Professor John Fauvel from the Open University in England delivered the following address at the 140th anniversary of Florian Cajori's birth. The celebratory tea was held on March 1, 1999 in the Gates Common Room at the Colorado College.
Marlow Anderson, John Fauvel, and Kathyrn Mohrman ( President of the College) cut the cake in honor of Florian Cajori's birthday.
It was ninety-five years ago last week, 23rd Feb 1904, that this building, the Palmer Science Hall, was opened and was soon widely recognised as one of the finest academic buildings in the country. The opening ceremonies had the usual grandiloquent speeches from visiting dignitaries, not least from President David Starr Jordan of Stanford University. In the course of an address whose loftiness well outreached its judgement, President Jordan summarized the history of education in terms which had long been recognised, in Europe at least, as entirely mythical. "The most wonderful thing in educational developments," he said, "since Alfred founded Oxford and Charlemagne, Paris, has been the rise of the state universities of America." ("Discuss", one feels tempted to say.) Then it actually got worse, about the virility of Colorado, how it expands one’s fearless manly chest, and flows red blood, which I suppose is colo-rado; but I will spare you that.
I mention it because someone in the audience that day to whom this nonsense would have been particularly galling was the Dean of Engineering and Head Professor of Mathematics, Florian Cajori, whose reputation as a scholar had been made by the History of Mathematics Education in North America which he had completed during his first year in Colorado Springs. Inwardly Cajori would have found it particularly tiresome as he knew he would have to print this interpretation in the series of Colorado College Studies which he had founded thirteen years before, and whose academic standards he was attempting to keep high. But as an institutional politician renowned for his soothing diplomacy, Cajori doubtless felt it was worth putting up with this for the sake of the students who would benefit so greatly from the new building, and whose scientific studies, in particular, were to be greatly furthered by its magnificent laboratory and lecture-room facilities. It was Cajori, after all, who had himself delivered the address at the laying of the corner stone of the building two years before, on March 3rd 1902, an address on The relation of the new building to the scientific work of the Rocky Mountain region, in which he spoke of the need to promote scientific studies for the new century, and for Colorado in particular: "This new era demands a new education", he said, in the course of an address in which he envisioned and predicted some of the scientific developments of the twentieth century.
My own interest in Cajori arose in the first instance as a fellow historian of mathematics, but the more I have discovered (with wonderful help from the College archivist Ginny Kiefer, which I would like to acknowledge) the more it has become evident that he was an absolutely crucial figure in the major development of the College that took place under President Slocum, and that he played an unparalleled part in establishing the solid foundations of excellence in teaching and scholarship on which the subsequent reputation of Colorado College has been built. For Cajori was not only a scholar of world renown, in the field of history of mathematics, which you’d have thought would take up most of anyone’s time, but he was also a superb administrator, who set up and headed the new school of engineering, of which he was Dean for fifteen years; he participated very fully in all aspects of College life (here he is with other members of faculty on the way to the 1896 baseball game between faculty and seniors) and on top of this he was also a highly regarded and much-loved teacher of mathematics whose memory lived on in his students until the ends of their days. In this talk I want particularly to celebrate Cajori as a person and to share with you how his particular qualities enabled him to accomplish so much for the good of the College, and indeed the country, which had taken him in.
Florian Cajori was born in Switzerland on February 28th 1859. His father was a leading civil engineer, Georg Cajöri, who was responsible for constructing several of Switzerland’s major roads and bridges; so engineering was in his blood, as it were. He came to this country when he was sixteen (a few years after this photograph of Florian Cajori in the 1860s was taken), and studied at the University of Wisconsin as an undergraduate. He was a graduate student at Johns Hopkins University in Baltimore, after which he became professor of applied mathematics at Tulane University. But within a couple of years he developed tuberculosis, had to leave the soggy moisture of New Orleans, and came to Colorado Springs for his health (as many others did, in fact: much of Colorado College’s early faculty was made up of folk who were too ill to live anywhere else) and Slocum offered Cajori too the opportunity to join Colorado College, as professor of physics. Or in the words of one of his mathematical colleagues, Guy Albright, writing many years later: "He was caught by Slocum years ago and bought for a song when Cajori, broken in health, came to Colorado to seek a few more years of life." At all events Cajori stayed at Colorado College, in one capacity or another, for the next twenty-nine years.
We’re fortunate that several students have left impressions of Cajori, both at the time and in memoirs and letters later. We can build up a picture of what it must have been like to be a student in his classes. There is a photograph taken in Palmer 122, just below us, in which Cajori is seen standing by the door. In calling the class roll he had students reply not with "yep" or "here" but with the number of overnight questions they had not managed to answer, a keenly efficient strategy both to gauge how he needed to play the forthcoming lesson and to ensure the students were kept up to the mark; his reputation was consistently that of a firm but fair teacher with high standards and expectations. A student of the class of 1910, Hattie Finlay, wrote to the Colorado College Magazine over fifty years later with her memories of Cajori’s mixture of firm jocularity & kindness:
I’m sure that I was the most trembly student that Dr Cajori had. Once when he called on me he shouted "Miss Finlay, you are de next victim!" All I could answer was "I know it, Dr Cajori." And yet he was very kind to give me extra help when I needed it. [Jones 1965, p.29]
Aside on Cajori’s accent: I remark that this is one piece of testimony we have to Cajori’s mode of speech. Although we know, if we think about it, that Cajori must have had a Swiss accent, we only have evidence of this in the attempts of his students to reproduce his speech patterns. For instance thoughout the early issues of the annual junior class production the Pikes Peak Nugget (which started in 1901) there are constant references to the word "shpeed" which suggest both that Cajori used the word "speed" a lot, and also that he had a Swiss-German way of pronouncing it. Here is a somewhat desperate student limerick of 1907:
There was once a Prof. called Cajori
Who taught mathematics, begorry,
Said he, "It is schpeed.
That the Freshmen need,"
But that is an old, old story.
(Perhaps poetic composition wasn’t one of the liberal arts being taught that year.)
Hattie Finlay tells a further story in which the tones of the turn-of the century pedagogue are brilliantly captured, mock-affronted at a slight on his own special subject of history of mathematics.
Once in the calculus class he asked a sort of wobbly student, "Mr R . . . , who was Liebnitz?" The young man replied, "Er, er, he was a Frenchman, wasn’t he?" "A Frenchman," thundered Dr Cajori, "he was an Irishman! An Eskimo! A Patagonian! (scornfully) A Frenchman!” [Jones 1965 p.29]
It’s from such small incidents that the evidence gradually builds up, small but clearly remembered for over fifty years, of the impression Cajori made upon his students. Harold Davies, for example, of the class of 1915, had a similar memory of an old-style actor-manager-pedagogue:
Professor Cajori was very intolerant of bad work. He was the terror of lazy students. On one occasion that I can remember, when the class had prepared itself very poorly, Cajori stretched himself to his full height, lifted his book until it almost touched the ceiling, and brought it down with a lusty bang upon the desk. “You are men of straw,” said he. “Get out!” And out we got. [Davis 1960, p.3]
The Colorado College Scientific Society
The high standards that Cajori expected of his students he encouraged also in his faculty colleagues. It is very noticeable how his senior colleague Frank Loud, the professor of mathematics and astronomy who had joined the College in its third year, blossomed and flourished as a research scientist once Cajori had arrived. There’s a clear mechanism by which this happened, and whereby the research atmosphere of the College as a whole was enriched and promoted: this was the foundation of the Colorado College Scientific Society, in 1890, which in my view was one of the most important things that Cajori did.
This may need further explanation, because on the face of it setting up a society might sound inconsequential or insignificant in the great scheme of things. But what it made possible was a pattern and a forum and a stimulus for the encouragement of research activity throughout the College—in much the same way as the Royal Society in 1660s England promoted research activity, albeit on a different scale. The meetings of Spring 1891 are typical of the early pattern— those attending on April 21st, for example, heard papers on St John’s Gospel, on defining elliptic functions, and on a topic in the history of mathematics education.
A vital offshoot of the Society was its research publication, Colorado College Studies, which published contributions to the Society’s meetings and provided a number of benefits for faculty and College alike: not only was there a place for research to be published, it was a good way of letting the outside world know about the work being done here. See what a range of things there were on the contents page of volume II: anthropology, political science, biology, linguistics, history of mathematics, mathematics, classics, physics, and “On a passage in the Frogs”, which I guess is from the joint major in classics and biology. All this was happening in 1890s Colorado College, and the outer world knew about it because of the Colorado College Studies. Furthermore the journal could be used to solicit exchanges with other research journals both nationally and across the world. This vastly improved the journal content of the library, and thus the intellectual resources of the College, at relatively little cost.
Cajori was both secretary of the Scientific Society and managing editor of the Colorado College Studies for the rest of his time at the College, nearly the next thirty years, and it was through his gentle encouragement and influence through these roles that the research standing of the College developed by leaps and bounds over this period—right across the faculty, as we’ve seen, by no means confined to mathematics and science. Insofar as it is the high standard of faculty research which is one of the prime reasons for Colorado College’s high national standing, from this period onwards, we can see how fundamental was Cajori’s influence on the development of the College’s stature as a foremost proponent of a broad interpretation of teaching and scholarship in the liberal arts.
As professor of physics for his first nine years at the College, 1889-1898, Cajori ardently promoted scientific studies at the college among students as well as faculty. He is celebrated particularly for taking, with his physics class, the first X-ray photographs in the West. On February 5th 1896 he read of Röntgen’s work in the local newspaper—this was in the days when American newspapers carried foreign news—realised he had all the right equipment here, and used his senior physics class that day to explore the new rays with them, and with his colleague Frank Loud whose foot was another early trophy.
Throughout his time at Colorado College, Cajori kept up an extraordinary research productivity in books and papers. His book, The Teaching and History of Mathematics in the United States (1890) was more or less finished by the time he joined the College, and he followed it up with three books in fairly rapid succession, The History of Mathematics (1894), A History of Elementary Mathematics, with hints on methods of teaching (1896), and A History of Physics in its Elementary Branches: including the evolution of physical laboratories (1899). It was through the title-pages of these widely- selling books that the name of Colorado College was spread across the world; hundreds and thousands of people who had not the slightest idea where Colorado is none-the-less knew the name of Colorado College through his writings. His History of the Logarithmic Slide Rule and Allied Instruments followed in 1909, and William Oughtred, a great seventeenth-century teacher of mathematics, in 1916. In between times he also wrote a mathematics text, An Introduction to the Modern Theory of Equations (1904), several school textbooks in arithmetic and algebra, and 111 research papers, mostly in history of mathematics, were also produced during his time at the College.
How did he do it? A question asked at the time, as well as presenting a puzzle for us, was just how Cajori managed to combine such phenomenal research productivity, far from a major research library, with so heavy a teaching and administrative load. One aspect of his personality which people commented on was his power of concentration, how he could fill every spare moment with productive work. For library research, he spent many summers in Chicago, in the John Crerar library, “summer after summer he toiled through the hot hours”, it was recorded, “foregoing the pleasures of vacation for the delights of scholarship.” [Davis 1960 p.4] We have rare first-hand testimony of Cajori’s work conditions, at home in Colorado Springs, from his student Harold Davis.
On one occasion I had the good fortune to visit the study in his house. [Which was in Wood Street, just over Cascade.] This was a scholar’s dream. I noticed that the door was kept locked and the answer was obvious. Never before or since have I seen such systematic disorder. A lone couch was piled high with reprints. The top of the desk, except for a small space reserved for writing, was a veritable mountain of papers through the top of which protruded the end of a stiff metal spring to which was attached a cord from which dangled a small pencil. Thus the author was never at a loss for the means of recording his thoughts. The floor was covered with books, but I noticed that there was little dust on their covers since they were clearly in constant use. . . . But it was obvious even to my untrained eye that this sanctum sanctorum had never been allowed the benefits of a woman’s touch. It was such a study as the scholar dreams about, but seldom possesses. [Davis 1960 p.3]
(It is good to see that some of the offices I have visited on the campus this semester seem imbued with the spirit of Cajori.)
Alongside his research interests Cajori was not only a dedicated teacher, but also, on top of this, a most gifted administrator whose skills were fully called on throughout the first twenty years of the century. The visionary plans for the Palmer Science Building ensured that the College possessed some of the best scientific teaching equipment, and the best conditions for scientific training, in the west, and along with these came plans for a new School of Engineering, of which Cajori was the founding Dean, a post he retained for the rest of his time at the College.
The school of engineering deserves more than the two lines allotted to it in the most recent history of the College, an allocation which underestimates, and indeed misunderstands, its significance. What was happening was a considered attempt to create here a liberal arts college which would also respond to Colorado’s need for engineers to develop the young state’s potential in irrigation, railroads, electricity, mining, and the like. To consolidate, indeed, a different vision of what a liberal arts college means in the Colorado context. From the very earliest days, when James Kerr organised evening classes for miners, and William Strieby carried on his tradition of teaching mining and metallurgy here, this college has been characterised by an attentiveness to hard science and technology which is somewhat rarer in the colleges of the east, but is perfectly attuned to a college growing with Colorado Springs and with the state of Colorado.
Florian Cajori, perhaps inspired by memories of his father, the Swiss engineer, as well as very conscious of the new state and new country he found himself in, had a vision of technological education progressing hand in hand with studies in pure science, as he strongly believed one depended on the other as he expressed in his 1902 address on "The relation of the new building to the scientific work of the Rocky Mountain region", and saw both as legitimate components of or complements to a liberal arts education. Students could acquire a professional engineering training as well as a liberal arts education. So the professors of English, of Romance languages and literature and of German language and literature were faculty members of the Engineering School just as were the professors of chemistry, of mining and of electrical engineering.
Several decades later in the 1930s, the College decided to phase out the School of Engineering, with its graduate programme, and re-integrated engineering teaching into a newly developed School of Natural Sciences; but as a change of policy rather than a failed experiment. While the School lasted it was a bold and effective venture, which produced a fair number of well-rounded engineers somewhat on the European model, and its influence still lives on today in the College’s high reputation in the natural and physical sciences.
While Dean of Engineering, Cajori was also Head professor of mathematics and carried a heavy teaching load. His own reputation as a teacher was by now a national one—indeed he was President of the Mathematical Association of America in 1917. Harold Davis of the class of 1915 still remembered fifty years later why he had come to Colorado College for his studies: it was because Cajori was here.
When I was contemplating the choice of a college, my high school teacher [that was in Canon City] spoke to me of the great mathematician at Colorado College. Were I to plan the pursuit of the higher culture in the direction of mathematics, said she, then there was no question that I would find the Fountain of Knowledge in the classes of that learned man. [Davis 1960, p.1]
Of course when he got here he found other things too. There is a picture of Davis as a Freshman being tossed in a blanket outside Perkins Hall—this would have been in 1910— which he said was the start of his interest in theories of gravitation. And of course some students must have found Cajori’s high expectations somewhat painful. A cartoon from the 1907 Nugget has a slight edge to it suggesting the draftsman might have suffered even more than poor trembly Hattie Finlay in Professor Cajori’s classes.
Generally speaking, however, the student comments were more gentle and affectionate than this. One of the most tender is a poem from 1910 about Loud’s and Cajori’s bicycling proclivities—really rather a fine poem by the standards of the Nugget, or any by standards. But we have to move now into an altogether different decade.
Cajori’s final years at the College must have been the most painful and stressful of his career, though that was nothing to do with the students. The golden age of Colorado College was to end in tears, as golden ages often do, because of a fundamental flaw or contradiction which emerged in the governance of the College as embodied in the frame of President Slocum: over the balance between democracy and autocracy in such an institution, over the balance between strictness and flexibility in accounting procedures; and eventually some scandals began to emerge about the President’s moral tone, which finally proved his undoing and very nearly the collapse of the College. (In some respects the parallels with recent events in Washington, involving another President, have been eery.) All this presented great problems for the senior faculty, notably Dean Parsons and Dean Cajori, who were attempting to keep the show on the road. And, it is fair to add, problems too for the Trustees who could not understand why the President did not keep his teachers in better order.
These are the three main players, seen in happier times twenty years before: President Slocum, the great but flawed leader, occupying about the same bulk as his two lieutenants; Florian Cajori, the tubercular Swiss immigrant who gave his heart and soul to the students and faculty of Colorado College; and behind him the slim shy figure of Edward Parsons, Dean of the Faculty, who Guy Albright declared to be “the most Christ-like man I ever met” —the father of Talcott Parsons, by the way, for those who know about such things—and whose dismissal by the Trustees triggered the greatest crisis in the College’s history.
It’s a complex story, which deserves fuller treatment on another occasion, not least to re-balance the somewhat tendentious account which appears in the latest history of the College, but it was Cajori, again, who was crucial in holding things together when things were very tumultuous. (You can find more details in my forthcoming paper, which is called ‘Monicagate on Cache La Poudre Street’.) It was Cajori who chaired the gang of three which governed the College latterly while the President was back east and before another President was appointed. (Though he too, President Duniway, was done away with after a few years, to sustain the College’s regicidal reputation: three in a row by that stage.)
There is a remarkable letter in the College archives written by Cajori’s younger colleague, the Mathematics and Astronomy professor Guy Albright, who in 1917 the College Trustees attempted unsuccessfully to get rid of, as well as the Dean of the Faculty, as part of the fallout of this business. From this letter and much other evidence it is very clear how close the College came to collapse, with Trustees and Faculty who had entirely lost trust in one another. It was only the sustained diplomacy of Cajori and other colleagues which found a path through, though in the process many of the best faculty, including Cajori in the end, left the College for pastures new. In the space of a few months of 1917-18, the College lost its four Deans (one by dismissal), three other Head Professors and five further professors, and a Museum Director, an attrition which the College has never experienced before or since, and we must hope never will again.
This is the last Cajori cartoon in the Pike’s Peak Nugget. The Prussian soldier has an uncanny resemblance to President Slocum so we could see this as a deep political comment by a perceptive student, but it may be an innocent coincidence.
In 1918, Cajori was translated to a chair in history of mathematics at the University of California in Berkeley, the only appointment in the world with that title at the time, and he certainly deserved his last ten years of happy and productive research free from the stresses and tensions he had left behind in Colorado Springs.
The College has, of course, not forgotten him. On the centenary of Cajori’s birth, in 1959, Colorado College sponsored a public lecture in his honour and memory. This was given on 25th February 1959 by the distinguished Norwegian mathematician and historian of mathematics Oystein Ore. (It was on ‘Pascal and the invention of probability theory’, and didn’t mention Cajori once.) The next year another Cajori lecture was delivered, this time by one of Cajori’s former students, Harold Davis of Northwestern University. Davis gave rather fuller attention to Cajori for the first part of his lecture, with several reminiscences which I have used earlier. The local newspaper the Gazette Telegraph reported this occasion as “the annual Cajori lecture”, but I haven’t been able to trace any subsequent one and it seems that while there was an annual Cajori lecture, it was only for the two years 1959 and 1960.
More recently, however, the Mathematics Department has instituted a Cajori Prize, as its top award for mathematical prowess, awarded most years since 1986, so that his name is still preserved in the Department. And Steven Janke has in the last few months been working on a history web page so that anyone consulting the mathematics department on the College web site will shortly have the opportunity to learn about the historical development of mathematics teaching here from the earliest days of the College, a development in which Florian Cajori played so major a part. So this year is also the 125th anniversary of mathematics teaching at Colorado College, as well as of the College itself.
Cajori’s leaving provoked one of the most moving editorials to have appeared in the Tiger, the Colorado College Newspaper of the time. It described Cajori’s resignation as “perhaps the greatest blow that has ever come to the student body of Colorado College”. And all the evidence is that the memory of his teaching and personality lived on in his students for the rest of their lives.
I end on one of the best examples of the warmth and regard in which his students held Cajori, through the generally gentle fun they poked at him year after year in the columns of the Pikes Peak Nugget. He was clearly a good sport as well, for they persuaded him on this occasion to pose for a photo-opportunity with a stuffed camel, on the steps of the Coburn Library (roughly where Armstrong is). This room that we’re in now, the Gates Common Room, was the Museum where the College’s collection of stuffed animals was kept, with a 60-foot whale skeleton hung from the ceiling, as some of you here remember, but the animals were occasionally liberated by the students for a variety of pretexts.
In 1904, then, a poetic composition appeared in the Pikes Peak Nugget, in a style which readers of Lewis Carroll’s The Walrus and the Carpenter may recognise: The camel and the mathman.
Friends of the College, friends of Cajori, President Mohrman, Professor Anderson, on your behalf I salute Florian Cajori on the occasion of his 140th birthday and invite you all to drink to his memory in a cup of tea, and to the future success of the College on the foundations he worked so hard to create. I hope that when the President comes to look back in twenty-five years time, on the occasion of Cajori’s 165th birthday, which will be the 150th anniversary of mathematics teaching at Colorado College, she will be able to report on a liberal arts College that has continued to sustain and develop the values of high quality teaching and scholarship, with mathematics in its historic place at the centre of the liberal arts, which is our heritage from Florian Cajori.
Davis, Harold T, Mathematics and the imagination, ms of lecture, 1960
Davis, Harold T, The adventures of an ultra-crepidarian, San Antonio 1962
Hershey, Charlie Brown, Colorado College—1874-1949, Colorado Springs 1952
Jones, Hattie Finlay, letter to the editor, Colorado College Magazine, 1965 p.29
Loevy, Robert D., Colorado College: a place of learning 1874-1999, Colorado Springs 1999
The Pikes Peak Nugget, vols i – xix (1900-1918), passim
Reid, J Juan, ‘Florian Cajori: first X-ray photographs in the west’, Colorado College Magazine Feb 1982, pp. 12-13