Mathematics at West Point in the Early Twentieth Century

(a very preliminary report)



V. Frederick Rickey
Department of Mathematical Sciences
United States Military Academy
West Point, NY 10996

Philadelphia Area Seminar on the History of Mathematics
Villanova University, February 19, 2004.


The United States Military Academy celebrated its centennial in 1902 but was it a vibrant intellectual center or a school with a hundred years of tradition unimpeded by progress? Since the study of mathematics occupied a substantial portion of the education of every graduate, this motivates us to look at all aspects of the department of mathematics: Who were the faculty? What was their education and experience? What was the curriculum? Which textbooks were used? How were the classes conducted? How did the department interact with the national mathematical community? How did world events impact the department?

In terms of leadership, during the first half of the twentieth-century the history of the Department of Mathematics is rather simple because the department had only four Department Heads. Wright P. Edgerton served from 1898 to his death in 1904 and was succeeded by Charles P. Echols who served from 1904 until 1931 when he retired at the mandatory retirement age of 64. Because of that long term, he will be the major player in our story. Harris Jones took up the post in 1931 and served until 1947 when he became Dean of the Academic Board. Finally William W. Bessell, Jr., was Head from 1947 until 1959 when he became Dean.

The Academic Board is empowered by law to make all academic decisions regarding the Academy and thus is an extremely powerful body. At the time it consisted of the Superintendent and the Department Heads. The position of Dean of the Academic Board was not created until 1945; before that the dean was an honorific given to the most senior member of the Board. One would think that the Superintendent would be the individual making the decisions, but that was simply not the case. He had but one vote. There were many instances where the Board disagreed with the Superintendent. Their usual strategy was to simply wait a few years until a new Superintendent was appointed.


Edgerton, 1898-1904

Wright P. Edgerton was born in Tallmadge, Ohio on November 14, 1852. In 1863, his father was appointed Chief Justice of Idaho and so the family journeyed for four months to their new home. This must have been an interesting trip for an eleven year old. Edgerton entered West Point in 1870 and graduated in 1874, fourteenth in the class.

At the Military Academy, he was beloved by all his classmates, not only for his social qualities, but for his gentleness that is always a proof of true courage of manhood. He had a keen sense of justice, duty and honor; loved and sympathized with his fellowman in all grades of life and was tolerant and charitable to the errors and faults of others. Love of humor and repartee were two of his principal characteristics. His room was the 'rendezvous' for the brightest, cleverest and best men of his class and many hours that should have been devoted to study, were whiled away in story telling, jokes and innocent fun.

For the next eight years he served his country at ten locations in six states. He returned to the the Academy in 1882 as Principal Assistant Professor of Mathematics, was promoted to Associate Professor in 1895, being the first person in the department to hold that rank, and became Professor in 1898. During the summer of 1898 he volunteered in Puerto Rico as aide de camp at the command headquarters. While there he was exposed to disease which took his life in 1904 at age 51.

He made two important changes in the curriculum. Since Thayer’s time, algebra and geometry had been taught in that order, but Edgerton decided to teach them simultaneously, with recitations on alternate days. The other change still echoes today. He started giving written tests for the general reviews, thereby allowing students who did well on them to be exempt from the final exams. Up to this time the examinations had been given at the end of each term and they were oral. In the spring the Board of Visitors witnessed the exam. They were an ever changing group of dignitaries appointed by the President of the United States, the President of the Senate, and the Speaker of the House. Besides attending the exam they also reported on every facet of the Academy and made recommendations. Their work was purely advisory; sometimes their suggestions – often they were prompted by the Superintendent – were accepted, but often they were ignored by Congress and the Secretary of War. It had been customary throughout the nineteenth-century to have three kinds of classes, “advance” where new material was covered, “partial reviews” when a portion of the material was reviewed, and then a “general review” before the examination. Beginning with Edgerton, cadets took written partial reviews, or WPRs, to use today's customary TLA.

Another individual involved in the war with Spain was First Lieutenant Albert L. Mills of the class of 1879. After graduation he taught tactics at West Point for a semester and then served on frontier duty, except for several years teaching at the Cavalry School at Fort Leavenworth in Kansas. In the battle of San Juan he was shot in the head but continued to lead his troops. For his bravery he received the Medal of Honor. While recovering in a Washington hospital President McKinley met him and took a liking to him. He wanted to promote Mills to a high rank, but that was impossible and so he appointed him Superintendent at West Point, the only First Lieutenant to hold that position. At West Point he held the local rank of colonel. Not surprisingly, this caused a lot of comment in the Army. Later Professor Edgerton said that Mills brought "a splendid reputation for gallantry in the field, he took up the novel duties of his new position modestly but earnestly; and it has been a pleasure to see him expand into the able, wise administrator he is today." [W. C. Brown, Obituary of Albert L. Mills, 1917 Annual Report, p. 65].

Undoubtedly the greatest contribution of Superintendent Mills was that he saw that if the Academy was to continue to meet the military needs of the country it would have to be greatly expanded. This necessitated a major building program. There was a call for proposals and eventually the architectural firm of Cram, Goodhue & Ferguson was chosen. Mills chose to keep the Academic Board in the dark on the plans and when they learned that he planned to build an administrative complex out on the point with the best view of the Hudson River and away from the academic buildings there was turmoil. Of course, the Academic Board won this battle. For this and other reasons Mills was relieved in 1906 but the building plan was underway. Among much else, the program included the East Academic Building (1903-1913, now Bartlett Hall), the Administration Building (1905-1910, now Taylor Hall), North Barracks, the Cadet Chapel (1906-1910), the Gymnasium (1906-1910, now Arvin Gymnasium), and the Riding Hall (1908-1911). During the half century under consideration the Mathematics Department was housed on the third floor of the West Academic Building (the "West" was appended to its name only after the East Academic Building was built. In the 1950s the Riding Hall was gutted and a modern classroom building was built within the shell. This is the current Thayer Hall, home of the Mathematics Department. For awhile wags called it the Far East Academic Building, but that name died out.

There is an interesting textbook in the library that was used during this period. It was owned by Ulysses S. Grant III, grandson of the president. On the back flyleaf [pictured in AAR, p. 266] Grant lists the cadets in the second section of the course and he is in the first seat. Then there is a second column, where Grant has moved up to the first section and ranks fourth. At the top of the section and of the class ─ was Douglass MacArthur, who continued in this position and graduated at the top of his class. Grant graduated sixth in the class of 1903, a class with 93 graduates. Also in the section is Thomas Etholen Selfridge (USMA 1903, #4152) who studied aeronautics with Alexander Graham Bell in 1906-1907 an died September 17, 1908, being the first person in the world to died in a crash of a motorized aircraft. Orville Wright was at the controls. The book in question was a 1890 edition of Charles Davies' Geometry and Trigonometry. A version of it was published in 1828 and was his most popular book. It was used at West Point from ????

To give a sampling of the curriculum at the turn of the century, let us consider Douglas MacArthur, a member of the class of 1903. At the end of his second year, after the study of mathematics was completed, he ranked first in the class of 104 cadets. When he graduated, he was first in a class of 94. He attended mathematics class for 220 days for 90 minutes per day for two years. That is a total of 660 hours. The textbooks used were:

In 1902, to allow more time for the teaching of Spanish, the mathematics curriculum was cut by 40 lessons and surveying was transferred from the Mathematics Department to Practical Military Engineering. This was not the ten percent cut that it appears, but only four percent, for surveying was still taught [Nye, p. 199-200].


Charles P. Echols, 1904-1931

Charles P. Echols was a 1891 graduate of West Point. His father, William Holding Echols, was an 1859 graduate. The senior Echols was assigned to the Topographical Engineers and his only assignment was in Texas from June June 1859 to February 1861. Secretary of War Jefferson Davis has imported some camels and it was Echols who lashed supplies onto their backs to explore the Big Bend wilderness. When the Civil War began the senior Echols resigned from the Army and joined the Confederacy. He was probably the first military engineer to use floating submarine mines for the defense of a harbor. After the war he was Chief Engineer for the Memphis and Charleston Railway and then a banker in Huntsville, Alabama, until his death in 1909. Echols and his wife had three children, the oldest and youngest both became mathematicians.

William H. Echols Jr. (1859-1934) was the oldest son of William Holdings Echols. He took his undergraduate degree at the University of Virginia in xxxx, was a railroad engineer in the South, a mining engineer in the West, taught at the Missouri School of Mines, and then returned to the University of Virginia where he took his undergraduate degree in 1891 as Professor of Mathematics.  He remained at the University until his death in 1934. Echols was a campus legend. At six foot four and with red hair and a mighty voice, he could hardly be missed. He became famous when the rotunda that Thomas Jefferson designed caught fire in 1895. Actually the fire began in the Annex, a building connected to the Rotunda by a Portico. Echols hauled a fire hose up a ladder in a lecture hall and fought the fire until the roof started to collapse. He swung under the ladder and went hand over hand to the floor and a safe escape. Next he got the idea of saving the Rotunda by destroying the Portico. He took 100 pounds of dynamite and put 25 pounds on each of the main columns of the Portico. This took out the pillars but left the roof. So he sent to town for more dynamite. He carried 50 pounds to the roof and threw it on the Portico. This created a blast that was heard 25 miles away but, alas, the Portico roof held, the fire crossed it and the Rotunda was destroyed. A more mathematical tale involves a student-faculty baseball game that he refereed in 1908. For one close play he flipped a coin to decide if the player was safe. The faculty won the toss and the game. I don't know if he ever visited West Point but I would assume that he did.

Charles Patton Echols, who was named after his grandfather Charles H. Patton, was born in Huntsville, Alabama, September 6, 1867. Like his older brother, Echols attended the University of Virginia, but only for three years. The University of Virginia "endowed him with that unmistakable hallmark of poise and gentle dignity with which she seems able, so strikingly, always to distinguish her sons." [Quoting the obituary by James Postell Jervey in the 1941 Annual Report]. Then Echols headed for West Point, graduating third in the class of 1891.

Charles P. Echols became head of the Mathematics Department in June of 1904. At the end of the fall term he declared forty percent of the yearlings deficient in mathematics. This incensed Mills, who ordered Echols on a study tour of eastern colleges to observe instruction in mathematics. He wrote a report on this trip, but I have not seen it. Then Mills ordered him to Europe for the following academic year to study military instruction there [Nye, p. 205]. In his absence the department experimented with eliminating daily marking in Fourth Class Mathematics [Nye, p. 211] and a committee studying the curriculum reduced the mathematics curriculum by seventy hours.

Professor Echols sailed from NY on July 20, 1905 for Paris. For one month he pursued a course in French Language and Literature at the Alliance Française. 50 lessons at the Berlitz School of Languages followed, and for four and one-half months in Paris he worked with a private tutor in the French Language. This extensive study of the language in France indicates that his study of the language as a cadet was useful only for reading, not for speaking; in fact that was the intent. After this period of study he was ready to use his French. "For one month lectures were attended in mathematics, mechanics, construction and descriptive geometry at the Beaux Arts. During 3 1/2 months lectures in various branches of mathematics (algebra, analytics and calculus) were attended at the University of Paris where I matriculated as a student." He visited a number of schools in France and then departed for Italy, Austria and Germany where, in each case he studied the language.

At St. Cyr in France Echols observed that one hour lectures were delivered by the instructor 3 times per week and each cadet was questioned at least once a week in a room alone with the instructor or one of his associates. This was quite different than at West Point where there were no lectures and the instructor quizzed each cadet each day.

Because of his time in France, Professor Echols became a Francophile. James Jervey, who served at West Point during part of Echols long stay there wrote

We then had the joy of being friends and neighbors for many years during our work as instructors at West Point. Our interest in French was kept up by weekly reading classes of good French authors and small dinners which we alternated between our two households. "Puckles' " skill in reading and speaking French were an inspiration and a joy to all of us who had the rare privilege of being members of the class. [Jervey obit]

He was a skilled chess player. Had a French cook. Was a lifelong bachelor.

Let me return to more detail about his European trip.

In Italy he observed that instruction was much the same as in France. "The sections are composed of from 20 to 40 cadets and the method followed in mathematics is for the instructor to give a short talk or series of explanations at the blackboard, asking questions from time to time to hold the attention; then to send one student at at time to work out a principle or solve a problem and explain the process as he writes his work on the board." At West Point the sections were much smaller, consisting of but 10 or 12 cadets and every cadet was sent to the board with one at the front board under the more careful scrutiny of the instructor. In Italy it is not clear if he met Peano, but he definitely met Burali-Forti.

At the Cavalry School at Moravian Weisskirchen Echols, observed the instructor use a model of the cone to explain Dandelin's proof that a section of a cone is an ellipse. Germinal Pierre Dandelin (1794-1847) discovered his proof using spheres in a cone to prove that a plane intersecting a cone is a conic. That was in 1822, but this is the first classroom appearance that I am aware of. Dandelin was a student at the Ecole Polytechnique and one must wonder how his study of descriptive geometry influenced his discovery of this proof.

Echols also witnessed computations made with a slide rule. "It seems advisable that time be found in the course in mathematics to resume the instruction in the theory and use of the slide-rule which was once taught in conjunction with the course in surveying and is now taken up in the course of Ordnance and Gunnery. It could be best added to the course in trigonometry of the 4th Class year, its use to continue throughout the next three years." The use of the slide rule at West Point has not yet been unraveled, but here is some information: According to the 1943 Superintendents report, p. 3, the Mathematics Department took over instruction in the slide-rule from the Department of Physics. The class of 1978 was the last class to be issued slide rules. The next class received calculators. Peggy Kidwell, Curator of Mathematics at the Smithsonian, is looking for a photograph of an individual wearing a slide rule on their belt. We know this was common in the 1960s, say, but documentation is lacking.

At the end of his report on his European trip, Professor Echols has a number of recommendations, including

Sadly, these recommendations were not heeded.

In 1908, President Roosevelt wrote that it was “a very great misfortune to lay so much stress upon mathematics in the curriculum at West Point and fail to have languages taught in accordance with the best modern conversational standards.” [Nye, 231, 253]. The Academic Board dismissed the idea and reiterated the long held view that a technical curriculum instilled mental discipline and indeed “Mathematical training at the Military Academy has been the main factor in all the accomplishments of graduates.” [Nye, 233].

An amusing aside:  One member of the class of 1930 was Paul "Echols" Chalmers. The editors of the Howitzer have this to say of him: "A brush with the mathematics department gave him his nickname ─ and for four years now he has been of the opinion that anyone above the last section was an unpardonable file-boner. A 2.1 to Echols meant just one-tenth of wasted energy."


The Class of 1917

During the 1913-1914 academic year the Department of Mathematics was staffed by one Professor, Colonel Charles P. Echols, one Associate Professor, Captain James F. Bell, one Assistant Professor, First Lieutenant Alexander G. Pendleton, and 17 instructors, one of whom was in Europe. Thus there were 19 individuals in the department. They taught 326 cadets making a student faculty ratio of 19.2. This does not sound especially small, but the average section size was 9.6 (each instructor taught two section, and I am assuming Echols just observed classes, and that Bell and Pendleton taught one section each). Traditionally the lowest sections were smaller. During the year 37 cadets were found deficient, a failure rate of 11%,  and of these, 9 were "turned back" to the previous year and 28 discharged.

Instruction in mathematics is given cadets for the first two years of their course. It embraces solid geometry, advanced algebra, analytical and descriptive geometry, conic sections, trigonometry, surveying, differential and integral calculus and least squares.

The material on least squares entered the curriculum in 1879 and remained until it 1942 when Professor Harris Jones converted part of the time devoted to that material to the study of statistics. Under Professor William Bessell everyone studied statistics.

The plebe mathematics classes met daily ─ that includes Saturday, but not Sunday ─ except for the last 66 days when mathematics alternated with surveying (which now does not seem to count as mathematics) for a total of 192 classes. Each class met for 85 minutes, so the time in class during the year was 272 hours.


Fourth Class, Fall 1913

Fourth Class, Spring 1914

Third Class, Fall 1914

Third Class, Spring 1915

Remark: The list in the 1914 Annual Report, p. 76, does not agree with the list drawn up by the Department.

You will note that Granville's calculus is in this list. It was used at West Point from 1907 to 1948 and again from 1953 to 1963. One might think that this is the longest any calculus book has been used at USMA, but no, that of Albert Church was used from 1843 to 1899, 56 years vs 52.

At the end of the 1913-1914 school year the Official Register of the Officers and Cadets for the year was published, listing the "Order of Merit and Proportional Parts in Fourth Class year" and for the other years. At the top of the fourth class one finds Harris Jones, the future Department Head. He was first in mathematics with 166.80 out of a possible 175. He was fourth in English, eighth in History, first in Surveying, second in Drill Regulations, and, curiously twenty-second in conduct.

The workload for the professors was particularly heavy and in 1911 Congress authorized one tenured associate professor in mathematics and modern languages.[i]  [Something is wrong here; I have Edgerton being Associate Professor in 1895]. The situation got even worse during World War I.  For example, during the 1918-1919 academic year there were eighteen instructors in mathematics operating under an emergency schedule. Each instructor was in the section room from 8:00 a.m. to 12:35 p.m. daily; three periods of one hour and twenty-five minutes each. “This is at a rate of twenty-five and a half hours per week of actual section room instruction, which, it is safe to say, is not undertaken ordinarily at any college in the country by an instructor in such subjects.”[ii]

Fortunately this was only necessary during World War I.


Superintendent Douglass MacArthur, 1919-1924

Brigadier General Douglass MacArthur assumed command at West Point on June 12, 1919, being the youngest Superintendent since Thayer. When appointing him, General Peyton March, Chief of Staff, told him that “West Point is forty years behind the times.”[iii] Thus MacArthur’s task was to revitalize the Academy. This required reinstatement of the four year curriculum (although March wanted three) after the shorter terms during World War I. The Academic Board was given the task of revising the curriculum and they worked on it throughout MacArthur’s first year as Superintendent, approving their report on July 20, 1920.

The system of recitations was reaffirmed; the practice of assigning review lessons after a few advanced lessons was continued; frequent grading and merit sectioning were retained. Finally, the report reaffirmed the essentiality of a faculty of Academy graduates, suggesting only that a year’s assignment to a civilian school would improve their instruction, and that a four-year tour was highly desirable.[iv]


Professor Echols, who had 21 years of experience in higher education as opposed to MacArthur’s just completed first year, was incensed that the mathematics program had been cut by one-third, so he issued a minority report. Echols was particularly disturbed by the dropping of descriptive geometry from the curriculum, a subject that had been taught at West Point for a century, and “a subject taught with painstaking elaboration at all the important military schools in the world.”[v] Although the new curriculum was approved in Washington, Echols waged a guerilla battle. At the end of the fall term Echols reported that 95 of 572 Plebes were deficient in mathematics. The Academic Board saved 11 by reducing the passing mark from 37.5 to 35.3.[vi]

 MacArthur appointed a committee of three young lieutenant colonels – each having but two year experience in mathematics as cadets at West Point  –  to investigate the high failure rate. The failure rate of 16.6% was not really that high, for the 1924 Superintendent’s Annual Report, reveals that 24% of each Plebe class was academically deficient after their first semester at West Point. They issued, in the words of historian Roger Nye,  “the most careful denunciation of the Professor of Mathematics officially recorded at the Academy.”[vii] Through actions such as this MacArthur lost the support of the Academic Board and soon after he left in 1924 his revisions of the mathematics curriculum were rescinded.

 In the penultimate year of P. Echols’ headship, the curriculum was as follows:

In the fourth class year algebra is completed in alternation first with plane and solid geometry, then with plane and spherical trigonometry. Plane analytical geometry is begun. The third class year embraces plane and solid analytical geometry and descriptive geometry, both being concluded in alteration. The calculus, differential and integral, and the theory of least squares complete the course. [Howitzer, 1930, p. 30]

The curriculum changes slowly. Echols, a lifelong bachelor, retired in 1931 and moved to New Jersey, but he spent much of his time in New York City, fond of bridge and chess, and a devotee of the opera. He was murdered in Bryant Park behind the New York Public Library in 1940.

While MacArthur was Superintendent, Omar Bradley was an instructor. Bradley graduated in the class of 1915. He was 43/177 in mathematics and 44/164 overall. He served as Assistant Professor of Mathematics from  1920 to 1924.  Despite his less than stellar standing in the class he was a superb instructor, being asked to stay a fourth year to instruct the new members of the department. Here are three quotations, the first describes his life as instructor and the later two show how he benefited and his opinion of MacArthur.

I taught all morning six days a week. In the afternoon I attended math refresher.  . . .  In the evenings I studied the work I would teach plebes the following day.

I know I benefited from this prolonged immersion in math.  . . .   In later years, when I was faced with infinitely complex problems, . . . mathematics helped me think more clearly and logically.

On the whole, I approved of MacArthur's liberalization of West Point academics, even if it did somewhat curtail the study of my specialty, mathematics.


Harris Jones, 1931-1947

Harris Jones, who served as department head from 1931 to 1947, attended Harvard for two years before entering West Point. As a cadet he earned the nickname “Prof” for his ability in mathematics and willingness to help his fellow cadets. He graduated first in the class of 1917 and was commissioned as a first lieutenant. A month later he was promoted to captain and was leading an engineering company into World War I. He earned the Distinguished Service Cross and was back at West Point for the next fall. The next year he was off to MIT for a year of advanced study and then he went back out into the Army for eight years, returning to USMA in 1931 as a Colonel to take up the post of Department Head. In 1947 he became the second Dean of the Academic Board, serving in that post for nine years.

 The class of 1933 is liable to go down in history, not only as the class that first eluded Descriptive Geometry, but also as the class that never saw the great depression of 1929-1933. We came in B. C. (Before the Crash), and it looks now as though we shall go out A. D. (After the Depression). And speaking of the depression, does anybody mind if we pause here just long enough to scatter roses on our nearly bald pate . . . for we said six months ago that 1933 would see the upturn. [The Pointer, June 9,  1933, p. 3]


The Zeroeth Putnam Exam

Along with academics, the Academy has always had strong athletic programs.  During much of the twentieth century, USMA was a leader on the football field.  However, due to the unique roll of the Academy, it has always had its detractors and skeptics, especially in the academic realm.  In 1932 West Point was called to defend its academic honor.  After winning the Army-Harvard football game of November 5, 1932 by a score of 46-0, Superintendent Connor and President Lowell of Harvard were at the home of Mrs. William Putnam.  Lowell commented that even though Army could beat Harvard in football, Harvard would surely win at an academic contest.  Superintendent Connor turned this comment into a challenge, and it was decided that a mathematical contest would fit the bill.  The contest took place at West Point over two days, May 19 and 20, 1933.  Ten sophomores from each school would be tested in plane and solid analytic geometry and the differential and integral calculus, i.e., the contest was restricted to the first two years of collegiate mathematics because that was all that was taught at USMA. The West Points cadet trained as if for battle, being given special treatment like that of athletic teams. One of their three coaches was future department head Lieutenant Charles Nicholas, who was Department Head from 1959 to 1967. Academy legend has it that the Harvard team prepared by talking about how easy a competition it would be. Articles appeared in The Pointer and the sports section of the New York Times. The week after the contest, the New York Times ran the headline, “Army ‘Mathletes’ Defeat Harvard 98-112.” Each contestant received a gold medal and a book.[viii]   

The contest was expanded in 1938 to a national event and the Putnam Competition continues to this day as the most prestigious contest for mathematics undergraduates. Alas, West Point has not won since the zeroeth competition, primarily because the exam covers the whole range of undergraduate mathematics and, until majors were introduced, cadets did not have the background. In recent years West Point has participated in the Mathematical Contest in Modeling and had teams ranked Outstanding in the past four years.

The first individual to teach mathematics at West Point that had a PhD was Robert C. Yates (1904-1963) a member of the Army Reserve who began in 1942 as a captain and was downsized in  1954 as a colonel. This is in marked contrast with departments across the country that taught engineers, for they already had PhDs on the faculty for half a century. Yates received his undergraduate degree at the Virginia Military Academy in 1924 and his PhD at Johns Hopkins in 1930. He taught at several schools before, during, and after his time at West Point. One of his duties at USMA was the design and teaching of a course in the techniques of teaching mathematics which was for the annual stream of new instructors.  “In performing this duty he was considered a superior instructor and also an excellent teacher of teachers.”[ix] He was the author of five books and over sixty papers; his text on differential equations being used at the academy from 1950 to 1963. The next individual in the department to have a PhD was the  Department Head BG (ret) Pollin (1974-1985). The first Department Head to have a PhD in mathematics was the previous Head, BG (ret) Arney (1995-2000).

 The 1942 Howitzer noted

As war becomes more and more mechanized, the study of mathematics assumes a greater importance in the education of a soldier. Without a background in mathematics it is impossible for one to study properly those sciences with whose principles one must be familiar in order to understand the functioning and operation of modern weapons.

Even though the cadets recognized the military applicability of mathematics, and this is doubtless more true today, in the same paragraph they cite the older view of mathematics, a view championed by the Academic Board throughout the nineteenth-century, as “one of the best methods of training a mind”. It was this viewpoint that retarded the development of the curriculum. The cadets noted this stagnation in the 1940 Howitzer when they remarked that the curriculum “in 1835 the course was fundamentally the same as it is today.” This was during World War II and it is noteworthy that the department had to once again use some cadets as instructors, something that had not been done since the Civil War.  

The 1947 Howitzer gives the cadet view about the department. We quote it in full:

From the day he first responds to the immortal battlecry of “Take boards!” to the day he graduates, a cadet at West Point makes constant use of the principles he learns at the capable hands of the Mathematics Department. To the cadet, no portion of his academic instruction is more important. During his Fourth Class year he wades through algebra, solid geometry, analytical geometry, and trigonometry. Barely able to distinguish an ellipse from a hyperbola, he is plunged into his Third Class course of differential and integral calculus and statistics. Emerging from this battle with sines, cosines, derivatives, integrals, and their assorted brethren, he possesses a sound mathematical foundation on which to base his scientific education. Although formal instruction in Mathematics finishes with his Third Class year, he continues to use his prowess throughout his courses in physics, chemistry, mechanics and ordnance; for if he forgets his math in any of them, he’s lost!

This unmistakable cadet style betrays both the disrespect of youth and an emerging maturity. It provides a good basic summary of the curriculum, an acknowledgement that the department is doing a capable job, and an understanding that what they are learning is useful. The 1940 Howitzer claims that “in 1835 the course was fundamentally the same as it is today.” This is not quite right, for the new addition is the statistics course.


William Bessell, 1947-1959

William Weston Bessell, Jr., was born on May 17, 1901 on an army post in San Juan, Porto Rico (as it was then spelled). He went to school in the Philippines and in Mesa, Arizona. After high school he spent an additional seven months (he seems to have quit high school early, but it is unclear). From a questionnaire we know which textbooks he used. In geometry, not surprisingly, it was George Albert Wentworth (1835-1906), Elements of Plane and Solid Geometry (1877). He entered West Point on June 14, 1918. Due to World War I, he graduated two years later. He was fifth in a class of 271. Since the war was over, he went to the Engineer School at Camp Humphreys, Virginia, for a year and then to Rose Polytechnic Institute where he taught Military Science to their ROTC Engineer unit. After doing this from 1924 to 1928, he reported to West Point to be Assistant Professor of Mathematics in charge of third class mathematics. He taught at West Point for four years, 1928-1932 and then went back out into the Army. He was stationed in Hawaii, Zanesville, OH, and then, from 1936 to 1939 with the American Battle Monuments Commission in France. Then he went to the Command and General Staff School in Fort Leavenworth, Kansas, and then he went to Washington. At the outbreak of World War I he was tasked to implement a program that would create and train engineer amphibious brigades. These units would prove valuable to the island hopping campaigns in the Pacific, and in the invasions of Africa, Italy, and France. His crash program raised the strength of the Corps of Engineers in one year from 800 to 22,000 officers and from 10,000 to 311,000 enlisted men. A few years later he was the Army Director of the Joint War Plans Committee, an agency charged with anticipating the conduct of the war and preparing campaign plans well in advance of probably need. At this time he was promoted to Brigadier General. In March 1945 he was assigned as Commanding General of the station where he was born in Puerto Rico. In 1947 he was assigned to West Point for a second time.

Colonel William Bessell replaced Jones as Head of the Department in 1947, serving until 1959 when he became Dean. In 1947 the Academic Board selected him for Professor from a pool of thirty-one nominees, 19 army officers and 12 civilians. Six of these names were submitted by Professor Jones, 14 by various agencies of the War Department, 12 by individuals at Harvard, MIT and Princeton, and 4 by personal application (there are 5 duplicates).

Curiously none of the officers considered were described as "mathematicians." COL Charles P. Nicholas, who succeeded Bessell from 1959 to 1967, and COL Warren N. Underwood, were "considered to be well qualified for the position but not quite so desirable." The other 28 were "lacking some essential qualification or to be definitely less qualified." LTC Robert C. Yates had "Superior professional qualifications but decided difficulties of temperament and personality for the position." It was also noted that he was "Physically qualified for limited service only."

It is interesting to note the civilians that were recommended. Several of them went on to become world class mathematicians. Haskell B. Curry of Pennsylvania State University became the founder of combinatory logic, Orin Frink also of Penn State was an algebraist, Marshall Hall was a distinguished group theorist, and D. C. Lewis headed up the mathematics department at Michigan for a number of years.

Bessell came with high recommendations. COL Echols wrote that he was "Highly capable, quick to accept a lead. Efficient. Magnetic personality. Altogether A-1."  General Pershing said that he was "A superior officer in every respect. Has demonstrated exceptional organizational ability and unusual loyalty." Bessell was chosen as the next Head. Of necessity, Bessell had to give up a star to join the Corps of Professors.

One of Bessell's first acts as Head was to offer the Probability and Statistics course to all cadets, rather than just the upper sections. It is said that "Through this decision alone, he placed the Military Academy at least a decade ahead of most American colleges in this important aspect of modern mathematics." [I have not yet tried to judge this statement.] He also

He conceived the idea of converting the Riding Hall (completed 1911) – it was little more than a parking lot after riding was discontinued in the 1940s –  into a modern academic building. Thayer Hall was “an entirely new structure, built within the walls of the old Riding Hall.  . . . of structural steel framing with reinforced concrete, completely air conditioned and practically windowless.”[x]  He was also instrumental in getting faculty members educated with advanced degrees from civilian universities and starting a computer center at West Point. He retired in 1965, having served from 1959 to 1965 as Dean, at the mandatory age of 64.

COL Bessell's first love was teaching. Years after his retirement, he wrote "When I come back and talk to some of the men I have taught at West Point, and they say how much they remember my teaching, I have my proudest moments.  .  .  .  When I look at it all, I would have to say that makes me the proudest."

In retirement he moved to 45 Bay View Avenue in Cornwall on Hudson (the lovely white house is still there).  He died there in 1977.


Overheads used:

  1. Department Heads. Two overheads.
  2. Davies, Algebra and Trigonometry owned by Grant with MacArthur's name.
  3. Drawing of post with Supe's quarters at Trophy Point. Could not find drawing.
  4. Thomas E. Selfridge working in the descriptive geometry classroom. Could not find picture.
  5. Textbooks used in 1900.
  6. Textbooks used in 1913.
  7. Credit hours required in mathematics, 1802-1994.
  8. Engraving of Echols from the 1930 Howitzer.
  9. Bradley quotes.
  10.  McArthur quotes.

Things to include:


[i] Nye, p. 221.

[ii] Annual Report of the Superintendent, 1919, p. 27.

[iii] MacArthur, Reminiscences (1964), p. 77; quoted by Nye, p. 302.

[iv] Quoting Nye, pp. 310-311, who cites the 1920 report, p. 37.

[v] Quoting Nye, p. 321, who is quoting the Minority Endorsement of Echols.

[vi] Nye, p. 321.

[vii] Roger H. Nye, The United States Military Academy in an Era of Educational Reform, 1900-1925,  p. 322.

[viii] David C. Arney, “Army beats Harvard in football and mathematics!,” Math Horizons, September 1994, pp. 14-17 and David C. Arney and George Rosenstein, “USMA-Harvard Math Competition,” Also see the Annual Report of the Superintendent, 1933, p. 3.

[ix] Curves and their Properties. This was first published in 1952 when Yates was at USMA. The 1974 reprint by the National Council of Teachers of Mathematics contains a note “About the author” that is quoted, p. viii.

[x] Catalogue of the United States Military Academy, 1959-1960, p. 107.