2007), 321-322.This is the story of two persons, one famous, the other not so famous. The famous one is G H Hardy (1877-1947), well known for his powerful contributions to analysis and number theory, his legendary collaboration with Littlewood, and his discovery of Ramanujan. We also know Hardy from A Mathematician's Apology and classic books on special topics: Dirichlet series, divergent series, inequalities, the theory of numbers. The second person in the story is Dorothy Wrinch (1894-1976), who was a Wrangler at Cambridge and the first woman to receive an Oxford D.Sc. She had published 50 papers in pure and applied mathematics by the time she was 40. ... This is a fascinating article that offers a detailed account of the early career of Dorothy Wrinch and provides examples of Hardy's dedication to the mathematical community and his willingness to give of himself in support of young persons and others in need of help.

**American Silk, 1830-1930: Entrepreneurs and Artifacts (2007), by Jacqueline Field, Marjorie Senechal and Madelyn Shaw.****7.1. Review by: Melinda Talbot Nasardinov.**

*Winterthur Portfolio***42**(4) (2008), 293-294.In the latest book from the Costume Society of America, Jacqueline Field, Marjorie Senechal, and Madelyn Shaw have combined their individual studies of three silk manufacturers to tell the story of the rise and decline of the American silk industry. The companies are well chosen to represent the early, middle, and late phases of American silk production between 1930. The authors outline the companies' often-complicated histories, focusing on entrepreneurs, innovation in technology and marketing, and products - both plain and fashion fabrics and utilitarian and domestic needlework threads. ... In part 4, Senechal provides a useful description of silk processing that is supplemented by the helpful glossary at the back of the book. She also describes the impact of Samuel Lapham Hill's development of "machine twist," a three-ply thread suitable for sewing machines, around 1850, which resulted in a symbiotic relationship with Isaac M Singer's sewing machine business.

**7.2. Review by: Laurence F Gross.**

*Technology and Culture***49**(3) (2008), 796-798.In American Silk, three authors develop a picture of the silk industry during overlapping periods. They focus on the role of "entrepreneurs [who] receive little attention because most industrial studies use a labour and social history approach and focus on factories and their effect on workers." Marjorie Senechal begins by describing the great interest in silk during the colonial period and the Early Republic. Enthusiasm for mulberry trees and silkworms pervaded the eastern seaboard to a degree quite out of proportion to any success in actually producing usable silk. Lack of skill and patience doomed efforts to move from cocoon to thread. Entrepreneurship and mechanical ability came together in an attempt at manufacturing in Northampton, Massachusetts, but without success until a communitarian society, the Northampton Association of Education and Industry, took over the effort. Though leading lights from Ralph Waldo Emerson to William Lloyd Garrison visited, and Sojourner Truth came to stay, the manufacturing effort attained success only after discovery of the advantages of three- rather than two-ply yarn or thread for use in Singer's sewing machines. Under the name Corticelli, machine twist or sewing-machine thread poured forth from the Nonotuck Silk Mills.

**7.3. Review by: Marla Miller.**

*The New England Quarterly***81**(1) (2008), 165-168.American Silk is unusual in that it embodies the work of three scholars engaged in three separate projects arrayed in succession more so than formulated in collaboration. The book has three parts, each of which, in the neighbourhood of ninety pages (mosses, if you will) discusses one element in the history of American silk: The Nonotuck Silk Company (183o-80) of Northampton, Massachusetts; the Haskell Silk Company (1874-1930) of Westbrook, Maine; and H R Mallinson & Company (twentieth century) of New York, New Jersey, and Pennsylvania. Together, these case studies provide an overview of the silk industry in the United States. Senechal's account quite usefully begins with the earliest attempts at sericulture in the future United States, including the settlement at Jamestown, where silk occupied some part of the colonists' attention until the starving winter of 1609 focused their thoughts on more pressing matters (the silkworm, we learn, was also featured on Georgia's colonial seal).

**7.4. Review by: Tami J Friedman.**

*The Business History Review***82**(2) (2008), 377-379.In American Silk, 1830-1930: Entrepreneurs and Artifacts, Jacqueline Field, Marjorie Senechal, and Madelyn Shaw have produced an interesting and often illuminating history of the U.S. silk industry. The book's uniqueness stems in part from its collaborative character: it combines in one volume the work of three scholars, each of whom researched a different firm and contributed part of the text. Senechal tackles the Nonotuck Silk Company of Northampton, Massachusetts (1855-1932). ... American Silk begins with Senechal's examination of early (and mostly disastrous) efforts to raise silk in the British colonies. Americans, she argues, faced numerous challenges - ranging from silkworm diseases to an inability to extract silk smoothly from cocoons - that inhibited the production of raw silk. In the end, U.S. entrepreneurs imported their materials, particularly from China and, later, Japan. Nonotuck became a leading manufacturer of silk thread, landing lucrative contracts with Isaac M. Singer of sewing-machine fame. Senechal traces the firm's rise in the late nineteenth century to its demise in the early years of the Depression, after falling victim to changing fashion trends in the 1920s and declining consumer demand.

**The Shape of Content: Creative Writing in Mathematics and Science (2008), by Chandler Davis, Marjorie Wikler Senechal and Jan Zwicky (eds.).****8.1. Review by: Kelly Edenfield.**

*The Mathematics Teacher***103**(4) (2009), 310-311.Over the number of years mathematicians, scientists, and writers have gathered at creative writing workshops to write about their interests through a variety of genres: poems, plays, short stories, and biographies. This book contains a selection of these workshops' results, in various states of completion. This anthology provides examples of all types of literary materials.

**8.2. Review by: Amir Alexander.**

*Amer. Math. Monthly***117**(1) (2010), 94-96.*The Shape of Content*is a selection from the works that originated and evolved at the BIRS workshops through this cross-disciplinary cooperation. With 37 different pieces by 21 authors,*The Shape of Content*is a testament to the dazzling diversity of artistic possibilities around the common theme of mathematics. ... Marjorie Senechal's "The Last Second Wrangler" is a true tale intertwining love and marriage, war and politics, brilliant scientific insights and fatal errors, with a steady mathematical current running through it all. It is the story of the English mathematician Eric Neville and his love for the brilliant but controversial Dorothy Wrinch. Their affair, in Senechal's telling, lasted through four decades, three marriages (never to each other), academic exile (for both), and physical exile (for Wrinch). When, from the 1930s onwards, Wrinch became embroiled in a fierce and long-lasting controversy over the structure of proteins, Neville stood by her and was the most stalwart of her shrinking band of defenders. Wrinch proposed a novel algorithm for deciphering the molecular structure of proteins from Patterson diagrams of their x-rays. In Wrinch's method, a "star" diagram is systematically replaced by a set of "pinwheel" diagrams that disclose the true position of the molecules. The problem, as Wrinch well knew, is that "in complicated cases, different pinwheels can match the same star. Then the algorithm forks, each branch leading to a different picture. And all of the pictures are true." And so it was for Neville and Wrinch, countless possibilities, roads taken and untaken, in life, in love, in career. Mathematics, in Senechal's telling, is both life-force for its adherents, and metaphor.**I Died for Beauty: Dorothy Wrinch and the Cultures of Science (2013), by Marjorie Senechal.****9.1. Publisher's Information.**Drawing on her own personal and professional relationship with Wrinch and archives in the United States, Canada, and England, Marjorie Senechal explores the life and work of this provocative, scintillating mind. Senechal portrays a woman who was learned, restless, imperious, exacting, critical, witty, and kind. ... Senechal presents a sympathetic portrait of the life and work of a luminous but tragically flawed character. At the same time, she illuminates the subtler prejudices Wrinch faced as a feisty woman, profound culture clashes between scientific disciplines, ever changing notions of symmetry and pattern in science, and the puzzling roles of beauty and truth.

**9.2. Review by: Charles Ashbacher.**

*Mathematical Association of America*(22 July 2013).While this book is about the life of Dorothy Wrinch and her role in mathematics applied to the structure of complex molecules, it is even more about the culture of science and how became more diverse in the twentieth century. There is no question that Wrinch was a superb scientist, but she was also stubborn and often very difficult to deal with, refusing to reject her theories when the experimental evidence demonstrated otherwise. The story of Wrinch's life includes some of the most powerful figures of science. She knew Bertrand Russell very well (there are even reports that they had an affair). People such as Albert Einstein, D'Arcy Thompson and Linus Pauling played significant roles in her personal and professional life. ... Senechal makes it a point to explain how powerful college presidents were back then; professors sometimes had to get their approval to make life changes such as getting a divorce. The ladies auxiliary of the wives of the professors could also be a powerful force on campus in those times, which could both help and hinder a female academic. This telling of the story of the life of Dorothy Wrinch is occasionally disjointed and contains some short tangential bits, yet it is a deep story about how science changed for the better as females began to be more numerous in the ranks of its practitioners.

JOC/EFR November 2017

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