Ih'i~-~.,~--~_,~r4[,~- David E. Rowe, Editor I

he mathematical scene at the Uni- that, he pointed this pistol at me, A Clash of versity of Texas was dominated and said, "Ah ha, what do you think T from the mid-1920s to the late of this?" I was absolutely terrified. I 1960s by two towering, yet very differ- thought he was actually going to Mathematical ent figures: Robert Lee Moore (1882- shoot me. I don't remember what I 1974), and Harry Schultz Vandiver said .... I realized that Moore and (1882-1973). Starting in the late 1930s, Daddy were not friends, and I had Titans in these two giants entered into a conflict the feeling that maybe he was go- that grew to mythic proportions and ing to kill me, but I think it was sort Austin: lasted for more than three decades. of a grim joke he was playing. The Though this affair permeated all aspects gun was loaded, that I could tell, so of departmental life, and even spilled I was not enamored of that moment. Harry S. Vandiver over into the wider arena of academic In R. L. Moore.. Mathematician and affairs in Austin, it became most visible Teacher, John Parker devotes an entire and Robert Lee in 1945 when Vandiver--whose re- chapter to this legendary feud, fittingly search focused exclusively on number entitled "Clash of Titans." Here I offer Moore theory and associated algebraic fields-- a fresh view of this rather bizarre was transferred to the Department of episode in the history of American Applied and Astronomy. In mathematics against the background of (1924-1974) this unlikely setting, the alienated east- the portrait of Vandiver--a somewhat erner and the feisty southerner carried forgotten figure--presented in my arti- LEO CORRY on their own private cold war that cle in the last issue of this magazine. 3 echoed the politics of the post-war era. There, the focus was on Vandiver's life- In retrospect this conflict may seem long pursuit of Fermat's Last Theorem rather preposterous. In fact, eye wit- (FLT); now I turn to broader themes in nesses at Austin have never been able his career, many of which reflect on- to say precisely when and how the en- going conflicts at the University of mity began, though many could later Texas, as well as the particular antag- remember the icy non-relations be- onism that existed between him and tween Moore and Vandiver. After the Moore. Some of the main elements of departments of pure and applied math- this sto W appear in Parker's book, but ematics were joined in the early fifties, I emphasize Vandiver's perspective and Moore and Vandiver made sure that complement the picture with some in- their offices in UT's new Benedict Hall teresting unpublished documents from not only were on different floors but the latter's archive in Austin. also could be reached by separate stair- It is also important, of course, to con- ways. 1 Vandiver's son, Frank (1926- sider this conflict in context and pro- 2005), a highly respected historian of portion. There are undoubtedly many the American Civil War and president such stories of local feuds in mathe- of Texas A&M University, remembered matics departments or of local figures Moore pointing a loaded gun at him who single-handedly dominated de- when he was a child: 2 partmental life. Still, this dispute had a I was.., walking home from school special intensity and tone, heightened one day, . . . and this car pulled up no doubt by the stature of both men in by me on the curb, and Dr. Moore the American context at the time. Moore was in it. I thought he was going to was certainly a much respected figure offer me a ride home which I was in the American community; he served willing happily to accept. Instead of as mentor to several students who went

1[Greenwood 1988, 47]. Send submissions to David E. Rowe, 2Frank Vandiver, interview with Ben Fitzpatrick and Albert C. Lewis, June 30, 1999 (Oral History Project, The Fachbereich 08--1nstitut for Mathematik, Legacy of R. L. Moore, Archives of American Mathematics, Center for American History, The University of Texas Johannes Gutenberg University, at Austin). D55099 Mainz, Germany. 3[Corry 2007].

62 THE MATHEMATICALINTELLIGENCER 2007 Springer Science+Business Media, Inc. on to positions of prominence. An as- Eugene Dickson (1874-1954) was the sessment of Vandiver's standing in the most prominent among the relatively community is a more complex matter, few mathematics students in those early as I pointed out in my previous article. years. After completing an M.A. degree Personal differences were no doubt in 1894, Dickson moved to Chicago to a central factor in igniting and then sus- become one of the first doctoral stu- taining and exacerbating this conflict. dents of Eliakim H. Moore (1862-1932). The gun incident with young Frank In 1899 Dickson accepted a three-year Vandiver was just one extreme exam- appointment at Texas, but soon left ple of Moore's often aggressive behav- again for Chicago, this time for good. ior. In 1944, for instance, a heated dis- One of the students in his cussion in the mathematics department course during his brief tenure at UT was reportedly ended up in a fistfight be- Robert L. Moore, who also took courses tween Moore and Edwin Ford Becken- with Halsted. R. L. Moore later went to bach (1902-1982), an associate profes- Chicago for doctoral studies as well, sor at Austin at the time. 4 As Albert C. working on Lewis has pointed out, "in Texas, at between 1903 and 1905. 9 least, the successful use of nonverbal Always outspoken and critical, Hal- language need not detract from one's Figure I. Harry S. Vandiver (Creator: sted eventually got into trouble with the reputation. In fact, for an established Walter Barnes Studio (HSV). Board of Regents, and at the end of 1902 male scholar it adds a cachet which can he was dismissed from his post. Math- probably only help one's reputation ematical leadership at UT devolved to outside the scholarly world. ''5 In his for taking frequent leaves of absence, Milton Brockett Porter (1869-1960) and younger years, Moore trained inten- drawing on the financial support of var- Harry Yandell Benedict (1869-1937), sively in boxing, and his rather aggres- ious foundations in order to visit other both of whom had studied at Austin and sive personality could occasionally slip departments both in the later completed Ph.D. degrees at Har- into physical intimidation and even as- and abroad. vard. As university regulations then al- sault. 6 Still, Moore was hardly a singu- The clash between these two mathe- lowed for only one professor in each lar case; his colleague and life-long matical titans thus operated at a variety department at UT, Benedict was ap- friend H. J. Ettlinger was involved, in of levels, including cultural and political pointed professor in applied mathemat- his youth, in physical incidents (one in issues that were charged with tense emo- ics. These regulations were later to response to an anti-Semitic insult), and tions. As I will show, personal differ- change, but the division into two de- later "was accused of using less violent ences by no means tell the whole sto W . partments would remain, and the rela- but still physical tactics in departmental This once-famous feud deserves closer tionships between them remained a controversies of subsequent years. ''7 attention because of its deeper, under- source of ongoing administrative trou- This rough-and-tumble Texas atmo- lying dimensions, which reflect how bles. 1~ The increase in student popula- sphere was not congenial to Vandiver's each of the protagonists saw himself as tion in the USA in the period following naturally reticent personality. He would a researcher and a teacher. Moreover, WWI heightened the demand for math- sometimes isolate himself for days to do the contrasting opinions and attitudes of ematics teachers across the country, research and listen to his large collec- Vandiver and Moore also had ramifica- Austin included. During the war, Goldie tion of classical records. Vandiver was tions for their respective mathematical Prentis Horton (1887-1972) had worked "hardly the athletic type," and in the activities. As we shall see, Vandiver took with Porter and in 1916 became the first winters he worked in a top coat with a a very different approach from Moore's recipient of a doctoral degree in math- portable electrical heater warming his when it came both to mathematical re- ematics granted by the University of feet and legs. 8 Moore, on the other search and mathematics education. Texas. Soon after graduating she joined hand, was a dynamo. A strongly au- the Austin faculty; she and Porter mar- thoritarian personality, he was directly Two Mathematicians, One ried in 1934. involved in, and made great efforts to University, Two Departments Porter's aim was to raise research shape, every detail of departmental life Soon after it opened in 1883, the Uni- standards at UT by hiring mathe- for decades. Vandiver always kept him- versity of Texas at Austin appointed maticians of proven quality; he was self at a safe distance from any kind of George Bruce Halsted (1810-1936) its obviously undeterred by unconven- administrative duties. He was famous first professor of mathematics. Leonard tional personalities. R. L. Moore was

4[Greenwood 1983, 53]. This incident has been confirmed to me in a personal communication by Richard Kelisky, one of Vandiver's students. 5[Lewis 1989, 225]. e[Parker 2005, esp. 84-6]. 7[Lewis 1989, 224]. 8Robert Greenwood, "The Benedict and Porter Years, 1903-1937," unpublished oral interview (March 9, 1988) (MOHP), p. 26. 9For historical information on mathematics at UT, I rely on various sources, and especially on [Greenwood 1983, 1988], [Lewis 1989], [Parker 2005]. 1~ 1989, 232].

92007 Springer Science+Business Media, Inc., Volume29, Number 4, 2007 63 appointed assistant professor in 1920 activity. Dickson also did much over the that Moore always saw as his second after a decade at the University of Penn- following years to promote Vandiver's academic home. sylvania. Moore's mathematical capa- career. In 1914 Vandiver published his In view of the deep differences in bilities had been recognized while he first article on FLT and for many years background and personality between the was just an undergraduate at Austin. In continued to present short communica- two men, one can hardly be surprised 1902 he succeeded in sharpening tions to the AMS on that topic. In 1920 that Vandiver and Moore did not develop Hilbert's analysis of the axioms of geom- he published his first truly substantial a strong friendship. Moreover, a glance etry (in an early edition of Grundlagen contributions to FLT, for which he be- at the trajectories of their respective ca- der Geometrie) by pointing out a re- gan to receive recognition. During his reers does suggest reasons why they be- dundancy. This research was part of a early years in Texas he continued this came such fierce rivals. Beginning new trend of enquiry known as postu- research, which led to a landmark pa- around 1930, Moore's research output lational analysis, which emerged in the per in 1929. He was subsequently gradually declined, both in numbers and United States in the first decade of awarded the first AMS Cole prize for out- in impact. Throughout the 1930s he pub- the twentieth century, n Three years standing research in number theory. 12 lished only five research papers, choos- later he completed his dissertation at Moore's first ten years at Texas were ing instead to devote most of his time Chicago under the supervision of E. H. similarly productive. In 1929 he pre- and efforts to teaching. By now he was Moore and (1880-1960) sented a summary of his work in the also supervising large numbers of grad- on "Sets of Metrical Hypotheses for Colloquium Lectures Series of the Amer- uate students, several of whom would Geometry," a study that followed the ican Mathematical Society. Published in become distinguished researchers. The same approach but focused on topo- 1932, his Foundations of Point Set The- Moore school flourished in no small part logical questions. For the remainder of ory came to be regarded as Moore's because the Texas topologist knew how his career--which began with brief magnum opus. 13 Other members of the to use his influence effectively when it appointments at Tennessee, Princeton, department of pure mathematics at the came to landing key positions for his and Northwestern, prior to his 10-year- time included John William Calhoun former students. Vandiver, by contrast, stay at the University of Pennsylvania-- (1871-1947), Edward Lewis Dodd (1875- would remain fully devoted to research Moore continued his research on these 1943), Paul Mason Batchelder (1886- for decades to come. At the same time, same topics. Thus, in an important pa- 1971), and Hyman Joseph Ettlinger he never distinguished himself as a lec- per from 1915 he investigated separa- (1889-1986). In 1925 Renke G. Lubben turer and attracted relatively few stu- tion properties in a strikingly innovative (1898-1980) was the first of Moore's stu- dents. Instead, he worked with a faith- way. By the time he returned to his Alma dents to join the faculty at Austin. Thus ful circle of collaborators, most of them Mater in 1920, Moore had published 17 Porter's efforts led to the consolidation from outside Austin. He met with them research papers in a field whose name of a respectable graduate faculty, with often, especially during his frequent he had coined: point-set topology. Moore and Vandiver as its central pillars. leaves of absence. Whereas Moore ex- Four years later Vandiver arrived in It seems that relations between celled in the classroom, Vandiver fa- Austin, having taught for five years at Moore and Vandiver began on reason- vored scholarship. His expository papers Cornell. A high-school dropout, Van- ably friendly terms. As an outsider and and authoritative accounts related to FLT diver had studied some college-level a later arrival in Austin, Vandiver was and the theory of cyclotomic fields were mathematics in Pennsylvania but never in a less advantageous position. He was widely read. took a college degree. In 1900 he be- also without formal academic training; These striking differences between gan submitting solutions to problems but in Porter's view "the mere posses- Moore and Vandiver went to the core posed in the American Mathematical sion of a doctoral degree (or any other of their respective identities as mathe- Monthly, some in collaboration with the degree) was small indication of abil- maticians, and there can be little doubt young (1884- ity. "14 Moore presumably felt the same that those differences contributed to the 1944). After spending more than ten way. But later, when Vandiver became mutual animosity that developed be- years as a customs house broker, Van- recognized world-wide for his research tween them. An anecdote from many diver obtained the position at Cornell in and was elected to the National Acad- years later is telling: In 1963, at the age 1919, thanks in part to Birkhoffs en- emy of Sciences only shortly after of 81, Vandiver submitted his final pa- dorsement. That same year he collabo- Moore himself, the latter took such mat- per to be published in the Proceedings rated with Dickson (then at Chicago) in ters of status very seriously. Moore of the National Academy of Science. 15 the preparation of the latter's book on seems to have been especially irritated On this occasion, Edwin Wilson (1879- the history of the theory of numbers, es- when in 1946, at the height of their 1964) wrote to express his delight that pecially the chapter on FLT. Dickson be- feud, an Honorary Doctorate of Science Vandiver was still working at an age came Vandiver's main source of inspi- was conferred on Vandiver by the Uni- when "most have had enough." To this, ration in all aspects of mathematical versity of Pennsylvania, an institution Vandiver replied that if people stop

11See [Corry 2004, 172-182]. ~2For details see [Gerry 2007]. 13[Moore 1932]. The revised edition of 1962 also contains many acknowledgements of results obtained by his students. 14[Greenwood, et aL 1973, 10929]. 15[Vandiver 1963].

64 THE MATHEMATICALINTELLIGENCER publishing at an old age it is not be- their own skills of critical analysis and a hastily built-up intuition that was cause they have had enough, but in creativity. Moore summed it up in just not substantiated by the axioms .... many cases, because "they permit eleven words: 'That student is taught The course continued to run in teaching duties and certain other acad- the best who is told the least. 17 this way, with Moore supplying the- emic pursuits to take up so much of To be sure, a precise definition of orems (and further axioms as their time that it is impossible to pre- the is not a straightfor- needed) and the class supplying pare any original mathematical paper of ward matter. Moreover, given the quan- proofs .... Moore put the students their own. "16 Vandiver evidently took tity and quality of mathematicians who entirely on their own resources so far pride in saying that he had never let came under Moore's direct and indirect as supplying proofs was concerned. this happen to him. He did not need to influence, one must presume that many Moreover, there was no attempt to add that the other Texas titan, who was developed their own versions of this cater to the capacities of the "aver- still teaching in Austin, had given up re- teaching method. 18 Parker gathers a age" student; rather was the pace set search decades earlier. large number of testimonials from grate- by the most talented in the class. ful and admiring students who went on Not everyone, of course, shared this Moore's Method and Vandiver's to successful careers; many pointed to enthusiasm for the Moore Method, Lack Thereof the training they received from Moore which was roundly criticized by stu- Nothing better signifies the stark con- as the single most decisive factor in the dents as well as established mathe- trast between the personalities of Moore consolidation of their mathematical out- maticians from the time the master first and Vandiver than their respective atti- looks and scientific personalities. One began to promote it. Vandiver was by tudes toward teaching. The subtitle of distinguished pupil, Raymond L. Wilder no means an overt critic, but he also Parker's biography very aptly captures (1896-1982), offered this vivid account clearly showed no sympathy for such the essence of Moore's character: "Math- of his former teacher's methodology: 19 a radical approach. Nor was he willing ematician and Teacher." If a reliable bi- He started the course with an infor- to invest a similar amount of time and ography of Vandiver is ever written, the mal lecture in which he supplied energy in teaching and supervision, word "Teacher" will most certainly not some explanation of the role to be and he remained essentially sceptical appear in its title. Even his closest col- played by the undefined terms and that any didactical method, including laborators and friends stressed his poor axioms. But he gave very little intu- Moore's, could systematically turn out abilities as a lecturer. His intellectual itive material--in fact only meager outstanding research mathematicians. and personal energies were never di- indication of what "point" and "re- Vandiver also disliked Moore's aggres- rected toward teaching or supervising gion" (the undefined terms) might sive tactics when it came to hunting graduate students Nor did he maintain refer to in the possible interpreta- down promising students in UT's en- close relations over the years with the tions of the axioms .... The axioms tering classes. In this manner, Moore few he did supervise (one in 1941 and were eight in number, but of these gained indirect control over many of four in the 1950s). he gave only two or three to start the best talents, including those who Parker emphasizes the centrality of with; enough to prove the first few received financial aid, while depleting teaching throughout Moore's entire ca- theorems. The remaining axioms funds that might have gone to students reer, including the development and in- would be introduced as their need associated with Vandiver and other, fluence of the famous Moore Method: became evident. He also stated, more passive, colleagues The 50 students he guided to their without proof, the first few theo- With regard to the training of grad- PhDs can today claim 1,678 doctoral rems, and asked the class to prepare uate students, Vandiver's views were descendants. Many of them are still proofs of them for the next session. close to those of another Dickson pro- teaching courses in the style of their . . In the second meeting of the t~g~, Eric Temple Bell (1883-1960). In- mentor, known universally as the class the fun usually began. A proof deed, Vandiver and Bell had much in Moore Method, which he devised. Its of Theorem 1 would be called for common, beginning with their mutual principal edicts virtually prohibit stu- by asking for volunteers. If a valid interests in number theory, though dents from using textbooks during proof was given, another proof dif- Bell's research never attained the level the learning process, call for only the ferent from the first might be of- of Vandiver's. Like his Texas counter- briefest of lectures in class and de- fered. In any case, the chances were part, Bell took a dim view of certain of mand no collaboration or conferring favorable that in the course of his colleagues at Caltech who were between classmates. It is in essence demonstrating one of the theorems constantly hunting for brilliant new stu- a Socratic method that encourages that had been assigned, someone dents. 2~ Nor did Bell ever distinguish students to solve problems using would use faulty logic or appeal to himself as a lecturer, 21 though he was

16Wilson to Vandiver, March 18, 1963; Vandiver to Wilson March 27, 1963. Like other letters cited in this article, this one is kept in the Vandiver Collection, Archives of American Mathematics, Center for American History, The University of Texas at Austin (hereafter cited as HSV). Letters are quoted by permission. 17[Parker 2005, vit]. 18For information on Moore's students as teachers, see [Parker 2005, 144-159], [Zitarelli & Cohen 2004]. 19[Wilder 1959]. 2~ 1993, esp. 261-265]. 21For a devastating criticism of Bell's didactic abilities voiced by a former student, Clifford Truesdell, see [Reid 1993, 284].

2007 Spnnger Science+Business Media, Inc., Volume 29, Number 4, 2007 65 much more active than Vandiver when ture sequence in his questions, with were strictly forbidden. Students should it came to supervising doctoral stu- prompts in between so he didn't just rely on their own capabilities. Dickson dents. Still, Bell's antipathy toward send us off and tell us to see what "tended to quickly deride that ap- teaching is apparent from a letter sent we could do. He was definitely lead- proach, but E. H. Moore, as was his to Vandiver in 1933 in which he bluntly ing students towards more and more wont, said little. He customarily gave expressed his views about the futility sophisticated thinking, towards re- some thought to new ideas before re- of training researchers. Concerning search with the goal of developing acting to them. ''25 Vandiver was work- Moore's avowed ability to produce research mathematicians, people ing in close collaboration with Dickson original research mathematicians, he who were really creative. at that time, especially on the latter's wrote: History of the Theory of Numbers, which I don't blame you for getting away Vandiver, on the other hand, would Dickson saw as highly important for from the damned students. The just come in sort of casually and ask both teaching and research in mathe- more I see of them, the more I am things and eventually gave up on matics. Whether or not Vandiver ex- convinced that trying to train peo- that and went to reading books, plicitly heard Dickson speak critically ple to do research is a waste of time. chapters from Albert's Algebra and about Moore's didactical method, he What few ideas a trainer has left af- from Vandiver's own books. 23 certainly shared a similarly critical atti- ter ten years of it are too precious To the extent that Vandiver did adopt tude toward it. to be thrown away. A man who is any pedagogical principles, these re- worth a damn will train himself. 22 flected a reliance on classical mathe- From Mounting Tension to Raymond Wilder's account of matical literature (preferably read in to- Open Clash (1937-1952) Moore's classroom technique, cited tal isolation). This approach he had The interwar period was one of thriv- above, highlights another aspect of de- learned from Dickson, as he repeatedly ing expansion for the departments of cisive importance, namely the close explained in later years: pure and applied mathematics at Austin. connection between the subject matter [Dickson] had an office adjoining the Some faculty members, above all Porter, taught, point-set topology, and the di- Mathematical Library, which fine li- did not think Texas was a truly first- dactical approach taken. As noted ear- brary was very quiel, a fact, of class university or that the atmosphere lier, R. L. Moore's mathematics was part course, which helped him in con- there was conducive to its becoming of the new trend of research in postu- centrating on any matter at hand. one but, arguably, the two mathemat- lational analysis through which he Also, if he wished to consult or re- ics departments came closer than any emerged as a central figure in Ameri- view any mathematical article, all he others at the time to meeting Porter's can mathematics. His didactical method had to do was walk a few steps to high standards. 26 This was, above all, thus arose as a natural concomitant of locate it .... This situation may have due to the combined presence of Moore this new research orientation. had a great deal to do with the fact and Vandiver, both of whom were as- In contrast, for Vandiver, axiomatic that as far as the publication of orig- sociate editors of leading mathematical analysis was of very limited interest. For inal mathematical articles is con- publications. Both were elected to the one thing, axiomatics simply were not cerned, Dickson was probably the National Academy of Sciences (in 1931 needed for the kinds of problems he most prolific mathematician of his and 1934, respectively), and both had was pursuing in number theory and the time. 24 received the distinction of being named theory of cyclotomic fields. In fact, his It is therefore interesting to notice as AMS Colloquium Lecturers, as well stance toward modern, structural alge- that back in the 1920s Dickson had as, respectively, President (1937-1938) bra was ambivalent at best. Vandiver's been among the early critics of Moore's and Vice-president (1933-1935) of the mathematical strengths lay in very dif- then-emerging pedagogical views. AMS. ferent directions, and because didacti- Moore himself reported that in the early Toward the end of the 1930s, how- cal concerns were not high on his math- twenties, during a summer visit to ever, when political tensions were ematical agenda, he did not develop a Chicago, he discussed effective meth- mounting in distant Europe, and Texas systematic approach to teaching that ods of teaching mathematics with E. H. politics entered a tumultuous period could be related to axiomatics. Moore and Dickson. R. L. Moore ex- that eventually swept UT into its midst, This was evident even in his occa- plained the approach he had been de- the personal clash between the two sional attempts to imitate Moore's method veloping at the University of Pennsyl- mathematical figures reached its height. in his own teaching. According to one of vania: posing questions or theorems for The first concrete evidence dates to Moore's prominent students, Richard D. students and insisting that they settle 1937 when Moore was nominated "Dis- Anderson, describing a course in 1941: them on their own. Assistance of any tinguished Professor" at UT. This re- Vandiver didn't realize that Moore sort, including conversations with fel- cently created status was not only an had a very carefully organized struc- low students and searching in books, academic honor reserved for "nationally

22E}ell to Vandiver: November 1, 1933 (HSV). Emphasis in the original. 23Quoted in [Parker 2005, 182]. Actually, Vandiver published no book of his own. 24[Vandiver 1960, 50]. 25[Traylor 1972, 92]. 26[Lewis 1989, 236].

THE MATHEMATICALINTELLIGENCER distinguished" faculty members, it also Martin Dies, who chaired the recently their political views is needed, bearing came with a substantial increase in founded House Un-American Activities in mind the difficulty of judging their salary. Moore was among the first three Committee (HUAC). Dies warned of actions in the absence of documentary recipients of that honor to be elected Stalinist and Marxist cells operating at evidence. by the entire graduate faculty. the university under Rainey's nose. Cap- Moore's politics--as Parker succinctly In 1939, Vandiver sent his long list italizing on this hysteria, O'Daniel nom- put it--"were firm and outspoken, and of publications and grants to his col- inated his own conservative supporters still steeped in the Southern principles league Calhoun, now acting president to UT's Board of Regents. These new by which he was raised. He would have of UT, arguing that his reputation might appointees were expected to carry out no truck with American left-wingers." 3o be damaged were he not to be consid- his policies for getting rid of "subver- This certainly applied to his active op- ered sufficiently distinguished. 27 His im- sives, Communists, and homosexuals," position to New Deal policies, but it also pressive credentials notwithstanding, but also to enforce tighter budget con- reflected his general views on the ero- Vandiver would not be named a Dis- trois and to influence academic life in sion of states' rights by those who ad- tinguished Professor until 1947. Even general. vocated an expansion of the powers of then, the title he received was Distin- And indeed, the Board of Regents the federal government. Clearly, Moore guished Professor of Applied Mathe- did its best to please the governor. Be- never equivocated when it came to is- matics and Astronomy, in accordance tween 1941 and 1945 the Regents un- sues like the right to bear arms. He was with the name of the department to dertook a series of aggressive steps to also far from enthusiastic about the ar- which he had recently been transferred. strengthen its control over academic rival of large numbers of European emi- Vandiver sarcastically commented to a matters. Rainey was ordered to fire pro- gres who were offered positions in friend that "he was the only distin- fessors of economics who espoused mathematics departments at American guished professor of applied mathe- New Deal views, and the board sought universities. Concerning Jews, Moore matics and astronomy in the world who to ban the study of literature they was outwardly respectful of their math- knew not a damn thing about either deemed subversive and perverted, ematical abilities, and he had close per- one. ''2s And indeed, the rather ridicu- works such as John Dos Passos's USA sonal relations with Ettlinger (who was lous transfer of Vandiver to applied trilogy. The Board also attempted to well-known also as a Roosevelt sup- mathematics in 1945 came as a conse- weaken tenure conditions and ordered porter). But Moore explicitly opposed quence of the by then unbearable rela- the cancellation of research funds for an open-door policy for Jewish mathe- tions between UT's two mathematical the social sciences. The peak of the cri- maticians. Above all, on the issue of titans. sis came on November 1, 1944, when segregation, Moore's record is unam- The broader background leading up the Regents fired Rainey for his liberal biguous: he was firmly reluctant to ac- to these events was marked by mount- policies and his lax attitude regarding cept African-American students into his ing general tension in Texas during the racial issues. Students protested this ac- courses. Moore once told Walker E. midst of the Great Depression. Texas tion and academic organizations ex- Hunt, "you are welcome to take my governor W. Lee O'Daniel (1890-1969) pressed their dismay. The American course but you start with a C and can was elected in 1938 on a Democrat Association of University Professors only go down from there. ''31 As else- ticket. After reneging on several cam- (AAUP) put the University of Texas on where in the South, the process of in- paign promises, he became an outspo- its blacklist, where it remained for the tegration was exceedingly slow in ken critic of the New Deal, especially next nine years, and The Southern As- Texas. Following a Supreme Court de- after Franklin Delano Roosevelt's elec- sociation of Colleges and Secondary cision, UT would open its doors to tion to a third term in 1941. O'Daniel Schools also put UT on probation. 29 black students in 1951, but only to those was particularly disgusted by the price- The situation at UT initially made na- accepted by the law school or the grad- fixing policies that affected the Texas tional headlines and attracted consider- uate school. Seen in this light, Moore's oil industry, but he also loathed Eleanor able attention, but of course the events traditional Southern outlook was in no Roosevelt's support for legislation in Austin were quickly overshadowed way outside the mainstream. And while aimed at racial desegregation. Soon af- by the far more dramatic events taking his flamboyant style and prominence no ter his appointment in 1939, UT Presi- place overseas. Press coverage of local doubt made his positions more visible dent Homer P. Rainey (1896-1985) affairs, like the one at UT, quickly faded, than those of other UT colleagues, his became a major target of O'Daniel's at- but the events that shook Austin in views were not exceptional for the time. tacks against New Dealers. Rainey had 1944-1945 were hardly forgotten. In or- Vandiver was less outspoken when openly challenged accusations of al- der to understand the respective reac- it came to politics, so one can only spec- leged un-American activities at UT, tions of Moore and Vandiver to this crit- ulate about his views. He worked for claims aired by Texas Congressman ical situation, some information about many years at a segregated university,

27See [Greenwood 1983, 20], [Lewis 1989, 235-236]. 28[Frank Vandiver, interview. Also quoted in [Parker 2005, 227]. 29See [Parker 2005, 194-205] for additional details on this story. 3~ 2005, 165]. 31Scott W. Williams, Professor of Mathematics at Buffalo, maintains a website called: "R. L. Moore, racist mathematician unveiled," with information on this matter. See http://www.math .buffalo.edu/mad/special/RLMoore-racist-math.html.

2007 Springer Science+Business Media, Inc., Volume29, Number 4, 2007 67 apparently without qualms. Although Clearly there was no love lost be- by the ideals of those who are more we have no direct testimonies of any tween Vandiver and Moore as the UT concerned with uniformity of standards initiatives he took to address the injus- crisis reached its climax, and these po- and 'fair' treatment of the mediocre than tice embodied by institutionalized seg- larizing events surely ended whatever they are with the establishment and regation, nevertheless, a letter that Van- chance they might have had for sal- maintenance of high standards and the diver wrote in 1951 suggests that his vaging a civil relationship. Vandiver discovery and fostering of outstanding political sympathies were essentially sided with most on the UT faculty, who ability.'37 very different from Moore's: felt that the Board of Regents had seri- In this highly self-serving perfor- You speak of visiting Austin again ously damaged academic freedom at mance, Moore obviously preferred to ig- next Christmas. The situation here is the university. Moore, on the other nore the potential abuses of a weaker such that I wish that matters were re- hand, was among the minority who tenure system, which could be ex- versed and that I was coming to supported the Regents' policies and ploited as a political weapon by the Princeton next fall. After you left here who actively opposed their critics. In a Board of Regents. And while it seems the Texas legislature really went af- letter to the secretary of AAUP he de- likely that Vandiver would have agreed ter our institution and the present in- clared that its recent decision to cen- with Moore on the need to avoid tenure dications are that the appropriations sure UT only served to discredit the schemes that might lead to low acade- for next year will be cut 40% below AAUP. "I do not know he adduced-- mic standards, he clearly opposed the what it was for the last biennial. They a single instance in the last twenty years intrusions of politicians in the univer- also demanded that one of our eco- in which any board of regents of this sity's academic affairs. By this time a nomic professors be investigated on University has violated what I consider deep chasm divided the Austin faculty suspicion of being a Socialist and so to be sound principles, either of acad- into two clearly defined camps. Van- the place is in somewhat of a tur- emic freedom or of tenure. ,,36 diver and Moore found themselves in moil. Perhaps their next move will be In a rare appearance at the General an additional and now very significant to have a faculty member fired for Faculty Meeting on May 12, 1945, Moore confrontation. being unkind to dumb animals. 32 presented in great detail his views on In both mathematics departments, Vandiver's close friendship with the issue of tenure, a main source of tensions only heightened as Moore be- Emma and Derrick Henry (Dick) contention between the UT faculty and came more powerful than ever. Faculty Lehmer may perhaps also be taken as the Board of Regents. At stake was a members had been long openly com- an important indicator of his political new scheme suggested by the faculty plaining that financial support was eas- inclinations, or at least his tolerance of whereby any instructor would, after ily available to students of Moore, Et- leftists. Dick Lehmer was among nine- four years of service, either be offered tlinger, and Wally but not those teen faculty members of the University a commitment for promotion or else working with Vandiver or other pro- of California who were dismissed in would receive one year's notice to find fessors in the department (Dodd, 1950 for refusing to sign a loyalty oath; alternative employment. Moore stated, Lubben, Betchelder, and Beckenbach). he was reinstated only after the oath axiomatically, two principles that in his The fistfight between Moore an Beck- was declared unconstitutional. 33 Lehmer view defined a first-class university: "(1) enbach took place at this time. Despite helped raise funds for the defense of a very substantial amount of really fun- the sudden availability of funds for colleagues prosecuted on charges of damental research of a high order is car- graduate students at the end of WWII, anti-American activities (most notably ried on by members of its faculty, and this situation did not change. Lee Lorch in 1957). 34 This was at the (2) there are some members of the fac- In 1945 Vandiver submitted his res- height of Vandiver's collaboration with ulty who are intensely on the alert to ignation. He gave no explicit reasons the Lehmers on the use of electronic discover and develop outstanding re- and many factors may have played a computers for increasingly high values search ability on the part of their stu- role, but surely the unbearable con- of exponents for FLT. 35 Political issues dents and who are both capable of rec- frontation with Moore and the highly related to the Supreme Court's deliber- ognizing such ability in the early stages politicized atmosphere at UT were high ations frequently appear in letters from of its manifestation and of developing among them. At that time, Vandiver was Emma Lehmer to Vandiver (though I it when it is discovered." He followed also deeply involved in his own re- could not find letters in which Vandiver this with a detailed argument leading to search and was overworked almost to explicitly addressed those issues and the conclusion that UT "will never be the point of exhaustion. But the uni- stated his own opinions). of the first class.., if it is dominated versity authorities, under increased pub-

32Vandiver to Ankeny: March 27, 1951 (HSV). 33An interesting website containing information on this topic is http://sunsite•berke•ey•edu/uchist•ry/archives-exhibits/••yalty•ath/symp•sium/timeiine/sh•rt.htm• 34Several letters related to the Lehmers' support are found in the Emma & Dick Lehmer Archive, UC Berkeley. 35[Corry 2007a]. 36Quoted in [Parker 2005, 205]. 37Quoted in [Parker 2005, 203]. Emphasis in the original. 38Hubert Stanley Wall (1902-1971) joined the faculty at Austin in 1946, at a late stage in his career, and became a devoted follower of Moore's method in teaching. See [Wall 1963]. See also, "In Memoriam. Hubert Stanley Wall," Memorial Resolution, Documents and Minutes of the General Faculty, The University of Texas at Austin, 1971, 10433-10438 http://www.utexas.edu/faculty/council/2000-2001/memorials/SCANNED/wall.pdf.

68 THE MATHEMATICALINTELLIGENCER lic scrutiny, worried that losing a math- told UT administrators "that there ous debates on reforms in US mathe- ematical star might expose them to fur- wasn't a single person in the Applied matics education, and the nomination ther criticism, external and internal, Mathematics Department who was a of Ed Begle (1914-1978) as director of They suggested instead that Vandiver real mathematician. ''4~ He obviously in- the School Mathematics Study Group be transferred to the department of ap- cluded Vandiver in his assessment. (SMSG), from which the New Math later plied mathematics. Initially Vandiver arose. 42 Moore's ideas can be seen in- saw this as a possible solution, but then A Mini-Cold War at Austin directly in the background of these de- for some reason the administration de- (1952-1969) bates, as Begle was a student of Ray- cided to leave him in pure mathemat- In 1952 Moore turned seventy, the age nqond L. Wilder. Likewise, Edwin Moise ics after all and appointed a committee at which, by university rules, a profes- (1919-1998), another well-known to work with Vandiver to find a com- sor became a "modified service" mem- Moore student, wrote influential high- promise. ber of the faculty. He continued to work school textbooks. Interestingly, Moise Typically, Vandiver conducted a full-time for half the pay, and his pres- emphasized that Moore himself never good part of his negotiations with the ence was felt in all aspects of depart- expressed any opinions on SMSG or university in writing, and from a safe mental life as it always had been. In about the New Math and made it clear distance; this time he did so in the calm many ways, his influence became more that he did not want to be regarded as surroundings of Princeton, where he visible than ever before. Thus, for in- a pedagogue. 43 was spending one of his frequent leaves stance, between 1952 and 1969 Moore Vandiver's ideas on teaching at this of absence. The correspondence, in the supervised twenty-eight doctoral stu- time appeared in a two-part research ar- summer of 1945, between Vandiver dents, and six of his former students be- ticle published in 1952-53 in the Math- and President Theophilus S. Painter came presidents of the Mathematical As- ematics Magazine, "A Development of (1889-1969), a well-known geneticist sociation of America (MAA) after 1950. Associative Algebra and an Algebraic and Rainey's successor, and Vice-presi- From a more general perspective, vari- Theory of Numbers." Perhaps it is not dent James Clay Dolley suggests the dif- ous versions of the Moore Method of a mere coincidence that this is one of ficulties the authorities had in dealing teaching became increasingly common the few places where Vandiver spent with Vandiver; he raised many different in American universities, even though some effort in a technical discussion topics simultaneously, discussed with Moore himself never made any specific about a new system of postulates. This Dolley recent baseball games he had effort to foster such a development. 41 was a system for defining associative al- watched, and continually changed his Vandiver, too, became a "modified gebras "in a bit unusual way," and he positions vis-fi-vis the administration's service" member of the faculty at this remarked that "many secondary school proposals. Finally, on December 12, time. His earlier transfer to the Depart- students are alienated from arithmetic 1945, 39 he asked to be transferred to ment of Applied Mathematics and his and algebra because the only way they Applied Mathematics, and there he new formal status only strengthened his learn these topics.., is by following a went. The Pure Mathematics Depart- natural tendency to estrange himself set of rules which are never stated ex- ment, surely under the initiative of from departmental life. Moreover, the plicitly by the teacher." Vandiver said Moore, insisted that Vandiver could not contrasts between the two mathemati- he learned this from his own experi- take his courses with him. Vandiver's cians became even more pronounced ence as a high-school student. The old course "Theory of Numbers" thus in their last years at UT, as Vandiver mathematically gifted students, he became, in his new department, "The- continued to be rather active in re- thought, deserved a clear presentation or'/of Integers." search, actively collaborating with other of "a few explicit postulates in arith- In 1952 the two departments were researchers in his fields of expertise, metic and algebra." united, but this administrative act did whereas Moore had long before with- The ideas discussed in the articles not immediately translate into full col- drawn. The conflict between the two are of limited mathematical interest, but laboration. Indeed, according to Robert entered a phase of "cold war" that even- they are clearly related to Moore's Greenwood (1911-1993), who spent his tually became a source of embarrass- method. Vandiver stated that he devel- 55-year mathematical career at Austin, ment for everyone at Austin. oped these ideas in his courses and a "spirit of antagonism developed in the Yet, strangely, at the twilight of his seminars over twenty years, and espe- minds of the young graduate students career Vandiver began to discuss pub- cially in a recent seminar in which three in the old Pure Mathematics Depart- licly his ideas about school-level math- of his five doctoral students partici- ment, and R. L. Moore was unrelenting ematical education and the proper train- pated. 44 He also "discussed these top- in keeping pressure on former Applied ing of teachers. This turn may have had ics with sophomores with apparently Mathematics members." Indeed, Moore some connections with contemporane- some success," and attributed this to the

39Dolley to Vandiver: Aug 13, 1945 (HSV). 4~ 1983, 47]. 41[Parker 2005, 232-234]. 42[Usiskin 1999]; [Raimi 2005]. 43[Anderson & Fitzpatrick 2000]. The possible influence of Moore's ideas on New Math is a topic that deserves some further thought, but it cannot be pursued here for lack of space. 44[Vandiver 1953, 4}.

2007 Springer Science+Business Media, Inc.,Volume 29. Number 4, 2007 69 Figures 1 and 3. Robert Lee Moore in his youth (left), and in October 1930 (right). Photos are published by permission of the Center of American History, the University of Texas, Austin; they are part of the R. L. Moore Legacy Collection in the Archive of American Mathematics. fact that he "did not do anything except qualifications of a teacher even better versity for a long period. In this case try to set up some rules to justify the than a professor who delivers lectures I think it would be excellent if the operations they were already used to in in a university. ''46 Euler, for example, university would pay for as many algebra." While in his advanced courses, had no students but, by virtue of his long distance telephone calls as he he "suggested to the students that they enormous original work, "was the deemed necessary in order to keep forget everything they know about greatest teacher of mathematics who in touch with other scientists with mathematics, since we would tiT to start has lived in the last 200 years." Gauss the idea of going forward in his from scratch"; he doubted this would too would rank among the greatest work. (p. 9) be a "good suggestion to make to a teachers of mathematics according to Vandiver was also concerned with sophomore.'45 Vandiver's definition, an individual A, problems faced by mathematics teach- Somewhat later, in an unpublished who "communicates in any way what- ers in elementary schools. 47 Elementary manuscript, Vandiver also addressed soever to an individual B some idea school teachers did not receive proper the question of the proper training of which is new to B and which B retains training. For example, an examination teachers of mathematics. Besides other in his mind." He concluded, of many textbooks showed that they possible motivations, one gets the im- At present I think the practice may were not taught the essence and mean- pression that Vandiver at least wanted be pretty widespread at universities ing of--of all things--the decimal sys- to stress what he saw as his own last- to give their teachers time off and tem. Vandiver claimed that if his advice ing contribution to the teaching of funds to travel to various places in was followed, in five years time foun- mathematics. A research scientist, Van- order to consult the various research dations would be able to save huge diver wrote, is actually a good teacher men in their own line of study; how- amounts of money currently devoted to by virtue of his very research activity, ever, some scientist may be so situ- coaching teachers. Vandiver sent the "and in some instances he fulfills the ated that he cannot leave his uni- editors of the American Mathematical

45[Vandiver 1953, 16]. 46[Vandiver, unpublished 1]. 47[Vandiver, unpublished 2].

7'0 THE MATHEMATICALINTELLIGENCER Moltthl3, a manuscript of 49 pages: a the communications gap. l)ickson significant R)r Vandiver; little wonder shorter version of five pages was not once said that "every mathematician that McShane's article struck a sympa- published either, though in several let- owed a debt to mathematics that he thetic chord with him. ters he mentioned that it would soon should repay by one hard job of Inspired by these ideas, Vandiver de- appear in the 1959 volume of the T~:vas scholarly writing." His Histoo; (),/'the cided to set forth his own views. Aside Quarterly. Tbeo W of NHmbers had been Dick- fi'om the publication of research papers, Whatever drew Vandiver into a dis- son's own way of paying that debt. he was convinced of the "desirability of cussion on pedagogical topics, we find McShane \~as aware that few would publishing complete bibliographies of here a rather ironical situation. On the consider an undertaking of such the literature on various branches of one hand Moore, who devoted so magnitude; nonetheless, he insisted mathematics, with reviews when possi- much of his professional energies to his that "each of us owes the debt, and ble." t9 The editors of the Bulletin of the university teaching, distanced himself should not repudiate it if he is math- AMS" may have had different ideas, from the debate about mathematics in ematicallv solvent." (p. 313) Expos- though more likely they rejected Van- secondary and primary schools. On the itory articles were needed for the diver's article on this topic as inappro- other hand, Vancliver, for whom teach- continued renewal of the teacher's priate lor their journal. The editors of ing was essentially a burden to his uni- activity. On the research side. he be- the Mo,ztbl3, were also initially unen- versity activities, contributed his own moaned the low quality of writing thusiastic, although they finally acqui- ideas and tried to influence mathemat- and the failure to make research pa- esced and the paper was published in ical education in the United States pers accessible beyond the limited 1960. through improved training of teachers. circle of specialists with whom au- Vandiver based his argument on thors were already in direct contact. Dickson's book, which he considered A Role for Mathematical As the author of accomplished ex- as important in 1960 as it had been at Scholarship pository articles in his own field of the time of publication. Quoting his As already suggested, mathematical expertise, Vandiver read McShane's own 1924 review of Volumes I and II,: 5~ scholarship was of major importance for speech with pleasure. In fact, McShane It often happens in the history of Vandiver but played a lesser role in made a flattering allusion to Vandiver's mathematics that a mathematician Moore's overall conceptions. This work: becomes a specialist in a particular emerges in certain initiatives Vandiver I am not recommending the writing topic, and, after years of experience undertook late in his career, when he of expository papers as a sort of pas- with it, he publishes a treatise giv- attempted to influence additional as- time for gentlemen (young, old, or ing a harmonious and comprehen- pects of mathematical life in the United middle-aged) who have determined sive development of the subject, the States. In 1957 Vandiver read with great by careful self-examination that they material being arranged and pre- interest the Retiring Presidential Address haven't a research paper left in their sented according to his own partic- delivered by Edward J. McShane systems. A man of thirty may have ular point of view. This treatise may (1909-1989) at the Annual Meeting of attained position and recognition become a classic, and its readers are the MAA in December 1956, entitled and broad knowledge: a man past likely to get in the habit of ignoring, simply "Maintaining Communication."''~s seventy may be active in research, to a considerable extent, the litera- McShane worried that modern research as the current volume of the Pro- ture that preceded its publication. In was running out of control and that ceediHgs of the A?ttional Academ.l' (),/" this way, the points of view of the mathematics had grown wild and un- Sciences will show. older writers are often lost sight of, structured during the last decades; this On the other hand, McShane's case for as these treatises rarely, if ever, re- could lead to a breakdown into sut)-dis- the importance of expository writing in produce all the older material on a ciplines in which only specialists could teaching ran contrary to the essence of particular topic. It would seem that understand each other. McShane was Moore's method, as one of Moore's there is too great a preponderance especially alarmed about the lack of maxims was that students not read of books of this sort in the literature general communication mnong modern other people's work (even though, in and too few histories of reports of researchers. He pointed to three main thesis work, Moore definitely expected the type of Dickson's work. spheres of mathematical activity which, novelty visq-vis the existing literature, Many works cited by Dickson con- in his view, should complement one an- which the students were expected to tained results that had been published other: teaching, research, and scholar- know in detail). McShane called for in- earlier by someone else. As Vandiver ship. Yet this third sphere of activity "is creased breadth of mathematical schol- wrote to one of his correspondents, he all to() often left unmentioned." arship in teaching from the ve W early himself had "been haranguing mathe- McShane lamented, in particular, the stages of a student's training. The fact maticians to do something about the dearth of good expository articles, that McShane mentioned Dickson's situation," with no visible result. 51 which were badly needed to bridge work in this context was also certainly Vandiver was aware of the immense

~S[McShane 1957]. a9Vandiver to R. D. James (Editor of the Monthly): August 6, 1958. 5~ 1924]. 5Wandiver to Leo F. Epstein: May 11, 1960 (HSV).

2007 Springer Science+Business Media, Inc. Volume 29, Number 4, 2007 71 effort that would be required to con- main source of dissatisfaction with the empowered to present any paper tinue Dickson's work. The number of current system was that "persons re- which they think fit. The system of relevant references between 1920 and porting on papers failed to remember anonymous refereeing which we use 1956 were about 8,500. If five mature, that they are supposed to be reporters now in most journals has so many top-rate number-theorists would collab- and not critics. ''52 To correct this situa- defects and so many abuses that I orate, with five years to complete the tion, authors should begin their articles think any unprejudiced observer job, each would need to write almost with an abstract that could later be pub- would say that it had failed almost one review per day. Dickson had re- lished in the Mathematical Reviews or completely. Oddly enough, it serves viewed 8,382 works--leaving out major in a future bibliography of the subject. the purpose of passing the mediocre issues like algebraic number theory, The referee for the journal would also paper along with no difficulty, and Bernoulli numbers, and the law of qua- approve the abstract for the Reviews. almost completely hindering the dratic reciprocity. And these papers, That such abstracts might merely reflect novel paper with original and un- Vandiver stressed, were far less difficult the opinions of the author was a minor conventional results and ideas. than more recent work, whose volume problem, Vandiver felt, compared with Vandiver summarized the reactions was rapidly growing. It would be diffi- the advantages gained in speed and ef- and his own responses to them in a de- cult to find mathematicians willing to ficiency. The situation was different for tailed, formal letter to the President of do the job. And this is just in number mathematical books; here criticism was the AMS, (1909- theory. In a field like differential equa- welcome and necessary, "since there 1992), and expected Montgomery to tions, the most one could hope for might be a question as to whether it raise this matter in a forthcoming meet- would be the "preparation of a nearly would be advisable to have money ing of the AMS Council. 55 It seems that complete list of references," while di- spent to add such books to mathemat- his initiative did not reach any further, viding the literature into sub-topics "so ics libraries. ''53 All of these ideas were and his ideas on reviewing were never that a research man does not have to inspired, Vandiver said, by what he had adopted in the Reviews, although Zen- look up too many listed papers to de- learned from his collaboration with tralblatt often uses "Autor-referats". cide that the results he has arrived at Dickson, especially on the History. Vandiver was involved in a second are new." Vandiver wrote to various mathe- undertaking that shows how he tried to Vandiver knew that "the work of a maticians, especially editors of known turn his views on mathematical schol- bibliophile on first glance is not attrac- journals, who he believed would sup- arship into a concrete plan of action. In tive," and indeed many mathematicians port this project, among them Leonard 1961 William J. LeVeque submitted a reacted with "deep disgust at the idea." Carlitz, J. Barkley Rosser, Max Shifter, proposal to the National Science Foun- Yet following McShane's lead, Vandiver Peter D. Lax, Joseph Walsh, Marshall dation calling for the publication of '% argued that such bibliographies were Stone, Richard Bellman, and Gordon General Survey of the Theory of Num- crucial for the advancement of mathe- Whyburn. Some reacted with useful bers Leading to the Compilation of a matical research and teaching. Mathe- comments. Walsh suggested that au- Topical History and Critical Review of maticians should undertake the task not thors should be instructed to choose the Theory of Numbers, 1915-1960." only as a duty to the discipline but also meaningful names for their papers Not surprisingly, Vandiver was enthusi- for its personal benefits. He himself had (rather than, say, "Proof of a Lemma astic about this project and wrote a found, preparing such lists for a num- due to Wye Zed"). Stone wrote that, al- highly positive report. 56 ber of topics in number theory (part of though he very much favored some of LeVeque mentioned three main top- which are kept in his archive), "that his the suggestions, he would not like to ics not originally covered by Dickson own knowledge of each topic increased have his name included as an uncon- that should be included: Analytic The- greatly thereupon, and the publication ditional backer. 54 One correspondent ory of Prime Numbers, Diophantine Ap- of a number of his papers was due to objected that reviewers sometimes proximations, and Algebraic Numbers. this." make valuable suggestions for exten- Vandiver suggested that a chapter on Vandiver received several letters in sions of results and this important in- Bernoulli and Allied Numbers should response to his article, most of them put would be lost under Vandiver's also be included, as well as the very positive. He decided to transform his suggestion. Belhnan fully supported important topic of Higher Reciprocity basic message into a plan for action Vandiver's initiative as he had a very that Dickson had left for a fourth vol- along two fronts. First, he wanted to re- low- opinion of the current state of the ume but never published. 57 He insisted form the existing reviewing system refereeing system: that only abstracts of articles should be (which is essentially the one still in use I think that the only intelligent and included, with somewhat longer ones today) to facilitate later compilations efficient technique is one based when the original paper had appeared of complete bibliographies. Vandiver's upon a board of associate editors in an out-of-the-way journal. If Dickson

52Vandiver to Bellman: May 12, 1960 (HSV). 53Vandiver to Bellman: May 12, 1960 (HSV). Emphasis in the original. 54Stone to Vandiver: January 21, 1962 (HSV). 55Vandiver to Montgomery: January 13, 1962 (HSV). 56Vandiver to Grad: February 27, 1962 (HSV). 57On this matter, see [Fenster 1999].

72 THE MATHEMATICALINTELLIGENCER had included criticisms in his book Silber brought in visiting scholars to time--was finally proved in 1994, it un- "such material would now be worth- evaluate the performance of various de- leashed a flurry of publiciW inside and less." Finally, he referred to the inten- partments and attempted to introduce outside the mathematical communiW, tion to rely on the Mathematical Re- mandatory retirement at the age of sev- but Vandiver's noteworthy achievements views: enty-five. This only raised tensions be- were completely overlooked. Since experienced reviewers are tween the administration and Moore's Some fifty years before their passing, hard to obtain in order to write re- still large and influential group of sup- Moore and Vandiver had begun their views for the Math. Reviews, I regard porters. A lengthy and rather nasW mathematical careers at the University most of the reviews appearing in process ensued that finally led to Moore's of Texas together. Each went on to be- that journal as quite inadequate. And forced retirement in September 1969 at come distinguished in his own particu- from what I have seen of the other age eighty-seven. Almost seventy-one lar way, but their paths parted quickly review journals, I do not think they years after he arrived as a freshman and and never again crossed. Vandiver died are much, if any, better. 58 tess than three years before his death, R. on January 4, 1973, aged 91; Moore was The NSF decided not to fund the pro- L. Moore walked oft the University of close to 92 when he passed away on ject, and it was postponed and even- Texas campus for the last time, refusing October 4, 1974. But both are buried in tually abandoned. 59 Grad explained to to attend any events to "honor" him. Austin's Memorial Park Cemetery. Vandiver that although most reviews When, in 1973, the new mathematics were favorable "the bibliography was building was named the Robert Lee ACKNOWLEDGMENTS considered to be of second importance Moore Hall, he was noticeably absent at Albert C. Lewis and David Rowe read as compared with research of the usual the dedication ceremony. 63 earlier versions of this article. I thank type. ''6~ Vandiver replied, "if the NSF Moore's long-time rival, Henry S. Van- them for their critical remarks, which led continues to support 'research of the diver, voluntarily took emeritus status in to significant improvement. Editorial usual type' to the exclusion of support 1966. Despite poor health in his later of bibliography projects, then as time years, he continued to do research and comments by Marjorie Senechal were goes on it will be supporting the pub- even received a research grant at the age also highly useful in preparing the final lication of the results of research which of seventy-six. Yet the only public hon- version. Primary sources used here were already are described in the litera- ors conferred on him at the end of his taken from the Archives of American ture. ,,61 career were quiet affairs that largely es- Mathematics, Center for American His- caped notice. In 1961 he was invited to tory, the UniversiW of Texas at Austin, Parting Company in Silence deliver the keynote address at the Texas and cited with permission. Mso some of Both Moore and Vandiver remained ac- Section of the Mathematical Association the important secondary sources cited re- tive until a very advanced age. For of America. 64 Five years later, a few lied on documents taken from the same decades, Austin's two leading mathe- friends and collaborators put together in archive. Mbert. C. Lewis played an im- maticians hardly exchanged a word so- his honor a special issue of the Journal portant role in putting together all of this cially, if at all, and their careers ended of Mathematical Analysis and Applica- material and more, and the writing of an quite differently. Not everyone in Austin tions, a publication otherwise devoted to article like this one would be impossible welcomed Moore's "volunteering spirit" topics unrelated to his own research. 65 without the basic work done at the when he continued to work at the de- No buildings were named after Vandiver, archives. partment after 1952 under a "modified nor did he leave a mark as a teacher at service" contract. On becoming Dean of the University of Texas. None of his five Arts and Sciences in 1967, John R. Sil- doctoral students went on to become a REFERENCES ber "made no attempt to conceal his leader within the American mathemati- Anderson, Richard D. and Ben Fitzpatrick view that Moore's very presence and cal community. Of his many interesting (2000), "An interview with Edwin Moise," reputation hindered the recruitment of contributions to mathematical research, Topological Commentary 5 (http://at.yorku. new faculty. ''62 Silber, formerly chair of only the conjecture of 1934 bears his ca/t/o/p/c/88.htm). the Philosophy Department, thought name, and this remains barely known, Corry, Leo (2004), Modern Algebra and the mathematics should be taught by ex- except to specialists. But most ironic of Rise of Mathematical Structures, Boston and perienced teachers in fewer sections all, when Fermat's Last Theorem--the Basel, Birkh~iuser. with more students in them. This, of problem to which he devoted so much --(2007), "Fermat comes to America: Harry course, ran counter to Moore's peda- of his energy and on which he became Schultz Vandiver and FLT (1914-1963)," gogical philosophy. the world's leading expert during his life- Mathematical Intelligencer 29 no. 3 30-40.

58Vandiver had considered not including this latter comment so as not to jeopardize the prospects of the project's being approved, but he obviously changed his mind. See Vandiver to Grad: February 7, 1962 (HSV). 59LeVeque to Vandiver: March 9, 1962 (HSV). 6~ to Vandiver: March 5, 1962 (HSV). 61Vandiver to Grad: March 13, 1962 (HSV). 62[Parker 2005, 322]. Ca[Parker 2005, 332}. 64[Greenwood, et al. 1973, 10939]. See [Vandiver 1961]. 65[Corry 2007].

2007 Springer Science+Business Media, Inc., Volume29, Number 4, 2007 73 --(2007a), "FLT Meets SWAC: Vandiver, the Lehmers, Computers and Number Theory," IEEE Annals of History of Computing (Forthcoming). Periodicals postage paid at New York, NY and additional mailing offices. Fenster, Della D. (1999), "Why Dickson Left Quadratic Reciprocity out POSTMASTER: Send address changes to The Mathe~atical D~telligencer, Springer Journals Dept., 233 Spring St., New York, NY 10013. of His History of the Theory of Numbers," Am. Math. Monthly 106 COPYRIGHT: Submission of a manuscript implies: that the work described (7), 618-629. has not been published before (except in the form of an abstract or as part Greenwood, Robert E. (1983), "History of the Various Departments of Math- of a published lecture, rex4ew or thesis); that it is not under consideration for publication elsewhere; that its publication has been approved by all coau- ematics at the University of Texas at Austin: 1883-1983." unpublished thors, if any, as well astacitly or ex-plicitly6by the responsible authorities at manuscript in the Greenwood archive, Archives of American Mathe- the institution where the work was carried out. Transfer of copyright to matics, Center for American History, The University of Texas at Austin. Springer becomes effective if and when the article is accepted for publica- tion. 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