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Home , Joseph Wedderburn, Julian Coolidge, Oswald Veblen

The Vision, Insight, and Influence of Steve Batterson

hen Oswald Veblen assumed the proof of the Jordan Curve Theorem. It was Veblen presidency of the American Math- who made Poincaré’s brilliant algebraic topol- ematical Society in 1923, there ogy concepts accessible to the ’s pioneers. was little support for mathemati- Among the students supervised by Veblen were cal research in the . R. L. Moore, , and J. H. C. Whitehead, WUniversity teaching loads varied from nine hours who went on to become leaders in the development to fifteen hours per week and higher. The birth of of their respective specialities. the National Science Foundation was over a quarter I first came to appreciate Veblen’s significance century in the future. Research when I began research for a book on the origins grants and postdoctoral positions of the Institute for Advanced Study. In discuss- (with little or no teaching) did not ing my project with others it became evident that exist for . Veblen’s contributions were largely unknown to As a professor at Princeton the mathematicians of today. Oswald was fre- University, Veblen himself was a quently confused with his more famous uncle, member of a premier mathemat- economist . The objective of this ics department. Yet just four of article is to review Oswald Veblen’s overall influ- Veblen’s colleagues were actively ence as , mentor, and advocate. I engaged in research, and, among am grateful to Michele Benzi and Albert Lewis for them, James Alexander, Einar their suggestions. Hille, and worked with no office space. Hille, Mathematical Ascendance as an instructor, was assigned Oswald Veblen was of Norwegian descent. His teaching duties that included two mother Kirsti Hougen was born in Norway while sections of trigonometry. Instruc- his father, Andrew, and Uncle Thorstein were tors at Columbia and Michigan first generation Americans from Wisconsin. The taught twelve and sixteen hours Oswald Veblen, 1924. Hougen and Veblen families settled on nearby per week respectively [1], [2], [3]. farms in Minnesota. Kirsti and Andrew married Veblen took up the task of improving the circumstances for research math- in 1877 [4], [5]. ematicians. His success in this endeavor was On June 25, 1880, Oswald Veblen was born in but one facet of a career that had an enormous Decorah, Iowa, where his father was teaching at impact on mathematics and the profession. For Luther College. Shortly afterward Andrew began example, due entirely to Veblen’s initiative the graduate study at Johns Hopkins. In 1883 the fam- young scholars Kurt Gödel and ily returned to Iowa for Andrew to teach physics were recruited for academic opportunities in the and mathematics at the . There United States. As a mathematician Veblen was Oswald was educated from elementary school no slouch. His work included the first rigorous through an undergraduate degree at the university in 1898. Two years later he received a second B.A. Steve Batterson is associate professor of mathematics and from Harvard. science at Emory University. His email address In 1900 Veblen began graduate school at the is [email protected]. . He arrived without any

606 Notices of the AMS Volume 54, Number 5 financial support, “but with a hope that something recommended Veblen. Veblen might turn up.” It did. Another student with a fel- and Eisenhart were joined by lowship dropped out during his first quarter, and Gilbert Bliss and J. W. Young as Veblen was awarded the US$320 stipend. [4/2/38, the first mathematics precep- 5/2/38 Oswald Veblen to John Howe, from Oswald tors [1]. Veblen Papers, Manuscript Division, Library of The selections were superb. Congress] Financial considerations aside, Chicago Each preceptor was both a rising was a wise choice for graduate study in mathemat- scholar and leader. Veblen and ics. The university, begun just eight years earlier, Eisenhart would work with Fine in was in the midst of a historic period in the edu- engineering Princeton’s advance- cation of American mathematicians. Among the ment. Bliss and Young remained rising generation of leaders to receive Ph.D.s there for three years before moving at this time were Leonard Dickson (1896), Gilbert on. Bliss returned to Chicago and Bliss (1900), Veblen (1903), R. L. Moore (1905), and together with Dickson became G. D. Birkhoff (1907). Each would later serve a term the department’s second genera- E. H. Moore, 1902. as president of the AMS. tion of leaders. Young eventually The head of the Chicago department was E. H. settled at Dartmouth where he Moore who was one of the most highly regarded initiated a transformation toward mathematicians in the country. Among Moore’s research. interests was ’s recent work on the At Princeton Veblen began foundations of . Veblen attended Moore’s to collaborate with Young on fall 1901 seminar covering this topic. Hilbert had . Their work employed the undefined terms of point, line, and culminated in a classic text on plane, to devise a scheme of 20 axioms. Questions the subject. The first volume soon arose over the independence of these axioms. appeared in 1910, with a second In the seminar Moore identified and sharpened the volume slated for the following independence deficiencies. Veblen was inspired year. The scheduling was opti- to go further in his 1903 thesis. Creating a frame- mistic. The authors were sepa- work based on just the two undefined elements of rated, and Young was moving point and order, Veblen proposed twelve axioms from the chair duties at Kansas to for . He showed the axioms the the headship at Dartmouth. were independent and that they were satisfied by Veblen, who had taken on other Henry Fine, 1911. a system that was essentially unique [6]. projects as well, finished the sec- Veblen remained at Chicago for two notable ond volume on his own in 1917. postdoctoral years. During this period he polished Some indication of the enduring his thesis for publication, proved a major theorem, value of these books is given by began a collaboration, and joined his advisor E. H. a mid-2006 ISI Web of Knowledge Moore in directing the thesis research of a newly citation search, which recorded arrived student. The student was R. L. Moore and twenty-seven hits among articles the collaborator a young Scottish algebraist, Joseph published since 2000. Wedderburn. The theorem was the long accepted The year 1905 marks the be- Jordan Curve Theorem for which previous proofs ginning of Princeton’s ascen- were unsatisfactory. Veblen was well prepared to dance to world class mathematics go out on his own. standing. Veblen’s fingerprints It was at this time, in 1905, that Princeton Uni- immediately appear all over the versity President Woodrow Wilson embarked on a university’s successful efforts to program to upgrade the university. A key element identify and recruit promising of his plan was the creation of a large number of young talent. Prior to the com- junior faculty positions to reduce class size and pletion of his first year, Veblen G. D. Birkhoff, 1913. individualize undergraduate education. These wrote to R. L. Moore to sound out “preceptors” were to teach traditional classes as his interest in a position. Moore well as provide one-on-one supervision to upper became the fifth preceptor, before going to North- class students. Selection of the mathematics pre- western University and then to the University of ceptors was in the hands of mathematician and Pennsylvania and the University of Texas. With archives. AMS Dean of the Faculty Henry Fine. the departures of Moore, Bliss, and Young, two Fine recognized an opportunity to change the outstanding mathematicians came to Princeton direction of a department that, aside from himself as replacements in 1909. Both had overlapped and the young instructor Luther Eisenhart, had with Veblen at Chicago. They were his collabora- no commitment to research. When Fine contacted tor Wedderburn and G.D. Birkhoff, a later E. H.

E. H. Moore to solicit nominations, Moore strongly Moore student. the from are page this on Photographs

May 2007 Notices of the AMS 607 Birkhoff was just twenty-five when his appoint- of mathematical research. According to longtime ment began at Princeton. Frequent walks there with Princeton mathematician Albert Tucker, Veblen the four-year-older Veblen cemented a lifelong was sufficiently concerned over the subject’s personal and professional friendship. It would standing that he advised Alexander to obtain his have been fascinating to listen in on these conver- Ph.D. in a more fashionable area [7]. In 1915 Alex- sations, for the interaction undoubtedly stimulated ander published two important papers. His thesis, subsequent developments at this historic time under T. H. Gronwall, was on univalent functions. in the emergence of mathematical research in In another article Alexander established that the America. Birkhoff and Veblen were pursuing dif- homology of a 3-dimensional polyhedron was in- ferent programs of Poincaré. With Birkhoff it was dependent of its triangulation. celestial mechanics that would lead to his seminal Veblen’s standing as a mathematician grew proof of the existence of fixed points for certain steadily at Princeton. An offer from Yale contrib- area preserving maps of the annulus. Veblen be- uted to his 1910 promotion to the rank of full came interested in Poincaré’s conceptualization of professor. At that time, one of the most prestigious algebraic topology (known then as analysis situs) recognitions for an American mathematician was which, to this point, was largely undeveloped. an invitation to deliver the Colloquium Lectures. Birkhoff remained at Princeton for three years and These opportunities arose every few summers then went to Harvard where he earned acclaim as when two prominent scholars were selected to the foremost American mathematician. showcase their work in a series of talks to the en- Poincaré’s publications on analysis situs ap- tire American Mathematical Society. The lectures peared over the period 1892-1905. Jean Dieudonné were closely followed and much discussed. provided the following assessment: When Veblen was invited to deliver the 1916 Colloquium Lectures, he might well have selected As in so many of his papers [Poincaré] the established topic of projective geometry. In- gave free rein to his imaginative pow- stead Veblen took the decision to proselytize the ers and his extraordinary “intuition”, less respected subject of analysis situs. Over six which only very seldom led him astray; lectures he developed the notions of Betti number, in almost every section is an original torsion, the fundamental group, and the topologi- idea. But we should not look for precise cal classification problem. definitions, and it is often necessary to As was customary with the Colloquium Lec- guess what he had in mind by interpret- tures, Veblen revised and expanded his presenta- ing the context. For many results, he tion into a monograph that the AMS published simply gave no proof at all, and when in 1922. In the preface Veblen stated his goal to he endeavored to write down a proof provide “a systematic treatment of the elements of hardly a single argument does not raise Analysis Situs”, but cautioned that it should not be doubts. The paper is really a blueprint viewed as “a definitive treatment. For the subject for future development of entirely new is still in such a state that the best welcome that ideas, each of which demanded the cre- can be offered to any comprehensive treatment ation of a new technique to put it on a is to wish it a speedy obsolescence.” The words sound basis. [Jean Dieudonné, A History were prophetic. Through Veblen a generation of of Algebraic and Differential Topology mathematicians was introduced to the concepts of 1900-1960, Birkhäuser (1989) p. 17] algebraic topology. The ideas quickly gained trac- In view of these obstacles it is not surprising tion, and new developments followed. However, that the concepts of homology and fundamental even after Lefschetz’ more modern discussion of group remained fallow for nearly a decade. Ve- the subject was published in 1930, Veblen’s book blen, a remarkable connoisseur of mathematics continued to serve as an important (and user- and mathematicians, appreciated the value of friendlier) primer. Poincaré’s ideas and saw the need to establish a The long lag between Veblen’s Colloquium solid foundation upon which they could be com- Lectures and their appearance in print coincided municated to other mathematicians. Veblen set with the onset of World War I. The war contributed himself to the task, recruiting a brilliant young to the publication delay in two ways. The AMS Princeton graduate student, James W. Alexander, underwent financial difficulties that set back its to join him in the effort. Their combinatorial book program. Second, Veblen shifted his intel- formulation of homology for polyhedra, deriving lectual and physical energy to the war effort. the Betti numbers, torsion coefficients, and their This career move illustrated his modus operandi. properties, appeared in the 1913 Annals of Math- Veblen was a visionary with an unusual capacity ematics. The notion of homology groups was still for implementation and realization of his ideas. In a dozen years in the future. this case he wanted to utilize his skills to benefit Even with this introduction to the subject, al- the army. That Veblen lacked both military and gebraic topology remained out of the mainstream applied mathematics experience was no deterrent

608 Notices of the AMS Volume 54, Number 5 to him. He would find a way to make a substantive His forceful personality, tall frame, and tweed contribution. In 1917 Veblen was commissioned as suits made him an effective advocate. However, it an army reserve captain and went through basic was Veblen’s faith in America’s potential and his training. He then assumed charge of experimental international per- ballistics at the new in spective that would Maryland [8]. shape his actions. Veblen took up the task of producing range Veblen had been tables for new weapons. These tables were de- quick to broaden signed for use by artillery officers in the field. The his experience be- objective was to specify values for the distance yond his midwest- D.C. Washington, a shell would travel, presented as a function of ern upbringing. In independent variables such as the angle of the the summer of 1905 cannon barrel and the amount of charge. There he traveled through is a long mathematical history to the problem of Europe to pursue configuring artillery to reach a target, accounting contacts that arose for drag and other factors [9]. At Aberdeen Veblen out of his thesis was to conduct test fires and then utilize the data research. The ap- to calculate the range table. pointment at Princ- Neither the existing theory nor the Aberdeen eton, in the fall, infrastructure were adequate to produce satis- coincided with the factory tables. The mathematical, logistical, and hiring of British sci- physical obstacles that arose are recounted in [8] entists James Jeans

and [9]. Veblen overcame the difficulties with a and Owen Richard- Congress, of Library Division, Manuscript Papers, Veblen Oswald 21, Box considerable combination of ingenuity and ad- son. Richardson Veblen in U.S. Army uniform. ministrative skill. Along the way he built up his had already done staff by recruiting young mathematicians such as the work that would Joseph Ritt and . Moreover, Veblen later be recognized with a Nobel Prize in physics. worked closely with the army office of theoretical When Richardson’s sister, Elizabeth, visited from ballistics, headed by University of Chicago as- England, Veblen met the woman he would marry tronomer Forest Moulton, to create the needed in 1908. The marriage lasted until Veblen’s death numerical methods. In [9], Goldstine portrays the in 1960. There were no children. Owen returned World War I ballistics project as a crucial step in to England in 1914, giving Veblen a connection to the development of computational mathematics high level European science. and the computer. The Veblens spent the fall term of 1913 tour- Veblen devoted two years to the army. Return- ing the mathematical centers of Europe, including ing to Princeton in 1919, he went to work on the Oslo, Göttingen, and Berlin. Sylow, Mittag-Leffler, colloquium book manuscript. In that same year Klein, and Schwarz were among the nineteenth Veblen was inducted into the National Academy of century legends whom Veblen met personally. Sciences. At the age of thirty-nine he had reached At each stop he keenly observed the scientific the pinnacle of American scholarship. His intel- culture, particularly noting local frameworks for lectual development, over the first two decades of promoting mathematical interaction and for facili- the twentieth century, occurred amidst an overall tating the communication of new results. Veblen advance of American mathematics. For the first was intrigued by how American mathematicians time United States mathematicians were gaining measured up to the higher status Europeans. He the respect of their European counterparts [6]. concluded that the United States was generally At the same time, mathematical scholarship was competitive with the Göttingen faculty, excepting becoming more prevalent in the United States. Un- Hilbert who was in a class by himself. This judg- like in the previous century, researchers were to be ment, weighing one German department against found, though certainly not in any abundance, at an entire country, may have been influenced by most quality universities. Despite these advances chauvinism. neither the American academy nor government There were fundamental differences in the Euro- had done much to support mathematical scholar- pean and American educational systems that made ship. Teaching and service loads remained high, for an uneven playing field. Especially significant particularly in comparison to those for professors to Veblen was the huge elementary service course at European institutions. Veblen was well aware of burden that fell upon United States mathematics these discrepancies. faculty. In Europe the syllabi for these courses were covered in the secondary schools. Their university Advocate for Mathematics faculty, unencumbered by high teaching loads, Membership in the National Academy gave Veblen were free to focus on research and advanced stu- the standing to represent research mathematicians. dents. Veblen’s vision was for American research

May 2007 Notices of the AMS 609 mathematicians to enjoy similar circumstances. It ply no precedent for extramural support in the was a laudable goal, but how could a single math- United States. Veblen was asking philanthropy ematician make a difference? Veblen would find an and government to begin perceiving mathemati- opportunity with his appointment to the National cal research as essential to the national interest. Research Council (NRC), the operating arm of the The cases for physics and chemistry had been National Academy of Sciences. based on the importance of these subjects to the The NRC was composed of representatives from military, medicine, and industry. Attempting the universities, private laboratories, government, and same argument for mathematics posed problems. professional societies. The NRC’s original mission Range tables were less compelling than explosives was to coordinate the American scientific contri- and gases. Any medical justification needed to bution to World War I, but its political roots went pass the scrutiny of Simon Flexner. Nevertheless, deeper. In the early twentieth century astronomer Veblen succeeded by making the indirect argument George Hale sought to upgrade the profile of the that mathematics was to chemistry and physics National Academy of Sciences. Hale’s ambitions as chemistry and physics were to medicine. In for the Academy became part of a power struggle the environment of the NRC, Veblen’s diplomatic over the direction of United States science policy. skills may have served him as well as his logic. It These issues were set aside when war appeared on is unclear whether the same analogy would have the horizon. At this time, in 1916, Hale conceived worked if put forward by another mathematician the NRC. Among those joining Hale’s team on the with the initiative to act. Council was the director of the Rockefeller Insti- When Veblen brought about the first research tute for Medical Research, Simon Flexner. grants for American mathematicians, he was serv- After the war, the NRC’s mission was unclear. ing both as president of the AMS and as one of the Meanwhile the debate resumed over how to chan- Society’s representatives on the NRC. During its nel science to serve a national interest that had previous thirty-five years the AMS had advanced been redefined by war. NRC members were among American mathematics through an agenda of orga- scientists urging that an infusion of funds for basic nizing meetings and publishing research. Veblen’s research in physics and chemistry was needed to 1923–1924 presidency marked an expansion of maintain American strength. Flexner’s endorse- AMS activity into the realm of advocacy. This move, ment influenced the Rockefeller Foundation to while largely the product of a new president’s vi- consider adopting this new cause. For some time sion, was also driven by financial necessity. Since the foundation grappled with whether to create the beginning of World War I, increasing publica- a pure science laboratory or to enhance existing tion costs had stressed the AMS finances. Print- university operations. The outcome, in 1919, was ing the Bulletin and Transactions had driven the a new mechanism for scientific support. Rather budget to five figures. Even with a 1920 boost in than allocate funds to laboratories, the Rockefeller dues to US$6 and a successful membership drive, Foundation underwrote a program of postdoctoral revenues were insufficient to keep up with the fellowships, in physics and chemistry, that was to rising costs. be administered by the NRC. The politically en- The 1923 incorporation of the AMS provided gaged NRC gained new influence and a connection new financial flexibility. To address the bud- to the Rockefeller resources [10], [11]. get shortfall, Veblen appointed Harvard math- Although mathematics had been entirely out- ematician to lead an endowment side the consideration for research support in campaign. A US$100,000 goal was established. pure science, the AMS was represented on the NRC. Coolidge raised one fourth of this sum through When a new mathematics appointee was needed, solicitations of AMS members. Late in 1923 Ve- Veblen’s war work and National Academy mem- blen joined Coolidge in bringing the appeal to the bership made him an ideal choice. Veblen joined private sector. A simultaneous campaign was un- the NRC in 1920. As a member of the Executive dertaken to increase awareness of the importance Committee and the Division of Physical Sciences, of mathematics to civilization. Out of this two- he became an insider in discussions on national pronged approach came the creation of the annual science policy. It was a role that suited him well. In Josiah Willard Gibbs Lecture on mathematics and 1923 Veblen became chair of the NRC Division of its applications [4]. Physical Sciences. Within a few months he single- Coolidge and Veblen worked hard to win over handedly persuaded the NRC, Flexner, and the chief executives. However, the tax system was not Rockefeller Foundation to expand the postdoctoral yet configured to promote corporate donations. program to include mathematics. When industrial officers expressed reluctance Given the abundance of postdoctoral oppor- to authorize outright contributions, Veblen and tunities in mathematics today, it is difficult to Coolidge devised a variety of inducements. The comprehend the magnitude of Veblen’s break- most successful was the patron membership, a through in the funding of mathematical research. forerunner of today’s institutional version, in Consider the obstacles he faced. There was sim- which companies paid annual premiums and then

610 Notices of the AMS Volume 54, Number 5 designated selected employees for gratis AMS of a US$3.5 million plan for the sciences. The Gen- memberships [12]. eral Education Board received the overall proposal The outcome of the endowment drive was with favor, but questioned the institute aspect. mixed. The US$55,000 raised in pledges fell well During the final Rockefeller-University negotia- short of the goal, but the patron memberships tions, the mathematics institute was deleted from added an uncapitalized US$4,000 in revenue to the plan. Princeton was awarded a US$1 million the annual budget. In addition Veblen secured sig- challenge grant toward the adjusted goal of US$3 nificant subventions from the NRC and Rockefeller million. Foundation to assist, over a period of years, with Fine played a crucial role in raising the US$2 publication expenses. The bottom line was that the million Princeton obligation. Alumnus Thomas budget problems were temporarily resolved. Jones, a long time friend of Fine, and Jones’ niece While working with Coolidge on behalf of the Gwethalyn endowed four chairs in the sciences. AMS, Veblen independently launched his most Veblen became the first Henry Fine Research Pro- ambitious attempt at advocacy for mathematical fessor of Mathematics, a position with no formal research. After the funding was in place for the teaching duties. postdoctoral fellowships, he sent new appeals to From the new science endowment the Princeton his NRC and Rockefeller connections. Veblen de- mathematics department gained an annual sti- scribed the plight of research mathematicians in pend to program for research. Out of these funds the United States as follows: Over the prior quarter Wedderburn, Alexander, and century American universities had come to select each received salary supplements to reduce their for mathematical scholarship, but had failed to teaching loads. The homegrown Alexander had make accommodations to cultivate it. The cur- joined the faculty in 1915 and gone on to obtain rent situation was that research mathematicians, fundamental results in topology. Lefschetz arrived although in demand, had little time for research from Kansas in 1924 for a visiting position that after completion of their teaching and service was made permanent the following year. With obligations. Even so, American mathematics had Lefschetz, Alexander, and Veblen, Princeton was a made enormous progress. In Europe conditions world center for the emerging subject of algebraic were much better. The teaching load of nine hours topology. The stimulating environment attracted at Harvard contrasted with three hours at the Col- European scholars Pavel Alexandroff and Heinz lège de . Hopf for productive visits in 1927–1928. Veblen suggested that the foundations carry Mathematics at Princeton had come a long way support for mathematics further. He portrayed since Veblen’s arrival in 1905. The department the NRC postdoctoral fellowships as a vital first stood with Harvard as the two leading mathematics step in providing research opportunities to prom- institutions in the United States. Yet infrastructure ising young scholars. “What remains to do is to remained essentially nonexistent. Fine and Eisen- find a way of assuring the continuance of their research to men who have proved their ability.” hart, as deans of science and of the faculty, had [6/10/24 Oswald Veblen to Vernon Kellogg and offices in an administration building. The rest of to Abraham Flexner, from Oswald Veblen Papers, the department operated out of a small portion of Manuscript Division, Library of Congress] Veblen the physics building that consisted of an office for proposed two solutions. The first was the creation Veblen, a library, and, according to Lefschetz, one of a mathematics institute where research, rather room for “everything else”. Wedderburn, Alexan- than teaching, was the primary business. The sec- der, and Lefschetz worked at home [1]. ond proposal was the endowment of a number of The lack of physical space limited interaction research professorships in which recipients would among the mathematicians. Veblen was a strong remain at their universities and have their salaries believer in the notion of a community of scholars. subsidized to reduce teaching loads. He had observed the rich cultures at Göttingen and While Veblen initially pitched a generic institute other European institutions. With planning under that could stand alone or be incorporated as part way for a mathematics building at the University of of a university, developments at his own university Chicago, Veblen pushed for Princeton to construct soon led him to customize the proposal. In 1925 a home for its department. Any prospect of moving President John Grier Hibben mounted a major fund forward on the project required the endorsement drive for Princeton. The needs of the sciences were of Fine, who had responsibility for the interests to be presented in a request to the General Educa- of other subjects as well. Outside funding was the tion Board of the Rockefeller Foundation. Veblen surest route to the head of the queue. By the fall lobbied for inclusion of a mathematics institute, of 1928 some hope existed that the Rockefeller targeted at applications of the department’s Foundation might finance the addition of a math- strengths in analysis situs and geometry. ematics wing onto the physics laboratory. This was With the support of Fine and Eisenhart, Veblen the situation as Veblen left for Oxford as part of a succeeded in having his institute included as part year long exchange with G. H. Hardy.

May 2007 Notices of the AMS 611 Joining Hardy at Princeton was Veblen saw an opportunity, through Fine Hall, who had accepted the Thomas Jones research to realize crucial elements of his mathematics professorship in mathematical physics. Weyl was institute. Comfortable offices, a first class library, on leave from his chair in Zurich, retaining the a modern lecture hall, and meeting places would option to return, which he would. However the bring together scholars for mathematical study presence for 1928–1929 of, arguably, the world’s and discussion in the manner that he had so ad- two leading mathematicians, Hardy and Weyl, was mired in Europe. Veblen quickly took over the plan- a coup for both Princeton and ning of the new building, incorporating features the United States. Max Mason from Oxford, and seeking to create the ambiance was impressed when he visited of Göttingen. Many of the measures were unusual Princeton in November, just a for the United States at this time. Undergraduate few months after taking charge education received no consideration. The scope of of the Rockefeller Foundation Fine Hall was restricted to research and advanced science program. Mason was an instruction in mathematics and mathematical American mathematician who physics. Each member of the research faculty had been a student of David in these subjects received an office. A spacious Hilbert at Göttingen. library, common room, and professors’ room In December 1928 Veblen were designed to promote study and interaction. received a letter from Fine pre- Policies of daily afternoon teas and 24-hour access dicting that Mason’s Rockefeller would make the first two venues into magnets for group “will give us the Math- mathematical activity. ematics Building.” [11/28/28 While Fine Hall proved itself to be a building of Henry Fine to Oswald Veblen, exceptional utility, the most striking feature was from Oswald Veblen Papers, its opulence. Lavish oak paneling, carved figures, Manuscript Division, Library and fireplaces were incorporated throughout. It

Photograph used with the permission of Ernest D. Courant. D. Ernest of permission the with used Photograph of Congress] A few weeks later was all Veblen’s doing. He believed that mathemati- Hermann Weyl (right) with Fine was dead, hit from behind cal research was a high calling and that scholars David Hilbert, mid-1920s. by an automobile while riding deserved comfort and consideration. Veblen his bicycle at dusk. Shortly after injected himself into every detail of the design, Fine’s death Thomas Jones an- including the selection of each piece of quality fur- nounced a further beneficence, niture and even down to the placement of electrical his intention to donate a new sockets and choice of trash baskets. The furniture mathematics building as a me- budget was over US$26,000. Nearly US$8,000 was morial to Fine. Money was no allocated for rugs. Fine Hall opened in 1931 setting longer an issue. The wealthy a new standard for American mathematical accom- Jones intended to place the modations. A large number of graduate students, mathematics department in a postdoctoral fellows, and visitors passed through home that would stand as a its hallways, later lobbying their own universities tribute to his friend Dean Fine. to adopt aspects of its design. Rather than a wing added onto physics, Fine Hall would be a Veblen Shapes the Institute for Advanced separate building with a corri- Study dor connecting it to physics. In the summer of 1930, as Veblen oversaw the The next step was to up- planning for Fine Hall, a front page article in the

Courtesy of the Archives of the Institute for Advanced Study. Advanced for Institute the of Archives the of Courtesy grade the plans that already New York Times caught his attention. A New Jer- Abraham Flexner. existed for the physics wing. sey family had donated US$5 million to endow Wedderburn was serving as the creation of an institution devoted entirely to the liaison between the depart- research and graduate education. The Institute for ment and the architects. The frugal Wedderburn Advanced Study (IAS) was to be located in the vicin- had been well placed when the budget and scale ity of Newark and be directed by Abraham Flexner. were limited, but he was ill suited to act on the Veblen was acquainted with Flexner through his possibilities opened by Jones’ generosity. Alex- brother Simon. When Veblen first pitched his ander wrote to Veblen asking him to intervene: mathematics institute in 1924, Simon referred “The only thing between us and really homelike him to Abraham who was then a key figure at the headquarters is Wedderburn’s rather puritanical General Education Board. Nothing had come from attitude. He acts, at times, as if he felt there was Veblen’s follow up. However, a few months prior something just a little immoral about material to the appearance of the Times piece, Abraham had comforts.” [12/28/28 James Alexander to Oswald initiated a seemingly innocuous correspondence Veblen, from Oswald Veblen Papers, Manuscript about the state of research in the United States. Division, Library of Congress] Now Veblen sent Abraham a short congratulatory

612 Notices of the AMS Volume 54, Number 5 note in which he proposed Princeton as the site Flexner had not contemplated more than one for the new institute. (For further details and refer- or two professors for any school. He allowed ences on the IAS see [14].) mathematics to reach three only when extraordi- Abraham Flexner’s ambition was to elevate nary opportunities arose to obtain Weyl and the scholarship in the United States. His plan was to physicist Einstein. After making the initial hires recruit a small number of world class scholars and in the School of Mathematics, Flexner expected to provide them with ideal conditions to conduct re- move on to economics and then to other subjects. search and train a few Ph.D. students. Flexner was He explained to Veblen that no more mathemat- interested in obtaining only the very best research- ics faculty were possible at the present time. Ve- ers. Subject area was less important. Over the next blen temporarily pulled back, but he would soon year Flexner traveled throughout the United States resume his campaign for expansion. Meanwhile and Europe for consultations. Although he himself Flexner searched, in vain, for an economist. Al- had no knowledge of mathematics, an interview though Veblen’s persistent advocacy generated with G. D. Birkhoff made a profound impression. occasional friction, time and again he persuaded Flexner decided then on mathematics as the first Flexner to go with one more outstanding mathema- IAS program (or school). He would delay making tician. By 1935 the School of Mathematics faculty Birkhoff an offer until further elements were in consisted of Veblen, Einstein, Weyl, Alexander, place. John von Neumann, Morse, and a one-year visitor, One of the most delicate matters was the se- Wolfgang Pauli. lection of a location for the IAS. The founders, Von Neumann’s path to the IAS, through Princ- Louis Bamberger and his sister Carrie Fuld, were eton University, illustrates Veblen’s connoiseur- set on Newark where they had made their fortune ship and his resourcefulness in building up the two in the department store business. Flexner was at- institutions. Veblen, along with Eisenhart and Fine, tracted to the aesthetic and university resources of always kept an eye out for young mathematical tal- ent, both at home and abroad. Veblen took notice Princeton. Moreover, if space could be rented for of von Neumann about the time of his Ph.D. from Birkhoff in Fine Hall, then, together with the uni- Budapest in 1926. Two years later they met at the versity mathematicians, the IAS would become a International Congress of Mathematicians where leading international center in its initial discipline. Veblen broached the possibility of von Neumann As Flexner moved quietly behind the scenes to coming to Princeton on an international fellowship. explore a Princeton relationship, he was naturally An opportunity at Hamburg halted von Neumann’s drawn to the support and discretion of Veblen. consideration of Princeton. When Weyl resigned Flexner worked out a Fine Hall arrangement, main- from the Thomas Jones chair the following year, taining IAS autonomy, that he was eventually able Veblen began thinking of the twenty-six-year-old to sell to Bamberger and Fuld. von Neumann as a possible successor. Veblen pro- In the midst of the diplomacy in Princeton, an posed to Eisenhart that von Neumann be given a important meeting took place between Veblen and visiting position as a tryout. Von Neumann came Flexner. It occurred late in 1931, several months to Princeton for the spring term of 1930 and then prior to an offer being made to Birkhoff. Flexner began splitting his time between Princeton and confidentially disclosed to Veblen his intention Berlin. The Jones chair remained vacant. to begin the IAS with mathematics and Birkhoff. The opportunity for von Neumann at the IAS Veblen informed Flexner that a recent letter from also arose out of Weyl’s career (in)decisions. Hermann Weyl indicated that Weyl might be mov- Throughout 1932 Weyl continued to waffle on able to the United States. Following this exchange the IAS offer, prompting Bamberger to question of inside information Veblen became Flexner’s his character and suitability for an appointment. most influential advisor. Flexner defended Weyl, taking the risk of alienat- Flexner’s first offers went to Birkhoff, Weyl, and ing his benefactor. Late in 1932, Weyl appeared to Albert Einstein. When Birkhoff decided to remain have decided on the IAS. Veblen then persuaded at Harvard, Flexner turned to Veblen as a replace- Flexner that the younger American, James Alex- ment. Weyl entered a long period of indecision ander, would add desirable balance to the School over whether to resign the chair in which he had of Mathematics. recently succeeded Hilbert at Göttingen. Veblen The appointments of Weyl and Alexander were and Einstein accepted in June 1932. Veblen im- on the docket for approval at the IAS trustees mediately went to work at realizing his institute meeting in mid-January. During the week prior to through Flexner’s. Along with his acceptance Ve- the meeting, Weyl sent three telegrams, alternately blen enclosed an elaborate plan for the School of accepting, withdrawing, and accepting again the Mathematics. His list of names to be considered for IAS position. The second telegram caused Flexner additional professorships consisted of Lefschetz, to face the unpleasant prospect of explaining Alexander, , Paul Dirac, , Weyl’s peculiar behavior to a skeptical Bamberger Alexandroff, and . and the board. Veblen seized the opportunity to

May 2007 Notices of the AMS 613 push for another mathematician. He knew that von superior faculty devoted to research. Outside pres- Neumann wanted a permanent, full-time position sures forced Gilman to revise his program and in the United States. Veblen urged Flexner to sub- include undergraduates. stitute von Neumann for Weyl. Flexner was one of these undergraduates dur- Flexner weighed his decision carefully. With von ing the early years of Johns Hopkins. Out of this Neumann already in Princeton, a quick acceptance experience he adopted Gilman as a hero. When was practically assured. Flexner liked the idea of Flexner began to formulate his own higher educa- giving the trustees the von Neumann good news to tion dogma, the Gilman influence pervaded his mitigate the Weyl bad news. The one reservation thinking. Among Flexner’s strongest beliefs was for Flexner was his genuine deference to Eisenhart that undergraduate and graduate education were who was moving to hire von Neumann for one of incompatible. Only Ph.D. candidates were in the the university vacancies created by Veblen and student plans at the founding of the IAS. In the Alexander. Then Flexner learned of Weyl’s third fall of 1932 Flexner went one step further. He telegram and everything suddenly changed. An eliminated all degree study, replacing it with a offer to von Neumann would not only weaken the new advanced educational class consisting of university, but it would require creation of a fifth freshly minted Ph.D.s. These “students” were to be position in the School of Mathematics. Despite selected by individual IAS professors from whom Veblen’s best efforts, Flexner decided to present they would receive further research mentoring. just Weyl and Alexander to the trustees. The IAS training was intended to strengthen the Two days after his appointment was approved, students’ preparation for launching their own in- Weyl sent a fourth telegram dependent research programs as rookie faculty. with another withdrawal. The switch from graduate to postdoctoral edu- Flexner then moved quickly cation occurred shortly after Veblen began promot- to secure von Neumann. The ing another European discovery, Kurt Gödel, for a IAS would open in 1933 year-long appointment. Flexner had at first balked with a faculty of Veblen, Ein- at consideration of the twenty-six-year-old logi- stein, Alexander, and von cian who was three years beyond his Ph.D. Gödel, Neumann. As for Weyl, his however, fit the revised profile of a promising erratic actions were taken pre-faculty scholar. Flexner penciled in Gödel as in the midst of a nervous Veblen’s (and the IAS’s) first student. breakdown. The timing was Veblen had his own vision for a mathematics catastrophic. Less than a institute: To bring together an exceptional group month after Weyl spurned of scholars and provide them with an opportu- the IAS, Hitler became chan- nity to interact and the freedom to concentrate cellor of Germany. Although on research. The differences with Flexner, aside Weyl himself was Aryan, his from the number of personnel, were subtle. Ve- wife was Jewish. Their fam- blen wanted a continuum of age and experience, ily was doomed. in contrast to Flexner’s polar student-professor During his recovery Weyl scheme. Moreover, Veblen regarded everyone, forthrightly poured out his even new Ph.D.s, as independent scholars. While feelings and fears in letters he happily followed up on Flexner’s suggestion of to the supportive Veblen. inviting Gödel, Veblen had no intention of acting Photo used with permission of Marina von Neumann Whitman. Neumann von Marina of permission with used Photo When Weyl regained his as a supervisor. John von Neumann. health and discovered the In January 1933 Veblen decided to push the state of German society, he envelope on postdoctoral scholars. He proposed to appealed to Veblen for reconsideration. This time Flexner that the IAS host one-year visits by young Flexner was easy to convince. The problem was mathematicians who already held positions at Bamberger, whose objections Flexner overcame. Harvard, Johns Hopkins, and Chicago. Since these The School of Mathematics got its fifth professor. faculty were too junior to be eligible for sabbati- Veblen would also be instrumental in the hiring of cals, Veblen suggested that their salaries be split Marston Morse who completed the first generation between the home university and the IAS. Flexner of IAS mathematics faculty. was negative. While he was anxious to advance the Despite his role in assembling an extraordinary development of rising faculty, he expected the IAS collection of scholars, Veblen’s greatest IAS legacy to exert its role while the scholar was still a free may be his shaping of its postdoctoral policy. What agent. Supporting the research of a faculty member follows is a brief description of how this crucial from a wealthy university struck Flexner as a one- IAS component evolved. Flexner’s vision for the sided arrangement in which the IAS was effectively IAS was inspired by Daniel Coit Gilman’s original making a subsidy to the other institution. 1875 plan for Johns Hopkins University. Gilman This reaction of the well meaning Flexner conceived a graduate (only) university built around indicates how radical Veblen’s proposal was for

614 Notices of the AMS Volume 54, Number 5 the time. Veblen defended his ground. He argued States. By this time Veblen’s own mathematical that all parties would benefit, with IAS personnel interests had shifted. He was working on differ- gaining stimulation from the interaction. Flexner ential geometry, influenced in part by Einstein’s agreed to try out the program on an experimental discoveries in relativity. T. Y. Thomas pursued basis. The salaries of Adrian Albert and Egbertus this thread. van Kampen were shared with Chicago and Johns Another distinguished Veblen student was the Hopkins. British topologist J. H. C. Whitehead. They became Twenty other postdoctoral scholars joined acquainted during Whitehead’s study at Oxford Gödel, Albert, and van Kampen at the IAS in 1933– in 1928. Veblen was then in residence through 1934. Several were NRC fellows or Europeans on the exchange with G. H. Hardy. Whitehead was so a Rockefeller Foundation program. Others found inspired by Veblen’s lectures that he transferred their own means of support. Together with the to Princeton where he completed his Ph.D. in 1932. faculty and graduate students, Fine Hall quickly Out of their collaboration Veblen and Whitehead attained the standing and atmosphere that had so introduced the modern definition of a differen- impressed Veblen at Göttingen. Whenever Flexner tiable manifold. Whitehead later returned to Ox- passed through the building he marveled at the ford. His contributions to algebraic topology were mathematical activity. The postdoctoral student recognized by election to the Royal Society. scheme was quietly abandoned. Flexner began providing Veblen with an annual Statesman of Mathematics budget to support a class of visiting mathemati- The success of the IAS enhanced Veblen’s already cians (who became known as members). The funds considerable prestige. Among American math- went a long way. Veblen and his colleagues needed ematical contemporaries, only G. D. Birkhoff and few incentives to attract the best to Princeton. Leonard Dickson stood as high. While his two In the second year of IAS operation the member E. H. Moore siblings had the better theorems, the roster numbered in the thirties and included more combination of Veblen’s scholarship, associations, senior scholars such as Georges Lemaître, Joseph and leadership gave him enormous stature in the Walsh, and . United States’ mathematical community. Under Over the past seventy-five years the School of the prevailing hiring practices of the day, depart- Mathematics model has influenced the creation of ments frequently identified their job candidates by numerous year-long research positions throughout soliciting names from prominent outside scholars. the world. It would be easy to regard these oppor- Veblen was a key node in this “old boy network”. tunities, along with the sixty or so current annual For some time Veblen used his influence to IAS mathematics memberships, as simply a natural assist Princeton graduates and NRC postdoctoral outgrowth of Veblen’s initiative and vision in the fellows obtain suitable positions. When Hitler and early 1930s. Were it not for Veblen, however, the the Nazis began to cleanse Jewish mathematicians IAS program might well have been too short-lived from German universities, Veblen immediately took for emulation. In the later 1930s severe financial on a daunting challenge. He joined the Emergency exigencies forced difficult choices on Flexner. To Committee in Aid of Displaced Foreign Scholars, keep the IAS solvent and complete its two other becoming a point person for the relocation of schools he reluctantly attempted to redirect money mathematicians to the United States. Through his out of the mathematics members budget. Each year European contacts Veblen kept abreast of the latest Veblen tenaciously battled to protect the endan- victims, and then pressed colleagues in American gered program. Cuts were made, but the essential mathematics departments to consider some form character was maintained. of adoption. Advocating, in the 1930s, on behalf There was one unfortunate by-product of the of European Jewish refugees was a delicate matter. IAS postdoctoral program. Its establishment The Great Depression was under way and jobs were prematurely phased out a notable career in the scarce for American mathematicians. In addition, mentoring of graduate students. Even so, Veblen elements of anti-Semitism and xenophobia were inspired a remarkable number of influential math- prevalent on many campuses. Veblen managed ematicians who went on to careers in diverse spe- to navigate this minefield while skillfully parlay- cialities. R. L. Moore and Alexander were leaders ing his connections with private foundations and in point set and algebraic topology respectively. American mathematicians to create new opportu- In the 1920s Veblen supervised the theses of two nities for Europeans. students, Alonzo Church and T. Y. Thomas, who Two examples, Richard Courant and Richard would follow Moore and Alexander into the Na- Brauer, provide some flavor of the range of these tional Academy of Sciences. Church, a Princeton activities. Courant was the director of the Math- undergraduate, was nurtured by Veblen to stay on ematics Institute at Göttingen while the thirty- for graduate school and to complete a thesis in two-year-old Brauer held a junior position at foundations [15]. He went on to become a central Königsberg. Both were dismissed in 1933. Veblen figure in the development of logic in the United and Flexner made personal appeals on Courant’s

May 2007 Notices of the AMS 615 behalf. These efforts eventually led to Courant’s United States. Neugebauer estimated that an an- consequential placement at New York University. nual subvention of US$20,000 would be required. A temporary position for Brauer developed out To understand the scale consider that in 1937 total of a more general Veblen call that reached Leon AMS disbursements, including all journals and Cohen at the University of Kentucky. Cohen had publications, were under US$33,000. In addition, recently completed an NRC fellowship at Princeton. there were other infrastructure demands of start- Grateful for his own career support from Veblen, ing up such a personnel-intensive venture. Cohen managed to bring Brauer to Kentucky. The Veblen was determined to begin an American following year Brauer went to the IAS as Weyl’s journal with abstracts of international mathemati- assistant. Local funds for both Courant and Brauer cal publications. He discussed the problem with were supplemented by the Emergency Committee AMS secretary R. G. D. Richardson and other promi- in Aid of Displaced Foreign Scholars [16]. nent mathematicians. A plan took shape to bring That Veblen was able to succeed Neugebauer to the United States to edit a new peri- in these humanitarian endeavors odical sponsored by the AMS. Placing Neugebauer, was likely what earned him the the world’s foremost authority on the history of unusual appellation statesman mathematics, in an American university seemed of mathematics. Indeed, Veblen’s doable. However, the journal start-up funds were bold diplomacy created manifold well beyond the reach of scientific organizations pathways that decisively improved and universities. The expectation was that at least the plight of mathematicians and five years of operation were required before the elevated American research. A deficit would reach a level the AMS could manage. final illustration is provided by his The only solution was a large grant from a wealthy role in the birth of Mathematical philanthropic organization, but few mathemati- Reviews. cians had any entrée to the Rockefeller Foundation The first issue of Mathemati- or Carnegie Corporation. cal Reviews appeared in January By the end of November, Veblen had laid the 1940. The notion of an American plans before Carnegie president Frederick Keppel journal of mathematical abstracts and Rockefeller Director of Natural Sciences War- dates back to at least the 1920s. ren Weaver. Given the disastrous economic events

Photograph from the AMS archives. AMS the from Photograph Veblen was among the early advo- of the past decade, both foundations were already R. G. D. Richardson. cates, but, at the time, the publish- inundated with requests from worthy causes. It is ing venture was infeasible for the amazing that within two months Veblen learned AMS. The need for an abstracting that Keppel was on board to back a US$66,000 journal was filled in 1931 by Berlin publisher Ju- grant. Meanwhile Richardson had secured a posi- lius Springer with the creation of Zentralblatt für tion for Neugebauer at Brown University. Mathematik und ihre Grenzgebiete under the able On a parallel track, Veblen and Richardson lob- supervision of Otto Neugebauer [17], [16]. bied the AMS leadership to formally sanction the From his 1933 dealings on refugee mathema- journal abstracts project. In late December 1938 ticians, Veblen was quick to anticipate future the AMS Council approved the idea in principle, conflicts between Nazism and Zentralblatt. Neuge- establishing a special committee. The committee’s bauer left Göttingen in 1934 when his political charge was to investigate, and, “in case it is deemed views, rather than his religious ancestry, made his wise,” to proceed with the journal on a five-year situation impossible. For the next several years trial. To avoid the appearance of a conflict of in- Neugebauer edited Zentralblatt from his new base terest with Zentralblatt, Veblen was deliberately in Copenhagen. Late in 1938 events unfolded rap- excluded from membership on the committee. idly. Springer removed the Italian Jewish mathema- Nevertheless, he served as an influential consul- tician, Tullio Levi-Civita, from the editorial board. tant, constantly pushing to bring the project to Neugebauer questioned this action, only to receive fruition. a new decree that émigrés be excluded from re- Some mathematicians were reluctant to impinge viewing the work of German authors. Neugebauer on Springer’s domain. The dismissal of Levi-Civita then resigned as editor of Zentralblatt. was attributed to outside political pressure. Sub- Veblen learned of these developments on No- stantial good will remained toward Springer for vember 7, 1938, and sprang into action. He imme- his contributions in scientific publishing. Even so, diately coordinated with Courant, Tamarkin, and world events cast doubt over how much control he Hardy to resign their own associate editorships en would have over future policy. The deliberations masse. The act of protest left unresolved the sud- took place as Hitler was conquering Czechoslo- den need for an objective international journal of vakia. mathematical abstracts. Two years earlier Veblen Out of deference to Springer, the AMS commit- had had the foresight to ask Neugebauer to outline tee waited until a personal meeting was possible. a budget for launching such an undertaking in the After several delays, Springer’s representative

616 Notices of the AMS Volume 54, Number 5 arrived in the United States in May. The discussions Were it not for Veblen, however, extramural were unsatisfactory, and the final decision was funding for basic research in mathematics would taken to proceed with Mathematical Reviews. Over not have begun when it did. His diplomacy per- the summer the Rockefeller Foundation and Carn- suaded the NRC and private foundations of their egie Corporation awarded grants of US$60,000 interest in supporting mathematical research. and US$12,000 respectively. Veblen continued to It is unlikely that anyone else would have filled negotiate with the American Philosophical Society Veblen’s role between the world wars. Today, for additional funds. the debate continues over mathematics’ share Without Veblen’s vision, influence, and initia- of the federal research budget. Oswald Veblen tive, Mathematical Reviews would not have come gave mathematicians the standing to participate, into existence, let alone in such a short time. singlehandedly championing the cause for the first Birkhoff, who opposed the concept, was the only twenty years. other mathematician in a position to obtain the funding. While Richardson and Neugebauer were Sources important players, Veblen was the impetus behind The sources for this article included records drawn the project. from the following archival collections: Veblen’s forceful actions could arouse strong American Mathematical Society Records, John feelings. Despite their differences on Mathematical Hay Library, Brown University Reviews and European immigration, Birkhoff and R. L. Moore Papers, 1898–1974, Archives of Veblen remained close friends. Others reacted dif- American Mathematics, University Archives, Uni- ferently. Among those with animus toward Veblen versity of Texas at Austin were Solomon Lefschetz, J. Robert Oppenheimer, G. D. Birkhoff Papers, Ar- and Abraham Flexner. Flexner’s feelings were chive understandable. As Veblen was working on Math- Archives of the Institute for Advanced Study ematical Reviews he joined other faculty and trust- Oswald Veblen Papers, Manuscript Division, ees at the IAS to force the seventy-three-year-old Library of Congress director into retirement. Although the coup had widespread support, Flexner blamed much of his References trouble on Veblen. Hostile attitudes of Lefschetz [1] William Aspray, The Emergence of Princeton as a World and Oppenheimer toward Veblen were reported by Center for Mathematical Research, 1896–1939, A Cen- IAS faculty of the time. tury of Mathematics in America, Part II, (Peter Duren, ed.), Amer. Math. Soc, 1988. Overall, Veblen was widely liked and respected [2] Edgar Lorch, Mathematics at Columbia During Ado- in the scholarly community. Some indication of a lescence, A Century of Mathematics in America, Part mathematician’s standing can be obtained from the III, (Peter Duren, ed.), Amer. Math. Soc., 1989. programs of the International Congress of Math- [3] Raymond Wilder, Reminiscences of Mathematics at ematicians. In 1920 and 1924 Leonard Dickson Michigan, A Century of Mathematics in America, Part became the first American to deliver two plenary III, (Peter Duren, ed.), Amer. Math. Soc., 1989. lectures. After Birkhoff was selected to speak in [4] Raymond Archibald, A Semicentennial History of the 1928, the Bologna organizers asked Gilbert Bliss of American Mathematical Society 1888–1938, Amer. the University of Chicago to choose another Ameri- Math. Soc., 1938. can. Bliss picked Veblen. Eight years later Birkhoff [5] , Oswald Veblen, A Century of Math- and Veblen repeated the roles in Oslo. Birkhoff ematics in America, Part II, (Peter Duren, ed.), Amer. Math. Soc., 1988. died before the next Congress which was held in [6] and David Rowe, The Emergence of the 1950. This gathering, in Cambridge, was the first in American Mathematical Community 1876–1900: J. J. the United States. Veblen received the distinction Sylvester, Felix Klein, and E. H. Moore, Amer. Math. of serving as president of the meeting. Ten years Soc., 1994. later he died at his summer home in Maine. [7] Albert Tucker interview on “The Mathemat- Given the ahistorical nature of mathematicians, ics Community at Princeton Before 1930” in The it is not surprising that appreciation for Veblen Princeton Mathematics Community in the 1930s: has evaporated since his passing. Courses do not An Oral History Project, on the Web at http:// cover topics such as the first proof of the Jordan infoshare1.princeton.edu/libraries/ Curve Theorem, how algebraic topology entered firestone/finding_aids/mathoral/math.html. the mainstream, or the evolution of the notion [8] David Alan Grier, Dr. Veblen takes a uniform: Math- ematics in the first world War, American Mathematical of manifold. More modern developments are pre- Monthly 108 (2001), 922–931. sented, and the pioneers’ names are lost, unless [9] Herman Goldstine, The Computer from Pascal to von they happen to stick to the theorem or definition. Neumann, Press, 1972. In Veblen’s case, an argument could be made that [10] Nathan Reingold, The Case of the Disappearing Labo- his discoveries were so ripe that others would have ratory, Science, American Style, Rutgers University come along and obtained similar results. Press, 1991.

May 2007 Notices of the AMS 617 [11] Alexi Assmus, The creation of postdoctoral fellow- ships and the siting of American scientific research, Minerva 31 (1993), 151–183. [12] Loren Butler Feffer, Oswald Veblen and the capi- talization of American mathematics, ISIS 89 (1998), 474–497. [13] Garrett Birkhoff, Some Leaders in American Math- ematics: 1891-1941, The Bicentennial Tribute to American Mathematics 1776–1976, Math. Assoc. Amer., 1977. [14] Steve Batterson, Pursuit of Genius: Flexner, Einstein, and the Early Faculty at the Institute for Advanced Study, A K Peters, 2006. [15] Alonzo Church interview in The Princeton Mathematics Community in the 1930s: An Oral History Project, on the Web at http:// infoshare1.princeton.edu/libraries/ firestone/finding_aids/mathoral/math.html. [16] Nathan Reingold, Refugee Mathematicians, 1933– 1941, Science, American Style, Rutgers University Press, 1991 pp. 249–283. [17] Everett Pitcher, A History of the Second Fifty Years, American Mathematical Society, 1939–1988, Vol. I, Amer. Math. Soc., 1988, 69–89.

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