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Sophie Germain and Fermat’s Last Theorem

May 22nd, 2014
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    by Tamara Caulkins*
    Germain_5On May 20, 2014, the OSU Department of Mathematics sponsored a history lecture by Dr. David Pengelley, of New Mexico State University. Dr. Pengelley presented an animated lecture on the French mathematician, Sophie Germain (1776-1831). Dr. Pengelley’s interest in Germain was sparked by his use of primary historical sources in his teaching of mathematics. This led him to a store of Germain’s original manuscripts at the National Library of France, which had not been studied in over two hundred years. Revisiting Germain’s work as a mathematician, Dr. Pengelley found that Germain had developed a sophisticated plan for proving Fermat’s Last Theorem, making significant contributions to number theory. Until recently, her work was known only via a footnote in another mathematician’s treatise (Legendre, Essai sur la Théorie des Nombres, 1823). Particularly in an age when women were not well-educated and when they were excluded from scientific academies, Germain’s substantial achievements were indeed remarkable.

    Sophie Germain was only thirteen when the French Revolution broke out, forcing her to spend most of her time indoors. During that period, she turned to her father’s library. Fascinated by books on mathematics, she taught herself against her parent’s wishes (Pengelley relates that at one point they even took away her clothes and candles to prevent her from studying at night!). Germain’s father was a silk merchant so it was not through his mentorship that she developed her abilities but rather through her own effort and perseverance. At one point, Germain took on the identity of a student at the École Polytechnique who had died (Antoine-August LeBlanc). When the professor discovered that it was really a woman who was submitting such fine work under LeBlanc’s name, he was astonished. Germain eventually corresponded with Johann Carl Friedrich Gauss (1777-1855) in Göttingen, one of the most celebrated mathematicians of the time. Pengelley recounts that upon receiving a letter from Germain, Gauss praised the way she contributed to the “charms of this sublime science,” as giving him great joy.

    Pengelley gave a cogent and fairly detailed explanation of the theorem by Pierre de Fermat (c.1601-1665) that Germain was hoping to prove. Basically, the theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. At the time that Germain was working on the problem, it was known that the theorem could be proven to hold for some numbers but much work remained before the theorem could be proven conclusively. Germain’s letters and manuscripts demonstrate that she had a good handle on the problem and that she had made considerable progress toward a solution. Pengelley found that she had made a mistake in one of her proofs but peering closer found scribbled in the margins, “voyez errata”—Germain’s own admission that she saw she had made an error!

    Germain did win a prize from the French Academy of Sciences for her work on elasticity and she eventually was able to attend the Society’s meetings, but she was never made a member nor was any of her work published. Her manuscripts were taken by Guillaume Libri, described by Pegelley as a “mathematician, historian, bibliophile, thief, and friend of Sophie Germain.” Because Libri ended up with her manuscripts, they were preserved and eventually made available for Pengelley’s research. Finding a proof for Fermat’s theorem has been a problem that has attracted the attention of mathematicians for a long time, however, in the twentieth century, it came to the fore because of its implications for cryptography. Andrew Wiley, a mathematician in England, finally solved the Fermat Theorem in 1995. It had been one of the most famous problems in mathematics and Sophie Germain’s efforts made an important contribution to the discovery of a proof. Dr. Pengelley’s work is of interest to historians in the way he has used primary sources to teach mathematical concepts but has also revived interest in an under-appreciated figure, Sophie Germain, whose achievements deserve to be more widely celebrated.

    *Tamara Caulkins is pursuing a Ph.D. in History of Science at Oregon State University.

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      The Wilderness Act at 50

      May 9th, 2014
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        by Joshua McGuffie*

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        What images does wilderness evoke? For many, wilderness means pristine landscapes, scenic vistas, quietude, and wide open spaces. Many Americans may be surprised to know that, legally, wilderness has only been enshrined as a public reality for 50 years. In 1964, President Lyndon Johnson signed the Wilderness Act, surrounded by an unlikely coalition of elected officials and preservationists. To celebrate the Wilderness Act’s 50th anniversary, Oregon State University’s Spring Creek Project hosted a panel discussion on 2 May to consider the Act’s genesis, life, and future.

        Dr. Jacob Hamblin discussed important environmental moments leading up to the act. He particularly singled out public outcry over the Bureau of Reclamation’s Echo Park Project. The Bureau planned to build a series of dams along the Colorado, including within Grand Canyon National Park. Hamblin argued that potential incursions into ‘protected’ federal lands raised popular environmental consciousness and incentivized politicians to support preservation measures. With this background in mind, he asked the question “Is it possible to have a community of sincerity without common purpose?” That the Wilderness Act passed, with a variety of definitions for ‘wilderness’ built into its text, seems to indicate that such a community did in fact coalesce in the early 1960’s. Read the rest of this entry »

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          A Marine Biology Student’s Education Through the Scientific Art of Biography

          April 10th, 2014
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            Ariana Snow and MJ Nyeby Ariana Meltvedt Snow*

            These reflections result from a February 2014 address at OSU’s Center for the Humanities delivered by Mary Jo Nye, Professor Emerita of History at OSU.  Professor Nye, who spoke on “Biography and the History of Science,” has written biographies of many scientists including the English physicist and Nobel laureate P.M.S. Blackett (2004) and the Hungarian chemist and philosopher Michael Polanyi (2011).  Professor Nye suggested that there are three principal forms of biography in which the subject is a scientist: the life of the scientist, the scientific life, and the life of scientific collaboration.

            Biographies of scientists, something not often encountered by undergraduate science majors like me, can enrich our knowledge of scientific practice and methods.  Good biographies can help us learn about and remember complex scientific concepts. I have come to think that the biography itself is a kind of science. Provided they are well-written and can hold the reader’s interest, biographies of scientists contribute to scientific literacy and allow for increased dissemination of information through the avenue of art. A biographer must be critical, aware, and objective in their work in order to produce writings that fully encompass the life and impact of the subject. Thus biography conveys scientific concepts in a way that this marine biology student and many non-scientists can grasp. Read the rest of this entry »

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              Dagmar Herzog and the Century of Sex

              February 24th, 2014
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                by Joshua McGuffie*

                herzogOn Wednesday, February 19th, Dr. Dagmar Herzog, of the City University of New York, graced Oregon State with her lecture, “Sexuality in Europe: A 20th-Century History and a History of the Present.” She offered a lighthearted but academically thorough treatment of themes in European understandings of sexuality. In her lecture, Dr. Herzog focused on two concerns: first, the history and periodization of sexuality in the 20th Century and second, recent history and the path into the future.

                After noting that “people are still made tense by a free and open discussion of sexuality,” Dr. Herzog launched into her talk, reminding the audience that the 20th Century has been called the “century of sex.” As such, the century has been characterized by a general liberalizing trend punctuated with sexually conservative backlashes. Sex, Dr. Herzog argued, became built into everything. Identity, privacy, civil rights, secularization, commerce and politics have internalized sex as a key theme. “Sex ends up annexing” almost every part of life in 20th Century Europe.

                How did this happen? Read the rest of this entry »

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                  God in Gotham: Jon Butler’s Re-examination of Secular vs Sacred in New York City

                  November 26th, 2013
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                    Jon Butler

                    by Emily Simpson*

                    On Thursday November 21, Oregon State’s School of History, Philosophy, and Religion was privileged to welcome esteemed scholar of American religious history Jon Butler as part of the Horning Lecture Series.  His presentation God in Gotham is an interesting re-interpretation of the relationship between religious and secular aspects of life in New York City between the 1880s and 1960s.  He provides a variety of evidence to upturn the common idea of New York City’s standing as the capital of American secularism–from the culture of various religious communities, changes in immigration patterns, to the prominence of well-known religious architecture within the city.

                    New York City is a critical example of a fundamental problem that Dr. Butler sees in interpreting the history of religion.  How do we draw strict lines between what is a secular age and what is a religious age?  To argue against the notion that the world of religion has fallen to secular society, Dr. Butler first re-evaluates the state of harmony that we often see when Western religious influence was at its peak-the medieval period.  According to Dr. Butler, there has never been a point in history where religion was not a disputed issue.  The total unity of ideas within medieval society is a myth.

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                      James Moore Illuminates Darwin’s Sacred Cause

                      November 4th, 2013
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                        by Mason Tattersall*

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                        Last Tuesday the Horning Lecture Series was pleased to present James Moore’s engrossing lecture on Darwin’s Sacred Cause. Moore, along with Adrian Desmond, penned one of the classic biographies of Darwin (1991’s Darwin).  As Moore related in his opening remarks on Tuesday, when the two had finished with Darwin, they were left with a nagging question: Given Darwin’s reclusive, gentlemanly, and non-confrontational personality, what could possibly have motivated him to produce and publish a theory so guaranteed to bring conflict down upon his head? In his talk on Tuesday, Moore presented his answer, explained in rich detail in Moore and Desmond’s Darwin’s Sacred Cause (2009).

                         

                        “Why did Darwin risk his reputation to promote an heretical theory?”

                         

                        Moore argues that it was Darwin’s hatred of the institution of slavery, instilled in him from early childhood that provided the motivating passion behind the scientific breakthrough. Through expert use of textual and visual materials, Moore led the audience through a brief overview of Darwin’s progress toward his theories of evolution through natural selection and the descent of man and sexual selection from the point of view of his connections to the world of anti-slavery activism.

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                          Mapping the Universe with Robert Fox

                          May 8th, 2013
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                            by Laura Cray*

                            23793_1As a self-professed library nerd, I was excited to attend Robert Fox’s lecture, Mapping the Universe of Knowledge, on Monday, May 6, 2013.  The lecture focused on work of Paul Otlet, Henri La Fontaine, and Hendrick Christian Andersen and their vision for a world united by knowledge.  Robert Fox is professor emeritus from Oxford University and currently visiting Oregon State University as this year’s Horning Visiting Scholar.  Monday’s lecture was the first installment in his three part series of lectures entitled, Science International: Universalism and National Interest in the Industrial Age.

                            Having spent most of my life in the age of Google, I think that it is easy to take Otlet’s vision for the Bibliographic Institute founded in Brussels in 1895 for granted.  But, his incredibly detailed Universal Bibliographic Repertory (a variation of the Dewey Decimal System) and the over 15 million entries in his card catalogue represent a vision which extended far beyond his ordered library shelves.  As Fox argues, Read the rest of this entry »

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                              Mina Carson’s new book: Ava Helen Pauling

                              April 24th, 2013
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                                Congratulations to Mina Carson, whose biography of Ava Helen Pauling provides a long-awaited study of a crucial yet often-neglected figure in the history of science and peace activism.  Among its many merits is how well the book highlights the rich collections we have at Oregon State University.  Here’s the book the description.  It is so wonderful to see this book come to fruition.  Thank you, Mina Carson!

                                The story of Ava Helen Pauling—her rich career as an activist first for civil rights and liberties, then against nuclear testing, and finally for peace, feminism, and environmental stewardship—is best told in the context of her enduring partnership with her famous husband, Linus Pauling. In this long-awaited first biography of Ava Helen Pauling, Mina Carson reveals the complex and fascinating history behind one of the great love stories of the twentieth century. Read the rest of this entry »

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                                  Exploring SCARC: Lavoisier’s Traité élémentaire de chimie

                                  March 26th, 2013
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                                    by Kelsey Kennedy

                                     

                                    Oregon State’s Valley Library is home to many resources, including the Special Collections and Archives Research Center (SCARC). There, students (and the curious-at-large) can find archives covering the university’s history, as well as a number of rare books, many of which are notable in the history of science. The two volumes of Antoine-Laurent Lavoisier’s Traité élémentaire de chimie (originally published in 1789) are among these delicate old tomes, and these books provide an insight into the beginnings of modern chemistry. Read the rest of this entry »

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                                      Reflection: Archambeau and the Voice as a Vessel of Healing

                                      March 13th, 2013
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                                        Reliquaries of St. Elzéar and Bl. Delphine

                                        by Tracy Jamison*

                                        Words are potent. Words can awaken memories, stir emotions and quiet the mind. Words have been used in the creation of groundswells that burst forth to bring down stalwart walls of injustice as well as to buttress vast empires: Word-for-word, Brick-by-brick. In her lecture, Dr. Nicole Archambeau examined the concept of the voice as a relic. How ‘mere words’ of admittedly melodic meter, manifested within the human body, and alleviated physiological and psychological distress during an era rife with mercenary invasions that razed fifteen cities,  populations forced to languish under waves of plague and that eventually saw the erosion of the Treaty of Brétigny and the continuation of the Hundred Years’ War.

                                        After parsing through medieval canonization inquests and Articles of Interrogation in order to divine how people foresaw and negotiated the curative continuum from medico to physico in their attempt to heal and restore the spirit, Dr. Archambeau chose the life of Delphine of Glandèves, more commonly known as the Blessed Delphine, as a paragon of 14th century healing pluralities. Delphine was a countess who was alleged to have the ability to mediate miracles through the melodic meter of her voice. As a miracle mediator, Delphine offered a distinctive healing option from the ‘despairing doctor trope’ that did not sanction the giving of false hope to those suffering from illness. The wife of newly canonized Saint Elzéar of Sabran, Delphine was not a doctrinaire and did not tout that she possessed any medicinal knowledge. Nevertheless, during her canonization inquest, Master Durand Andre testified that through her voice, Delphine touched him from the inside and he felt contrition, compunction and consolation.  As Archambeau articulated in her lecture, witnesses for Delphine’s candidacy for canonization related to the papal court that Delphine ministered miraculous healing that actively managed the care of their soul, a vital part of personal health. Read the rest of this entry »

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