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Home , Denison Olmsted, Elias Loomis, Hubert Anson Newton, Joseph Liouville, Josiah Willard Gibbs, Mathematician

The Father of the Father of American Steve Batterson

t the turn of the twentieth century, of mathematics in 1855. Another five years later University of Chicago Yale began the first Ph.D. program in America. As E. H. Moore supervised three doctoral himself never earned a Ph.D., he may be students who went on to lead the regarded as both the root and the grandfather of to its standing as an American mathematics. A Some of Newton’s accomplishments are known. international center for mathematical . Moore’s students Leonard Dickson, Oswald Veblen, When the National of was and George D. Birkhoff were the first domestically incorporated in 1863, he was one of the initial cultivated Ph.D. recipients (other than their advi- 50 scholars invited for membership. Moreover, sor) to attain distinction through their mathemat- Newton was the confidant and sounding board for ics and their academic progeny. E. H. Moore’s role J. Willard Gibbs, the greatest American of in this chronology has earned him the appellation the nineteenth century. Most of Newton’s own re- search involved the study of meteors and comets. “father of American mathematics” [1]. In 1895 he became vice president of the American The biography and achievements of Moore are Mathematical Society. well documented [2]. Less accessible is informa- Hubert Newton died in 1896. His associations tion on Hubert A. Newton, Moore’s advisor at Yale with Moore, Gibbs, the first American mathemat- University [3]. Newton received a B.A. from Yale in ics Ph.D. program, and the National Academy of 1850 and became the institution’s only professor Sciences make Newton an intriguing figure in the Steve Batterson is associate professor of mathematics and history of American . This article employs computer science at Emory University. His email address archival materials to flesh out Newton’s develop- is [email protected]. ment in the context of the meager intellectual Partial U.S. Mathematics Family Tree

Adrian Albert Alonzo Church Marshall Stone Chicago 1928 Princeton 1927 Harvard 1917 Harvard 1932 Harvard 1926

RL Moore Chicago 1905

Leonard Dickson Oswald Veblen GD Birkhoff Chicago 1896 Chicago 1903 Chicago 1907

EH Moore Yale 1885

Hubert Newton

352 Notices of the AMS 55, 3 opportunities present in mid-nineteenth century United States. I am grateful to Diane Kaplan and the Yale archives staff for kindly helping me to locate let- ters and records at the Memorial Library. I thank Ellen Neidle, Michele Benzi, and Albert Lewis for reading an early manuscript draft and offering their suggestions and encouragement. Conversations with David Borthwick clarified the celestial .

Becoming a Mathematician in the 1850s was born in the central town of Sherburne on March 19, 1830. His parents, William and Lois Butler Newton, were descended from families that migrated from England to the United States in the seventeenth century. William’s father, Ashael Newton, fought in the Revolutionary War. When William’s woolen factory was destroyed by fire for the second , he became a contractor for the construction of the Erie Canal and other projects. Eventually the New- University. Yale Archives, and Manuscripts 686). (RU 1879–1989 University, Yale Affairs, tons acquired a farm in Sherburne where Hubert Public of Office the by maintained individuals affiliated Yale of Photographs #11811: MADID was the ninth of eleven children. In January 1847 Hubert followed his older Hubert Newton. brother Isaac to Yale. Living Yale alumni would not recognize the program then in place at their the Junior Exhibition when the better students alma mater. Entering class enrollments numbered were selected to deliver orations and dissertations. about 100 [4]. Attrition was high. Students were Although Newton was a dedicated member of a required to begin their day in the chapel at 6:30 for debate society, he was not a scintillating speaker. prayers. Recitation classes immediately followed One contemporary account mentions “a certain the worship. The undergraduate college faculty hesitation of speech and slowness of utterance” consisted of just the president, seven professors, and a similar number of recent graduates who held [4, page 397]. Nevertheless, Newton delivered an the title of tutor. The curriculum was heavy in Latin oration entitled “India” at the Exhibition. The text and Greek with emphasis on rote learning. of his presentation is available in the Yale archives. All students took the same sequence of courses To a modern reader Newton’s well written narra- through the middle of their junior year. The of- tive reeks of ethnocentrism and condescension: ferings in mathematics were at a low level and “there are indications that show a bright and glo- had remained largely unchanged over the prior rious day to be near. The time when the Hindoos quarter century. Topics included , , shall be freed from idolatry and become a Christian trigonometry, navigation, conic sections, spherical nation cannot be far distant” [5]. geometry, and mechanics. was among the For Newton and the Class of 1850, their senior options available to students for their first elective year took place with Zachary Taylor as United opportunity which arose at the end of the junior States president, California seeking to become year. Most students selected a modern language the 31st state, and talk of southern secession in instead. the air. The complex struggle over slavery was Hubert Newton was a strong, but not excep- focused on the prospect of California tipping the tional student. Despite joining his classmates in delicate Congressional balance between free and the middle of their first year, Newton shared the slave states. Such current issues drove the topics freshman mathematics problem-solving prize. for the debate societies. One week Newton as- In his sophomore year Newton was the outright siduously prepared his position on the political winner. No further prizes were awarded, perhaps compromise proposed by . The next because study of the subject was essentially com- week he readied an argument over whether the plete. dissolution of the Union would be more injurious Most Yale students were destined for legal or to the North or the South. theological careers. Between the importance of In a letter to a cousin on March 23, 1850, Newton honing oratorical skills and the absence of athletic discussed college activities, family news, and his and other campus diversions, debate societies future plans [6]. Two other cousins were among flourished. Well into the third year of study came the drawn to California by the recent gold

March 2008 Notices of the AMS 353 strike. One was in the “diggins” and the other sessions of 1850–51 were an especially bad time was in Panama making the overland trip between for Newton or for anyone to study mathematics at the major boat voyages. Newton was skeptical of Yale. Stanley, still the only mathematics professor, his relatives “realizing a very enormous was debilitated with . Over the year fortune.” he would travel the world seeking a climate to The debate preparations and his facilitate his recovery [9]. studies had worn Newton out. He After his graduation Newton returned home to was looking forward to graduation Sherburne. Having decided to pursue mathemat- on August 15, expecting to stand ics further, he sought advice from Olmsted over about fifteenth in his class. The how to proceed. Only Newton’s November 1, 1850, Yale calendar provided a vaca- reply survives of their correspondence. That Ol- tion for seniors in July and Au- msted raised the possibility of study at Yale, or gust, except for those preparing elsewhere, may be inferred from the context of addresses at commencement. Newton’s words: With none of his friends planning to attend the ceremony, Newton I have pretty much concluded to pursue was inclined to select leisure over my studies at home this winter. I ought an oratory opportunity on the po- to look over a part of the mathematical dium. studies of the College course. There are As for his future plans, Newton also some books which I think I can had only ruled out joining the gold rush. read with nearly the same advantage He wrote to his cousin: “What I shall do here as elsewhere. These are elemen- . after graduation I do not know. I may tary mathematical books which I have prepare to teach. I may study theology— not studied. I am now reading Analyti- perhaps shall study . I hardly think I cal Geometry. These books I ought to shall be a lawyer though I may.” Notably absent, understand to receive the most benefit from today’s point of view, is any consideration from a teacher. Such reading would of of obtaining a Ph.D. The explanation is simple. In itself be too dry and for a change I shall 1850 no American university offered a doctoral read books upon the Natural Sciences. degree. Yale, however, had recently taken a step Afterwards I expect to avail myself of in the direction of graduate education. the direction of a teacher…If I can have Yale consisted of its undergraduate college, a good offer to teach I may yet accept divinity, law, and medical schools [7]. For many it. But unless it was a good one I shall years some Yale graduates had remained on cam- refuse [10]. pus to continue, informally, their studies of Greek and other college subjects. Meanwhile interest It is notable that Newton recognized the im- was increasing in applications of sciences such as portance of further mathematical training. He that were largely outside the traditional continued his reading at home, returning to New undergraduate curriculum. In 1847 Yale created a Haven in May 1851. By this time Stanley was on MADID #10594: Images of Yale individuals, ca. 1750–1976 (RU (RU 1750–1976 ca. individuals, Yale of Library. Images University #10594: Yale MADID Archives, and Manuscripts 684). Department of Philosophy and the Arts to provide his way back from Egypt, but there was little hope courses for both constituencies. The staff con- that he could resume his duties. Quiet discussion sisted of two new together with profes- was under way concerning the contingency of a sors already on the university faculty. vacancy in the mathematics chair. Olmsted had in mind James Hadley [9, page 290]. Hadley was a Although the Department of Philosophy and brilliant young Greek professor whose wide rang- the Arts would evolve into a , no degrees were initially offered. The Master of Arts, ing expertise included mathematics and Sanskrit. authorized in the founding of the college in 1701, These circumstances led to a meeting between remained under the control of the undergraduate Newton and Hadley that Hadley described in his division. To obtain an M.A. a Yale student merely journal: needed to wait three years after his B.A., pay five Friday, May 9…Newton, class of ’50, has dollars, and, “in the interval, have sustained a good come to New Haven to study mathemat- moral character” [8, 1856–57]. ics—with me, if he can. Should like to In its first year the Department of Philosophy hear him, but believe it is impossible. and the Arts advertised calculus and analytical My new textbook in history, my Greek mechanics among its offerings. These courses optional, my labors in two biennial were to be taught by Anthony Stanley. Stanley had examinations and in that for the Wool- become Yale’s professor of mathematics in 1836 sey scholarship, and besides all, the when Denison Olmsted’s responsibilities changed claims of a courtship nearing its close from mathematics and natural philosophy to will leave me little time for a study so natural philosophy and . The academic arduous.

354 Notices of the AMS Volume 55, Number 3 Saturday, May 10…more of the time found himself in charge of the entire mathematics talking with Newton, whom I had seen program at Yale. at 9. He will study by himself, French Newton had taken an important step toward an first and afterwards mathematics. Ad- academic career. Stanley, Olmsted, and Hadley each vised him to procure Moigno’s Calculus had apprenticed as tutors at Yale prior to obtaining [9, page 214, 215]. their professorships. However, with vacancies in a particular chair arising once a generation or so, In the mid-nineteenth century the best advanced only an exceptional tutor with fortunate timing mathematical texts originated in . For an had any realistic expectation of promotion. Many American student a reading knowledge of French tutors went on to careers outside the academy. was essential. Hadley’s Friday entry indicates a Some obtained positions at other colleges. Olmsted desire to take Newton on as a student. Courtship taught at the University of North Carolina for eight may have been the decisive obstruction. Hadley years before being called back to Yale. had recently become engaged. He and his fiancée Anthony Stanley died in the of 1853. had just begun seeing each other every day. The For a replacement, Yale would want the leading injection of Hadley into the story demonstrates mathematician from their alumni. On this the dearth of mathematical expertise in America. Newton’s few months of experience as tutor Yale was one of the best universities in the United paled in comparison to the credentials of William States. Yet their second authority on mathematics Chauvenet and Theodore Strong from the classes was a 30-year-old full time Greek professor. of 1840 and 1812 respectively. Chauvenet had Hadley recorded one further meeting with New- been instrumental in the recent founding of the ton. It occurred later in the summer of 1851. The United States Naval Academy where he was the entry mentions that Newton was studying a book professor of mathematics and astronomy. More- by the French mathematician Jean-Marie Duhamel. over, Chauvenet had written a highly acclaimed In the fall Newton returned to Sherburne. It is un- textbook on trigonometry. Strong was a math- clear how he was supporting himself. Perhaps New- ematics professor at Rutgers. He had published ton relied on his family or worked on their farm. In research, but was nearing the age of 63. the second year after graduation he followed the The Yale mathematics chair was offered to same routine of study as in his first, remaining at Chauvenet who decided to remain at the Naval home until May and then going to Yale. Academy [11]. In his declination letter Chauvenet While Newton was in Sherburne, Stanley aborted explained that the question was “so nicely bal- an attempt to return to the classroom. The tuber- anced that it required but little to turn it either culosis was headed into a terminal stage. Hadley way.” He went on to leave the door open by stating moved into the breach to handle calculus in the “that some of these [reasons] which have weight summer of 1852. By this time the college catalogue with me at the present are of a temporary charac- lists Newton as a student in the Department of ter.” The position would remain unfilled as Newton Philosophy and the Arts. Although there is no soldiered on with the responsibilities of a profes- record, it is likely that Newton took calculus from sor, the standing of a tutor, and an opportunity Hadley in 1852. to impress. The situation in mathematics at Yale was unten- Today, a young mathematician is advised that able. Stanley was unable to teach. Hadley, whose research, publication, and networking are the sur- real love was Greek, had a full plate of other est paths to advancement. The 1853 culture was responsibilities. Yale needed another teacher to vastly different. The notion of a mathematics pro- cover the mathematics instruction. Tutors were fessor doing research was, literally, foreign. In the always recruited from the best recent graduates. entire country only Strong and Benjamin Peirce, at Newton’s mathematics prizes and two years of Harvard, were committed to research. Stanley and subsequent study gave him a solid resumé, even Chauvenet had attained their standing by being if he were not a valedictorian or salutatorian. In knowledgeable and writing textbooks. July 1852 Newton accepted a tutorship. The annual In 1853 no mathematics journal existed in the salary was $550 (professors received $1,300). United States, nor was there any community of Tutors held temporary positions that normally , either locally or nationally. Never- lasted a few years. Among the tutors there was theless, societies promoting scientific scholarship a seniority system under which the newest hires functioned effectively at both levels. The Connecti- taught the courses left over after all others made cut Academy of Arts and Sciences was established their selections. Thus a new tutor with a specialty at the beginning of the nineteenth century. In in mathematics might be stuck with conducting Newton’s time the Academy was essen- Latin recitations. Whether through luck or a special tially a of Yale faculty that periodically hosted concession to the needs of the college, Newton scientific discussions in their homes. Linkage to a got mathematics when he assumed his duties in wider geographic community came in 1848 with January 1853. Moreover, at age 22, he immediately the founding of the American Association for the

March 2008 Notices of the AMS 355 Advancement of Science (AAAS). The fourth AAAS courses at the Sorbonne. As might be expected, meeting was held in New Haven in 1850, bringing Newton encountered some surprises upon arrival. to town the American scientific elite of Joseph On November 28 he wrote to the Yale treasurer Henry, , Alexander Dallas Bache, and librarian, Edward Herrick, with this update Benjamin Peirce, and Benjamin Gould. on his classes: Tutor Newton took advantage of these oppor- For the last two months I have been tunities, participating in the activities of both the at Paris waiting for the lectures to Connecticut Academy and the AAAS. In July 1853 commence and employing the time he traveled to the semiannual meeting of the AAAS quite profitably in learning the spo- in Cleveland. There he met Benjamin Peirce. New- ken language of France. The lectures ton described some he had done in spherical commence two months later than I trigonometry on the effect of the ’s was informed—those at the Collège on an orbiting body. The conversation with Peirce de France beginning next Monday. Of led to Newton’s first publication [12]. The one-page the 11 courses of scientific lectures at paper, and a later revision, appeared in Gould’s the Sorbonne but three or at most four recently established Astronomical Journal. are worth my while to attend. At the In 1855 Newton, with this single publication, Collège de France there may be two or became the Yale Professor of Mathematics. At the three more which would make about age of 25 he was slightly younger than Stanley two lectures a day. I cannot remain here and Hadley when they received their permanent through these courses and how long appointments. It is unclear what deliberations the I shall remain here after I have fairly administration conducted during the two years seen and understood the men is yet to that elapsed after the original offer to Chauvenet. be decided. Perhaps they hoped that Chauvenet would change his mind, or possibly they were waiting to become Chasles has done an excellent work convinced of Newton’s suitability for the posi- in reducing to a system the modern tion. labors in the higher Geometry. He has published a “splendid” upon The 1855 European Experience it and gives also an interesting course There was little more that Hubert Newton could of lectures. Lamé lectures upon the then do in the United States to reach the frontiers Math. Theory of and gives a very of mathematical research. The latest discoveries profound discussion of the subject. and their exposition were taking place in Europe. The lectures of Sturm and of Cauchy I Although a transatlantic voyage was then a miser- have attended thus far for the two-fold able two-week ordeal, it was not unusual for Yale reason—to see the men—and in hopes students to make the journey for further study. they would soon leave the elements. In 1854 a few recent graduates were in Germany Duhamel, Lefébure de Fourcy, Delau- and writing back of their experiences. Letters from nay—I have dropped [13]. Europe circulated around the Yale campus [9]. The Newton’s enthusiastic report on exotic descriptions of educational opportunities and Gabriel Lamé to Herrick contrasts with this would naturally have made an impression on the gloomy excerpt from his letter the previous day to ambitious Newton. The next step for him was to his college roommate John Brewer: learn at the feet of the Parisian savants from his texts. This morning after taking a cup of cof- Fortunately for Newton there was a precedent. fee and a crust of bread (in France the His predecessor Stanley had been permitted bread is all crust) I considered more or to defer his duties in order to study in Europe. less attentively some propositions in Newton’s request for a one-year leave was granted Geometrie Superieure until 10 o’clock with the stipulation that the compensation for a when I took my breakfast. At 10 1/2 replacement come out of his $1,600 salary [15, was a lecture. I was there 10 minutes July 1855]. Newton planned his year of European late and waited five minutes for the travel to begin with extended study in Paris. Other prof. The lecture room does not com- Yale people had spent time in France, but their pare with ours for comfort there being academic experiences were largely restricted to no backs for the seats and no alley so nonmathematical subjects at German institu- that to reach the front seats we walk tions. Despite the limited information resources down stepping on the seats. A clumsy of 1855, Newton would have known some of the arrangement that. The Prof. has so far French names. held the mathemat- been uniformly late. Perhaps his watch ics chair at the Collège de France while Duhamel is slow. It must run too slow he finished and Augustin Cauchy were among those giving about 1 3/4 hours after the time for the

356 Notices of the AMS Volume 55, Number 3 beginning. But here he comes. He is a later Newton and Adams would both contribute to man about 65 a little more probably. the prediction of meteor showers. He has a raw beefy looking counte- That Newton and Herrick shared an interest nance and his appearance otherwise is in astronomy provides some explanation for the not much different as he need not be extended discussion of this topic in ashamed to place himself on the other the letters. Still it is striking that beam of the scales from Mr. Skinner. Newton so aggressively sought He certainly does not give his personal out telescopes throughout countenance to the remark I have heard his trip. He had previously made that Mathematicians are spare visited an observatory in and skeleton–like…he stands sideways. Paris. With one hand in his pocket he chalks out diagrams and formulas with the Newton went from other. He never looks up at the class. I England to Italy. The mistake, he did once look up and the Italian itinerary included expression was so ludicrous that we Rome, Naples, Florence, could not help laughing. In time he fin- and Venice. Aside from ished. That is at the close of one of his an observatory in Rome, sentences without changing his manner it seems that his activities or looking up he closed a book he had consisted of sightseeing

on the table walked towards the door and viewing museums and Library. Andrews St. of University the of courtesy Photograph and taking his hat stepped out while galleries. Newton was espe- cially impressed by Florence. In we waited to hear the next sentence. We looked at the spot where he disap- May he reached Vienna where he peared then at each other then laughed wrote his last letter to Herrick. At this then concluding the lecture was over point Newton was planning to remain disbursed. This lecturer is [obscured in Vienna for at least a month, visit some German word] one of the greatest mathemati- cities, and then return to America in August. He did cians in all Europe [14]. make contact with fellow alumnus and tutor, Timo- thy Dwight, who was studying in Bonn and . The obscured word in the last sentence is pos- In his own memoir Dwight, a future president of sibly “Sturm”. At this time Sturm was just 52 years Yale, mentions that he and Newton were “traveling old, but three weeks from his death. Cauchy was companions” for “a short time” [4, page 395]. 66. Newton went on to describe more of his day. Establishing a Research Program In the afternoon he watched the Emperor, Louis Napoleon, review his troops. The “pageant” of With his return to Yale in 1856, Newton took up “helmets and plumes, cannon and bayonets, horses his duties as professor of mathematics. Meanwhile, and men” made for a “sight [that] was truly splen- inspired by Chasles’ synthetic approach to projec- did.” Newton felt “fortunate in having witnessed tive geometry, Newton continued his own study the parade,” but uneasy with his first close encoun- of the subject. A key technique was the principle ter with militarism. The “bayonets are the empire of polar inversion which transforms points and and make the peace of Paris. God grant we may curves into other points and curves with similar never need (I will not say have) such an empire, or intersection properties. Newton considered the such a peace in America. …I am glad we have no problem of constructing a circle tangent to three army. I had rather enter upon a war unprepared given circles. If two of the given circles intersect, if necessary than to support in peace as France Newton employed the inversion approach to re- does 500,000 men in going through unprofitable duce to the situation of finding a circle tangent to evolutions and tempting our powers that be to another circle and two lines. Although the solution bring on a war.” of the general case was already known, he had Information on the remainder of Newton’s year found a nice alternative construction. abroad is based largely on two subsequent letters As with the publication of his earlier paper on to Herrick [13]. In February Newton went to Eng- orbital mechanics, Newton’s timing was fortuitous. land for three weeks. His description of this period For much of the nineteenth century there was no is dominated by accounts of visits to observatories American mathematics journal. However, Newton’s at Greenwich, Kew, and Cambridge. At Cambridge geometric discovery coincided with the founding Newton enjoyed an informative conversation with of the short-lived The Mathematical Monthly. His the British astronomer John Couch Adams. Ten solution to the circle problem appeared in vol- years earlier Adams had predicted the existence of ume 1. Two years later Newton followed up with the planet Neptune through calculations based on a more substantial contribution to the third (and irregularities in the of Uranus. Ten years last) volume of the journal. This paper described

March 2008 Notices of the AMS 357 and extended Chasles’ intricate straight edge con- with a comet-like nebulous body that was moving structions for obtaining points on curves that are in a different elliptical about the sun. He set stipulated by certain specified data (such as a conic out to determine the ellipse, relying on a mistaken with given points, intersections, or tangencies). inference that the nebulous body was at aphelion Between the printing of the two geometry pa- (maximum distance from the sun) when meeting pers, Newton published an article on a different the Earth. Olmsted then looked for a feasible orbit subject. In 1860 his “On the meteor of November that both intersected and was shorter than that of 15th, 1859” appeared in the American Journal of the essentially circular path of the Earth. In the in- Science and Arts. Others had previously provided vestigation of the 1833 shower, historical accounts detailed accounts of sighting the meteor from vari- surfaced of a similar event in South America on ous eastern locations in the country. Newton col- November 12, 1799. One year earlier, on the same lated the data and used triangulation techniques day in 1832, another shower had been observed to calculate the visible path of the meteor. The from the Red Sea. underlying objective of his study was to infer the Olmsted pondered an elliptical orbit that revis- backward trajectory of the meteor’s orbit. To do ited the same point after one year and 33 years. To this he posited a lower bound for the body’s veloc- accomplish the former he reasoned that the body ity based on the observers’ estimates of the time must complete an integer number of revolutions that elapsed while the meteor was visible. Newton each year. By Kepler’s third law, for an orbiting then went further, making the dubious assertion: body the cube of the length of its semimajor axis “The result of my investigation has been to estab- is proportional to the square of the period. Using lish almost beyond a doubt the conclusion, that units of years for the period and astronomical this body was not a member of the solar system but units for the semimajor axis, the proportionality came to us from the stellar regions.” factor is one for about the sun. Since the Publishing research, rather than textbooks, semimajor axis must be at least one half for the was very unusual for an American mathematics orbit of the nebulous body to reach that of the professor in 1860. Newton would continue to do Earth, the period must be greater than the square so, writing over 40 papers on meteors and comets. root of one eighth. But the period was assumed to He is best known for his work, described below, be the reciprocal of an integer, forcing it to be at on the November Leonid showers. Meteors had least one half year. Since he believed that the orbit long been the subject of considerable interest at was inside that of the Earth, Olmsted concluded Yale. The fascination began in 1807 when a bright that the period of the nebulous body was one half overhead explosion of a meteor prompted Yale year. scientist Benjamin Silliman to perform an analysis Verification of Olmsted’s theory could be pro- on specimens recovered from the event. One de- vided by showers on subsequent annual anniver- cade later Silliman founded the American Journal saries. Each November Olmsted enlisted a cadre of Science and Arts. A spectacular meteor shower of students and enthusiasts to watch the sky and on November 13, 1833, attracted the attention of record data on shooting stars. For the next several professor Denison Olmsted and members of the years possible recurrences were observed, albeit Connecticut Academy. Silliman’s journal became in much smaller and diminishing intensity. By a vehicle for accounts of observations and for the 1838 even Olmsted had to admit that a shower proposal of theories about meteors. probably had not occurred [17]. Still he continued Little was understood about the origin, mecha- the annual vigil. The thread arose in his 1850 cor- nism, and orbits of meteors. Occasional shoot- respondence with Newton. Olmsted arranged for ing stars of varying intensities were well known his former student to observe the Sherburne sky to stargazers. What set apart the early morning on the morning of November 13 [10]. November 13 event was the extraordinary sight Olmsted died in 1859, about the time that of the sky filled with streaks over a two hour Newton began his research on meteors. By then, period. Olmsted set out to provide a scientific ex- Olmsted’s six month period model was out of planation for the phenomenon, publishing a long favor. In the intervening years showers had been article about the shower in the American Journal observed in April and August. Intensive literature of Science and Arts [16]. He began with verbatim searches had identified occurrences in various eyewitness testimonies and followed with his own months over the prior thousand years. The spread analysis. He noted that several observers, including of data was confusing. Were all the showers linked himself, stated that all of the meteors seemed to to a single system? Some claimed that the phe- originate from a common point in the sky toward nomena originated from a terrestrial cause such the constellation Leo. The identification of this as the weather. radiant was a significant step in understanding Examining texts from the Middle Ages was meteor showers. challenging. To fix precise dates often required Olmsted concluded that the shower was the interpretation from contextual references such result of the Earth coming into close proximity as the death of a king or a now obscure holiday.

358 Notices of the AMS Volume 55, Number 3 After making these determinations and converting ring some nonnegative number of . Kepler’s to the current Gregorian calendar, the years of the third law limits the number of revolutions to less

October-November showers were revealing. The than three. Since h33.25​ is the identity, h1​ is either showers clustered around the same three stages , 1 , or 2 revolutions where ​1 . The τ​ ​​τ​ ​​τ​ τ ​ 33​.25 ​ of each century. These were at the 0th year, the corresponding± ± periods are 33.25 years, =354.6 days, 33rd year, and the 66th year. For example, spec- 376.6 days, 180.0 days, and 185.4 days. tacular 1366 and 1202 showers were described in Newton argued that while all five periods were Portuguese and Arabic writings respectively. The possible, 354.6 days was the most probable. He pattern was strikingly consistent with the previ- then offered this program to narrow the possibili- ously known instances of 1799, 1832, and 1833. ties: Accurate coordinates for the radiant (which The one problem was that the day of the month did not then exist) would permit calculation of a moved gradually with the year from November 13, tangent vector to the ellipse and then the plane of 1833, to October 29, 1366, to October 26, 1202. the orbit. This information, together with a period The several-day variation required reconciliation and the intersection node, determine the orbit for with the notion of a fixed point of intersection the two body problem (in conjunction with the from the Earth’s orbit. sun). Corresponding to each of the five hypotheti- In 1863 Newton began to bring some clarity. Both cal periods the perturbations due to the planets the Gregorian and Julian calendars were based on could, in theory, be computed. These results could the tropical year (going from solstice to solstice). then be compared with the known drift of the in- Due to precession of the Earth’s axis, the tropical tersection point. Implementation had to wait for year is about 20 minutes and 24 seconds short of the next shower when a more precise identification the sidereal year which is calibrated by a complete of the radiant could be made. revolution of the Earth about the sun. Thus every Two years later, in 1866, a shower was seen 70 years or so the hypothetical intersection node in Europe on the morning of November 14. John should move ahead a day. Newton converted the Couch Adams, whom Newton had met earlier in earlier shower dates to an 1850 sidereal scale and, Cambridge, then went to work on the hypothetical for the events above, arrived at November 5, 1366, orbits. Adams showed that the four shorter paths and November 4, 1202 [18]. These were closer to were not feasible. However, the effects of Jupiter, November 13, giving a stronger indication of some Saturn, and Uranus on the highly elliptical 33.25 sort of periodic dynamic. year period orbit summed to an excellent fit for Newton put forward his model in 1864 [19]: the drift that Newton had computed [20]. an elliptical ring (annulus) containing the orbits As Adams was performing the formidable calcu- of a nonuniformly distributed collection of small lations in 1867, Giovanni Schiaparelli reported that bodies that are concentrated over a small sector. the bodies generating the annual August showers The sun is one focus of the orbits, but the plane were in the same orbit as a comet first observed is slightly inclined to that of the Earth’s orbit, and in 1862. It was subsequently determined that the the motion is in the opposite direction. The Earth’s Tempel-Tuttle comet was shadowed by the No- orbit intersects the annulus. Showers occur in the vember in its orbit [21]. The apparent years that the Earth passes through the loaded sec- one-to-one correspondence between comets and tor. Newton looked for a periodic orbit where inter- meteor showers raised a chicken or egg question sections could happen for two or three consecutive which was not fully resolved until the middle of the years and then resume after a third of a century. twentieth century. Each time a comet approaches Examination of the data indicated that the show- the sun, particles from it are ejected into nearby ers of 902 and 1833 occurred at about the same clumps. It is the bodies of these dust trails that phase of a cycle. Dividing their difference by the 28 produce meteor showers when they enter the thirds (of a century cycles) they spanned, Newton Earth’s atmosphere. Today, supercomputers track adopted the assumption that each body returned the spread of the orbiting dust trails, projecting to its original location after 33.25 years. future encounters with the Earth [22]. The name for It remained to determine the ellipse and the the November shower, Leonid, follows the conven- prime period of the flow. Newton gave the fol- tion of derivation from its radiant. lowing analysis: Configure the loaded sector to be centered at the intersection node z​ where the First Mathematics Ph.D. in the United orbit meets that of the Earth. For each point x on States? the ring let ht ​(x) represent its position on the ring As Newton began research on meteors, he partici- after t​ years. Now consider what happens after pated in one of the landmark events of American one year. To have another shower z​ must be in higher education. In 1860 Yale became the first the loaded sector. So h1​ maps some other point institution in the United States to offer the doctor of the loaded sector to z​. Then h1​(z​) is near z​, on of philosophy degree. All Yale ’s graduates one side or the other. During the year that z​ moves were eligible to become candidates, as well as oth- to h1​(z​), the orbit of z​ passes through the entire ers meeting additional conditions. Requirements

March 2008 Notices of the AMS 359 for the Ph.D. consisted of two years of study from at least two branches of learning, a final exami- nation, and “a thesis giving evidence of high at- tainment in the branches they have pursued” [8, 1860–61]. At the 1861 Yale graduation, on July 25, Eugene Schuyler, Arthur W. Wright, and James Whiton received the first Ph.D.s ever awarded on Ameri- can soil. Those in attendance could not have an- ticipated how many institutions would adopt their own doctoral programs. As might be expected, many of today’s conventions were not yet in place. For example, neither subjects nor advisors were associated with the individual awards. Separate departments such as , Latin, or history did not then exist at Yale. Newton, as the professor of mathematics, was a member Wright’s Ph.D. diploma. of the Academical Faculty as well as serving in the Department of Philosophy and the Arts, the covered by the professor of natural philosophy umbrella grouping that administered the new and astronomy. With Olmsted’s death, the chair degree. In the twentieth century, with partitioning into disciplinary departments, retrospective as- was vacant during Wright’s first year of graduate collection, ca. 1702–1950 (FU 150). Manuscripts and Archives, . Yale Archives, and Manuscripts 150). (FU 1702–1950 ca. collection, Manuscripts and Archives, Yale University. Photo at right: MADID #6825: Yale diploma diploma Yale #6825: MADID right: at Photo University. Yale Archives, and Manuscripts Photo below: MADID #6272: Images of Yale Individuals, ca. 1750–1976 (RU 684). 684). (RU 1750–1976 ca. Individuals, Yale of Images #6272: MADID below: Photo signments were made of subject to study. In 1860 succeeded Olmsted. earlier degree conferrals. Doubts arose The previous year Chester Lyman became profes- in these determinations under which sor of industrial mechanics and physics for the the “guiding principle” was to have Scientific School. The Scientific School was a sepa- been the “subject of the disserta- rate division of Yale that had been formed around tion” [23]. While not all disserta- the applicable sciences. Members of its faculty tions, or even their titles, had also served in the Department of Philosophy and survived, in most cases there the Arts. Wright was examined on his studies in was considerable information mathematics, modern languages, mineralogy, and about the subsequent career of botany [25]. the recipient. Classifying Wright’s thesis among the fields of Under this process, John astronomy, mathematics, and physics runs into the Worrall (in 1862) and Charles difficulties of ill-defined subject boundaries and Rockwood (in 1866) were iden- overlaps, both of which have shifted over time. It tified as the first recipients of is unfortunate that there are no extant copies of Ph.D.s in mathematics [24]. Both the thesis. Analysis must devolve to the title and went on to careers in mathematics must be placed in the context of the contemporary education. Worrall taught at various research scene. Meteors were not then a topic in Arthur W. Wright. levels in West Chester, Pennsylvania. the mainstream of American astronomy. However, Rockwood became a mathematics astronomy was a most active of mathematics professor at Bowdoin, Rutgers, and in general and American mathematics in particular. then Princeton. Rockwood’s thesis was “The Daily Benjamin Peirce worked on the orbit of Neptune. Motion of a Brick Tower Caused by Solar Heat”. The third and fourth presidents of the American The title of Worrall’s thesis is unknown. Mathematical Society, George Hill and Simon New- Arthur W. Wright was among the three students comb, specialized in . who finished one year prior to Worrall. Wright’s dissertation was entitled “Having Given the Veloc- Newton published papers on meteors in every ity and Direction of Motion of a Meteor on Entering year of the 1860s. Loomis’ limited study of meteors the Atmosphere of the Earth, to Determine its Orbit came much earlier in his career. Lyman was more about the Sun, Taking into Account the Attractions interested in the observational and equipment of Both These Bodies”. Given that Wright served aspects of astronomy. The title of Wright’s thesis over thirty years as a physics professor at Yale, it places the work at the heart of Newton’s current is not surprising that his 1861 Ph.D. was deemed interests. Newton almost certainly served in the, to have been in physics. With further hindsight, not yet defined, role of Wright’s thesis advisor. there is a strong argument that Wright’s degree Considering the examination areas, thesis topic, was actually in mathematics. and faculty of the time, Arthur W. Wright should Wright received his B.A. in 1859 and began be regarded as the first student to receive a math- graduate work at Yale. At this time physics was ematics Ph.D. in the United States.

360 Notices of the AMS Volume 55, Number 3 Wright maintained his interest in meteors. New- the summer the Gibbs were met by Addison Van ton’s 1863 meteor observation reports cite Wright Name, the valedictorian from Willard’s class who as a partner or teammate. At this time Wright held was engaged to Julia. The were married in the title of tutor. Over the next several years he Berlin and returned to New Haven. Anna remained taught Latin and physics to undergraduates. After with Willard in Germany. Over the next a year of study in Germany and a professorship at two years he studied mathematics Williams, Wright joined the Yale faculty in 1872. He and physics from professors that was professor of molecular physics and chemistry included Weierstrass, Kronecker, until 1887 when the designation of his chair was and Magnus. changed to experimental physics. The trip to Europe stands The research interests of Wright and Newton out as one puzzling aspect continued to overlap. Wright analyzed occluded of Gibbs’ insular life. Trans- gases in meteorites and drew implications on the atlantic travel and study in relation between comets and meteoroids. Later he those days required a sort of became a pioneer in X-ray experiments and was initiative that otherwise ap- known for his work on “the deposition of metallic pears to have been absent in films by the cathode discharge in exhausted tubes” Gibbs. The course with Chasles [26]. In 1881 Wright was inducted into the National indicates a connection to New- Academy of Sciences. He died in 1915 at the age of ton. It is reasonable to speculate 79. The A. W. Wright Nuclear Structure Laboratory that Newton played some role in at Yale honors his memory. persuading Gibbs to take advantage Library. Manuscript and Book Rare Beineke the from Photograph of the resources abroad. Gibbs and Moore In 1869 Willard and Anna returned J. Willard Gibbs. By all indications Newton was an effective mentor. to America and joined the Van Names J. Willard Gibbs was the Yale salutatorian in 1858 to form a household. Only Addison, as Yale librar- and E. H. Moore the valedictorian in 1883. Both ian, was employed. Willard continued his indepen- won undergraduate mathematics prizes, obtained dent study. The household was supported by Van Yale Ph.D.s, studied abroad, and went on to have an Name’s salary and the Gibbs’ inheritance. Newton enormous impact on scientific scholarship. Their was a neighbor. The Newton children recalled Gibbs as a daily visitor, discussing science with careers were also shaped, in the formative years, by their father [28]. the influence and support of Hubert Newton. Gibbs was raised in the Yale community [27]. His During 1871 Yale was in a period of transition father, also named , was a sa- between presidents. A committee that included cred literature professor who died in 1861. Willard, Newton and Van Name produced a report entitled the son, was then in graduate school. He passed The Needs of the University. Among the recommen- examinations in mathematics, ethics, and modern dations were an infusion of new funding and the languages. There remains some doubt surround- creation of additional chairs in physics and other ing Willard’s thesis. After his death, a manuscript subjects. Newton was the only member of the com- entitled “On the Form of the Teeth of Wheels in mittee with expertise in mathematics and physics. Spur Gearing” was found among his papers. Those Shortly after the report was issued, Willard Gibbs associated with the university concluded it to be was appointed as professor of mathematical phys- Gibbs’ 1863 thesis. Accordingly, Willard Gibbs’ ics in the Department of Philosophy and the Arts. Ph.D. is listed as in engineering. The position carried no salary. Essentially it was a After completing his degree, Gibbs was ap- research professorship that would involve a small pointed to a tutorship. During this period, and amount of graduate teaching. possibly earlier, he was involved in Newton’s re- The exclusion of undergraduate teaching was search on meteors. In Newton’s 1864 Leonid orbit understandable in that Gibbs had unfavorable paper, Gibbs is the one person acknowledged for reviews as a tutor. Still, the appointment of an valuable suggestions. In particular, Newton singled unpublished scholar involved considerable risk out his help with a delicate aspect of narrowing the to the parties at both ends. Yale was conferring periods. Their relationship is especially notable in its imprimatur, and Gibbs was embarking on view of Gibbs’ social isolation. an uncertain path with dim financial prospects. Willard and his two sisters, Julia and Anna, lived Whatever role Newton had in choreographing this the rest of their lives together in the house left to relationship, the returns were immediate and far- them by their father. Only once did Willard venture reaching. From 1873 to 1878 Gibbs published his far from New Haven. In 1866 the three siblings seminal work that established a thermodynamic sailed for Europe where he would study in Paris, foundation for . Recognition Berlin, and Heidelberg. Gibbs set out in Newton’s came slowly, and he remained without a salary footsteps, taking courses at the Sorbonne and until 1880. Johns Hopkins then offered a profes- Collège de France from Chasles and others. Over sorship with a $3,000 salary. Yale countered with

March 2008 Notices of the AMS 361 $2,000. Gibbs remained in New Haven where he At Chicago, Moore’s career flourished [2]. An died in 1903. appreciation of mathematical developments in The founding of the in Germany influenced his research, teaching, and 1876 changed forever the landscape of United States administration. To complete his staff Moore hired scholarship. A few other universities had commenced the German émigrés Oskar Bolza and Heinrich doctoral programs, but, at Hopkins, research and Maschke. Chicago became the first American uni- graduate education were the priorities. Moreover, versity to offer mathematics training at the level its president, , secured the and breadth available in Europe. Moore himself personnel to implement his vision in mathematics, supervised the theses of Leonard Dickson (1896), physics, and other subjects. Gilman had graduated Oswald Veblen (1903), and George D. Birkhoff from Yale two years after Newton, traveled through (1907) who became the leading mathematicians Europe, and then returned to his alma mater be- at Chicago, Princeton, and Harvard respectively. coming a member of the Scientific School faculty. Their descendents included Adrian Albert, R. L. He had served with Newton and Van Name on the Moore, Alonzo Church, Marston Morse, Marshall needs of the university committee but left Yale Stone, and Hassler Whitney. shortly after a more conservative colleague was In 1899 the University of Göttingen awarded selected over him as president. an honorary Ph.D. to E. H. Moore. Over the early When E. H. Moore received his Ph.D. from twentieth century Moore and his progeny were Yale in 1885, mathematics was germinating in at the forefront of the stunning ascendence of the United States. However, American mathematics. Moore’s contributions Europe remained the center went beyond paternity and his own research. It for important investigations. was largely through his initiative that the New As Moore’s thesis advisor, York Mathematical Society became, both in name Newton foresaw how Moore’s and character, the American Mathematical Society talents would be cultivated [30]. Moore was a driving behind the start-up, by further work in Germany. in 1900, of the Transactions of the American Math- Newton facilitated Moore’s ematical Society. Under Moore’s painstaking editor- study abroad by loaning him ship the journal showcased the excellent research money to spend a year “at produced in America. In just one half century, the Göttingen and Berlin for a United States had advanced from a backwater to a promise to pay at some future font of mathematical scholarship. time” [29]. Moore attended lectures The 1896 Generational Change by Kronecker and Weier- Hubert Newton is known to mathematicians of today, if at all, as the thesis advisor to E. H. Photograph from the AMS archives. AMS the from Photograph strass, prior to beginning an E. H. Moore. academic career in the United Moore. During his lifetime, however, Newton was States. His first lower level one of the most honored mathematicians in the positions were at Yale and United States. In the 1860s he was inducted into Northwestern. Despite the arduous teaching loads, the American Academy of Arts and Sciences, the Moore continued his research and publication. His National Academy of Sciences, and the American real opportunity came in 1891 when Yale Divin- Philosophical Society. In 1868 Newton was awarded ity Professor William Rainey Harper became the an Honorary Doctor of Laws by the University of founding president of the University of Chicago. Michigan. Twenty years later he received the At Chicago, Harper would bring about the big- J. Lawrence Smith Gold Medal from the National gest advance in American scholarship since the Academy of Sciences. Other recognitions included creation of Johns Hopkins. As had Gilman before foreign membership in the Royal Society of London him, Harper put considerable effort into recruiting and the 1885 presidency of the American Associa- a faculty suited to carry out his plans. tion for the Advancement in Science. Harper’s choice of Moore to lead mathematics Newton’s resumé was not that strong in 1863 contrasted sharply with the experienced scholars when President signed the law selected to head other departments. Moore was to establish the National Academy of Sciences. an assistant professor at Northwestern which did Two weeks earlier Louis Agassiz, Alexander Bache, not then have a doctoral program. While Harper Benjamin Peirce, and Benjamin Gould had met with was no doubt impressed by Moore from their Senator Henry Wilson to consider an Academy pro- interactions at Yale, mathematics was a subject posal conceived by Captain Charles H. Davis [31]. outside Harper’s expertise. As Moore’s advisor and Out of this meeting came the draft of the legisla- Harper’s colleague, Newton was ideally positioned tion which was to sail through the Congress. The to supply a decisive endorsement (no record of any purpose of the organization was twofold: to assist evaluation has been found). the government on matters requiring scientific

362 Notices of the AMS Volume 55, Number 3 expertise and to recognize investigators who had [7] Brooks Kelley, Yale: A History, Yale University Press, made significant advances. 1974. The bill named 50 men for inclusion in the Na- [8] Catalogue. tional Academy. The old boy selection process and [9] Laura Hadley (editor), Diary (1843–1852) of James the low level of American science led to a loose in- Hadley, Yale University Press, 1951. terpretation of the standard for original research. [10] Natural Sciences manuscripts collection, Box 8, Folder 287, Manuscripts and Archives, Yale University Recall that Yale began to award the doctoral degree Library. just one and one half years earlier. Mathemati- [11] Woolsey family papers, Box 13, Folder 215, Manu- cians joining Newton on the incorporating list scripts and Archives, Yale University Library. were Peirce, Chauvenet, and Strong. They were the [12] 8/13/1853, 10/24/1853 Newton to Peirce, Benjamin leading names of the time. The early influence of Peirce papers, Houghton Library, Harvard Univer- the National Academy was limited. Committees sity. advised on a variety of maritime and other issues. [13] Edward Herrick papers, Box 3, Folder 54, Manuscripts Newton participated in an unsuccessful initiative and Archives, Yale University Library. to advocate adoption of the metric system. Over [14] Anson Phelps Stokes Autograph Collection, Box 6, the Academy’s first decade, Strong and Chauvenet Folder 398, Manuscripts and Archives, Yale University died. Peirce resigned in 1873 in a dispute over the Library. exclusivity of membership [31, page 119]. [15] Yale Corporation Minutes, Manuscripts and Archives, Newton, the youngest of the four mathemati- Yale University Library. [16] Denison Olmsted, Observations on the meteors of cians, was the last to die. His death, in 1896, oc- November 13th, 1833, Amer. J. Sci. and Arts 25 (1834), curred as Moore’s first student completed his Ph.D. 363–411 and 26 (1834), 132–174. A transition was taking place in American math- [17] ——— , On the meteor shower of November, 1838, ematics. The most prominent senior mathemati- Amer. J. Sci. and Arts 35 (1839), 368–370. cians were Hill and Newcomb. Both worked in as- [18] Hubert Newton, Evidence of the cosmical origin of tronomy and were domestically educated without a shooting stars derived from the dates of early star- Ph.D. The rising stars were Moore, William Osgood, showers, Amer. J. Sci. and Arts 36 (1863), 145–148. and Maxime Bôcher. Osgood and Bôcher had done [19] ——— , The original accounts of the displays in for- their undergraduate work at Harvard and traveled mer times of the November Star-Shower; together with to Germany for their Ph.D.s. Moore completed his a determination of the length of its cycle, its annual formal education at Yale but needed to go abroad period, and the probable orbit of the group of bod- to prepare for a research career. Moore’s student, ies around the sun, Amer. J. Sci. and Arts 37 (1864), Leonard Dickson, had received a complete gradu- 377–389 and 38 (1864), 53–61. [20] J. C. Adams, On the Orbit of the November Mete- ate education. Although Dickson did spend the ors, Monthly Notices of the Royal Ast. Soc. 27 (1867), following year in Leipzig and Paris, the European 247–252. experience was no longer an essential ingredient in [21] Mark Littmann, The Heavens on Fire, Cambridge the training of American mathematicians. Birkhoff University Press, 1998. did not travel to Europe until 1926, thirteen years [22] Peter Jenniskens, Meteor Showers and their Parent after he achieved international renown with his Comets, Cambridge University Press, 2006. proof of Poincaré’s last geometric theorem. It is [23] Harold Dorwart, Mathematics and Yale in the fitting, and no coincidence, that Newton’s lifetime nineteen twenties, A Century of Mathematics in spanned the struggle of the United States to be- America Part II, Amer. Math. Soc., 1989, 87–97. come self-sufficient in mathematical research. [24] Doctors of Philosophy of Yale University, Yale Univer- sity, 1927. References [25] Yale College in 1868, unpublished document pro- [1] David Zitarelli, Towering figures in American math- duced by the Executive Committee of the Society of ematics, 1890–1950, Amer. Math. Month. 108 (2001), the Alumni. 606–635. [26] Arthur Williams Wright, Science 43 (1916), 270– [2] Karen Hunger Parshall and David E. Rowe, The 272. Emergence of the American Mathematical Research [27] Lynde Wheeler, Josiah Willard Gibbs, Archon Books, Community: J. J. Sylvester, , and E. H. Moore, 1970. Vol. 8, American Mathematical [28] Margaret Whitney, One of the Prophets, 1937, un- Society and London Mathematical Society, 1994. published paper in Gibbs–Van Name Papers, Beinecke [3] J. Willard Gibbs, Hubert Anson Newton, Amer. J. Sci. Library, Yale University. and Arts 3 (1897), 359–376. [29] G. A. Bliss, Eliakim Hastings Moore, Bulletin Amer. [4] Timothy Dwight, Memories of Yale Life and Men, Math. Soc. 39 (1933), 831–838. Caxton Press, 1903. [30] Raymond Archibald, A Semicentennial History of [5] Yale College commencement orations and poems, the American Mathematical Society 1888–1938, Amer. 1742–1930, Box 2, Folder 12, Manuscripts and Ar- Math. Soc., 1938. chives, Yale University Library. [31] Rexmond Cochrane, The National Academy of Sci- [6] Hubert A. Newton Papers, Box 1, Folder 1, Manuscripts ences The First Hundred Years 1863–1963, National and Archives, Yale University Library. Academy of Sciences, 1978.

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