The Value of Mathematical Archives, Volume 50, Number 11

The Value of Mathematical Archives Steve Batterson with Charles Curtis, Albert Lewis, and Karen Parshall Archives are indispensable resources to scholars Karen Parshall on James Joseph Sylvester in many disciplines. It is at such repositories that In 1870 one of the two most renowned mathe- the papers of Thomas Jefferson and William maticians in England, the fifty-five-year-old James Faulkner are stored. Unpublished materials, in- Joseph Sylvester, found himself out of a job; the cluding correspondence and manuscript drafts, regulations governing the Royal Military Academy, Woolwich, where he had held the professorship of may reveal important insights that are not appar- mathematics since 1855 had just been changed to ent in published works. Thus it is understandable prohibit any civilian over the age of fifty-five from that colleagues in the social sciences and human- holding a teaching position at the school. Sylvester ities rely on archival study to advance their re- spent the next five years unemployed and living off search. The case for mathematical archives may of his pension in London, but he was restless and seem less compelling, especially since few mathe- eager for another position in mathematics. In the maticians have ever ventured into an archive. Yet winter of 1875 the London newspapers carried the papers of John von Neumann, G. D. Birkhoff, news both of the death of the professor of math- and other leading mathematicians are readily avail- ematics at the University of Melbourne and of the able. search for his replacement. Writing to his friend, The purpose of this article is to promote the do- Arthur Cayley, England’s other most renowned nation and use of archival material by mathemati- mathematician, Sylvester confessed to being “more than half inclined to go out to the Antipodes rather cians.1 Below are three accounts, by Karen Par- than remain unemployed … in England” [4, shall, Charles Curtis, and myself, of how page 144]. It would have been a very bold move for unpublished records have contributed to studies the sixty-year-old Englishman, but he had a clear in the history of mathematics. sense of life not yet fulfilled. —Steve Batterson By the summer of 1875 news of more job open- ings, this time in America at the newly forming Steve Batterson is associate professor in the department Johns Hopkins University in Baltimore, reached of mathematics and computer science at Emory Univer- sity. His email address is [email protected]. England. Sylvester’s friends both at home and in the United States wrote to the University’s presi- 1This article grew out of the meeting of the AMS Archives Committee in Baltimore in January 2003. The members dent-designate, Daniel Coit Gilman, with their unan- of that Committee are Steve Batterson, Robert Daverman imous recommendation for the professorship of (ex officio), Albert Lewis (chair), and Karen Parshall. mathematics. Joseph Henry, the first Secretary of Karen Parshall is professor in the departments of history the Smithsonian Institution and a friend since and mathematics at the University of Virginia. Her email Sylvester’s first sojourn in the United States in the address is [email protected]. 1840s, described Sylvester to Gilman as “one of the DECEMBER 2003 NOTICES OF THE AMS 1409 very first living mathematicians”, Hopkins on the international mathematical map. one whose “appointment would These successes did not come without their prices, give a celebrity to the institution however. which would at once direct to it Sylvester could be difficult. In February of 1881, the attention of the whole scien- he blew up at his teaching associate and the asso- tific world” [5, page 72]. Like ciate editor of the American Journal, William Story, Henry, Benjamin Peirce, the and in taking the matter to Gilman, blew up in the Perkins Professor of Astronomy president’s office, too. That fit brought a stern, and Mathematics at Harvard and written rebuke from Gilman. “I have always in- another longtime friend of tended to treat you with the respect due to an hon- Sylvester’s, knew that Gilman was ored colleague,” Gilman stated, “but I must refuse in search of proven researchers to be again exposed to such a scene as occurred in Photo printed with permission of Johns Hopkins Photo Hopkins Johns of permission with printed Photo who would train future re- my office on Thursday for no business can be Archives. searchers and in so doing make transacted wisely when either party is excited” [4, James Joseph Sylvester a name internationally for the page 199]. Eighteen months later Sylvester was new university. Peirce minced no once again displeased, but this time with Gilman’s words in telling Gilman that handling of an invitation to Lord Kelvin. In a letter Sylvester was the mathematician for the job, at dated 10 August 1882, Sylvester carped about the the same time that he was not the teacher for the invitation before dropping a bombshell on the un- undergraduate classroom. “[A]s the barn yard fowl suspecting president. “I am wearied and dispirited cannot understand the flight of the eagle,” he ex- and feel no longer equal to the discharge of what plained to Gilman, “so it is the eaglet only who will I consider to be the duties of my office in a man- be nourished by his instruction…. Among your ner satisfactory to myself or conducive to the best pupils, sooner or later, there must be one, who interests of the University,” Sylvester stated. “I has a genius for geometry. He will be Sylvester’s spe- write therefore (after much anxious deliberation) cial pupil—the one pupil who will derive from the to request that you will take the first opportunity master, knowledge and enthusiasm—and that one to lay my resignation before the Board of Trustees pupil will give more reputation to your institution to take effect as soon after the 1st of October next than the ten thousand, who will complain of the as may be found not too inconvenient” [4, obscurity of Sylvester, and for whom you will pro- pages 209–210]. Sylvester, debilitated by the heat vide another class of teachers” [5, pages 73–74]. and humidity and depressed by the fact that he had After personal interviews in London, Gilman remained in the United States for the first summer had settled on Sylvester as his choice for the pro- since he had taken the job at Hopkins, had clearly fessorship of mathematics by the late fall of 1875, overreacted. Several carefully penned letters from but the mathematician played hardball. Writing on Gilman, who had become Sylvester’s personal friend 17 December 1875 in response to an official letter in the years of their professional association, from the Hopkins Board of Trustees, Sylvester ac- calmed and heartened the mathematician. The cri- cepted the University’s offer only “if the $5,000 sis was averted. salary therein named be understood to mean gold Not even this brief sketch of Sylvester’s associ- and if a house and the club fees be attached to [his] ation with Hopkins would have been possible with- appointment” [4, page 150]. Sylvester had been out archives. Sylvester, never very organized, made burned financially by the Royal Military Academy, no provisions for his papers at the time of his and he was not about to take a financial risk in ad- death. The relatively large collection of his letters dition to the risk he would already be taking in mak- that exists at his alma mater, St. John’s College, ing a transatlantic move. After numerous telegrams Cambridge, is there only because Cayley was or- and letters back and forth across the Atlantic in Jan- ganized, because Susan Cayley, his wife, preserved uary and February and after at least one with- them after Cayley’s death in 1895, and because after drawal of his acceptance of the post, Sylvester and her death they fell to the mathematician W. W. the Hopkins authorities agreed on Sylvester’s terms, Rouse Ball, who saw to their deposition. Without and the Englishman made a move not to the An- these letters, we would have no hint of the lengths tipodes but to Baltimore in the spring of 1876. He Sylvester considered going to—literally the other was once again gainfully employed, and this time side of the globe—in securing another job in acad- he had the chance, for the first time in his career, eme. If the letters Cayley saved were all that re- to train students at the graduate level. mained, moreover, we would know little of Sylvester’s seven-and-a-half years at Hopkins were Sylvester’s stay in Baltimore beyond the mathe- a marked success. Nine of the “eaglets” Peirce envi- matics he worked on while there. Gilman’s presi- sioned completed their doctorates under Sylvester’s dential papers, held at the Johns Hopkins Univer- influence; the American Journal of Mathematics began sity, contain everything from letters of in 1878 under Sylvester’s leadership; Sylvester put recommendation like those from Henry and Peirce 1410 NOTICES OF THE AMS VOLUME 50, NUMBER 11 to correspondence to and from individual faculty impressions of Frobenius, Burnside, Schur, and members like Sylvester to letters of application Brauer as persons and how their mathematics fit- from potential students and annual reports from ted into their lives. For this I needed to consult graduate students on their progress in their pro- archives containing their personal records, corre- grams. The Sylvester letters there represent a major spondence, etc. cache that allow us to flesh out not only Sylvester The first item of correspondence available to me the professor of mathematics but also to glimpse, that hinted at what might be found in the archives in ways not possible through published mathe- was a letter about Burnside from W.

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