# Harry Clyde Carver

### Born: 4 December 1890 in Waterbury, Connecticut, USA

Died: 30 January 1977 in Ann Arbor, Michigan, USA

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**Harry Carver**received his primary and secondary education in his home town of Waterbury. After graduating from high school, he entered the College of Engineering of the University of Michigan where he studied for the year 1909-10. Then he changed to study for his B.Sc. at Michigan and was awarded the degree in 1915. During his undergraduate studies he married Lucy E Merkle (born about 1893) on 2 September 1913. Their first daughter, Ruth Jane Carver, was born on 17 September 1914. They had one younger daughter.

While an undergraduate, he represented the University as a half-miler in the Track Team [7]:-

After graduating he spent the year 1915-16 doing actuarial work for three insurance companies. He was (i) an Assistant Actuary with the Savings Bank Life Insurance Company, at Boston, Massachusetts, (ii) a statistician with the Associated Companies located in Hartford, Connecticut, and (iii) an actuary for the United States Branch of the London Guarantee and Accident Company based in Chicago, Illinois. In 1916 he returned to the University of Michigan where he was appointed as an Instructor in Mathematics. He was promoted to Assistant Professor in 1918 and was granted a year's leave of absence during 1918-1919.He wasn't an outstanding runner during his varsity days, but he won his share of points for Michigan and made things interesting for the opposition.

James Waterman Glover (1868-1941) had joined the Mathematics Department at the University of Michigan in 1895 and remained there until 1937. He developed a strong programme in actuarial mathematics and served as chair of the Department from 1926 until 1934. He was setting up this actuarial sciences programme when Carver was a student and he was pleased to be able to appoint Carver as an Instructor in 1916 to continue the building process. Glover wanted to extend the range of courses that was being offered by adding courses in probability and in various statistical topics. Carver, with the actuarial experience he had gained in the year 1915-16 working for insurance companies, at first taught courses based on his experience in actuarial studies [6]:-

James Glover was working on producingCarver's early career in the Mathematics Department coincided with an increase of enrolment in actuarial science courses and with the introduction of further courses in statistical method as it bears on economic and sociological determinations. The vigour and enthusiasm of his teaching contributed much to the unusual success, which the University has enjoyed in the dissemination of statistical skills.

*Tables of Compound Interest Functions and Logarithms of Compound Interest Functions*with the aim of publishing the Tables. One of Carver's early tasks was to assist Glover in this task. The book was published in 1923 and reviewed by Rietz who writes [10]:-

In 1921, Carver was promoted to associate professor. One of his most important contributions was his founding of theThese tables are designed primarily for use in connection with college textbooks on the mathematics of finance, insurance, and statistics. They are admirably adapted to this purpose. Furthermore, the tables are of such wide scope as to be of great use to the student after graduation; they are sure to be of practical service to anyone who has occasion to make computations in compound interest, insurance, or statistics, particularly bankers, engineers, actuaries, and statisticians.

*Annals of Mathematical Statistics*. Here is the account from [3] of Carver's role:-

Carver himself published two papers in the first volume of theBy1930Carver had become concerned by the fact that the 'Journal of the American Statistical Association', then the only scholarly publication in the United States devoted to statistics, was closed to papers with any real mathematical content, and he decided to start a journal in which papers on mathematical statistics could be published. This was truly a courageous and pioneering venture for at that time there were only a few workers in this field in this country. Not only did Carver edit the new journal, but he personally assumed the financial responsibility for it, and he met considerable deficits out of his own pocket. He did have support from his close friend, J W Edwards, the founder of Edwards Brothers, who was developing the litho-printing process which he used in printing the new publication. The 'Annals of Mathematical Statistics', as it was named, survived and gradually gained circulation and scholarly recognition. In1938it became the official journal of the young Institute of Mathematical Statistics, which assumed the responsibility for it, and Carver turned the editorship over to Samuel S Wilks.

*Annals*, namely

*A mathematical theory of seasonals*(1930) and

*Fundamentals of the theory of sampling*(1930).

In [2] Stephen Stigler explains in detail what happened to

*Annals of Mathematical Statistics*in 1933. When Carver founded the journal in 1930 he had financial support from the American Statistical Association. The early papers that were published in the journal were a strange mixture with few original ones that one would classify as mathematical statistics. The Great Depression meant that, like most organisations, the American Statistical Association hit hard times financially and a decision was taken that little damage would ensue to the Association if they stopped providing financial support for the

*Annals*. But Carver, who was the editor, was not going to see his journal die for lack of funding, so, from January 1934 he kept the

*Annals*running at his own expense and without support from any institution. In October of 1934 Carver went back to the American Statistical Association suggesting that they might set up a group within the organisation consisting of mathematical statisticians who would then provide a base for the

*Annals*. The American Statistical Association discussed this proposal but rejected it on the grounds that it might lead to the break-up of the Association. Carver decided that if the American Statistical Association would not play ball, then he would approach fellow mathematical statisticians to see if they would support setting up their own association. The inaugural meting of the Institute of Mathematical Statistics was held at Ann Arbor on 12 September 1935. The

*Annals*, still being run entirely by Carver, became their official journal. Only in 1938 did the Institute of Mathematical Statistics fully take over running and financing the

*Annals*and, at this time, Samuel Wilks took over as editor from Carver.

Carver spent the year 1934-35 as a Visiting Professor at UCLA. In 1937 he was promoted to a full professor at the University of Michigan. The University of Michigan reported employing Carver's daughter as a clerk in the Statistical Division [9]:-

Ruth Jane Carver had been awarded a B.A. by the University of Michigan in 1939. She had taken some courses in music in her Arts degree.We were very fortunate and happy in securing an additional full-time staff member in the Statistical Division, Miss Ruth Jane Carver, who was appointed in March,1940. This division has been assuming new duties very rapidly during the past few years, and this addition to the staff will aid materially in accomplishing the work.

Carver was an all-rounder when it came to sports and games and we describe some of his sporting interactions with his students at THIS LINK.

However, Carver had another passion which began with a love of cars and motorcycles when he was at high school. He raced motorcycles and in the 1920s he would buy old cars and rebuild them, driving them 'fast and skilfully'. Looking for even more excitement than fast cars led Carver to take up flying. He went into partnership with a friend in the 1930s and they purchased a plane that they flew. When the United States entered World War II, Carver thought he could use his skills towards the war effort and, although 52 at the time, joined the Army Air Corps and volunteered to take the course of instruction for aviation cadets at Kelly Field. Such instruction was aimed at men half his age but, given Carver's experience and skills, he was given permission by the Secretary of War to take the course. The idea was that after taking the course he would be in a position to construct a course on air navigation. Indeed he did so and after taking the aviation cadets course he returned to the University of Michigan where he set up a course on Air Navigation. Material for this course he published as the book

*An introduction to Air Navigation*in 1943. In the Preface to this work he advocated the use of computing machines rather than logarithms in doing the necessary calculations:-

After setting up this course, Carver went to England as an Operations Analyst with the Eighth Air Force. He served during 1944-45 and was cited for his work "in the solution of some of the most vital problems faced by the Eighth Air Force" during the war. In [8] Carver gives an indication of the types of problems that he was being asked to solve. We quote the first few paragraphs to give a flavour of this interesting paper:-... logarithms must be considered now as a tool of the past. Present-day commercial institutions almost without exception use computing machines rather than logarithms in the conduct of their business in the interest of efficiency in both time and labour: moreover progressive schools now have installations of these machines that enable their students to work more problems in less time than formerly ...

Although Carver's work was solving these problems using what today would be called Operations Research, he did not spend all his time working at his desk but flew over France, studying from the air, and later from the ground, the effects of heavy bombing operations by the Germans. After the end of World War II, Carver continued to work for the United States Air Force improving the methods of teaching at Air Training Command. Between 1950 and 1953 he worked on developing new methods of navigation and devised a new approach to the teaching of navigation. For these contributions he received the Exceptional Service Award in 1954. In the following year he publishedAir force operations against an enemy fall into two general categories, 'tactical' and 'strategic'. Tactical operations are carried out directly against the armed forces of the enemy; strategic operations are primarily directed against the sources of the matériel and the transportation facilities that deliver supplies to the enemy's armed forces. Every strategic bombing mission attempts to accomplish a very definite objective that merits a high priority at that time. For example, the first targets hit by the Eighth Air Force in World War II were the German submarine pens. The object was plainly to counteract the German efforts to sink the ships that were transporting our troops and supplies overseas. Our attacks against these submarine bases were not very successful, since the pens were protected by many feet of solid concrete through which our bombs, such as were available at that time, were unable to penetrate. Next Hamburg, Bremerhaven, Wilhelmshaven, and other German ports were assigned high priorities in an effort to reduce the amount of vital war supplies that were being shipped into Germany from various neutral countries. These missions were fairly successful. For a time in1944the so-called "no-ball" targets held top priority, since it was feared that these V-1buzz-bomb launching sites might be capable of blowing the British cities and our air force bases in England right off the map. The no-ball targets were well camouflaged and when hit were quickly repaired; consequently our results against these targets were far from satisfactory. However, other means were found t combat the flying bombs and only about25per cent of those launched reached their objectives. Although a serious menace, the V-1did not prove to be a decisive weapon. The synthetic oil plants were always worthy of a high priority, and the combined English and American efforts were so successful against these targets that the German Air Force and tank Command were almost fighting each other for their respective gas and oil requirements.

*Distance and Azimuth Computations*, a work designed for use by the United States Air Academy. When he retired in 1961 [3]:-

In 1961 Carver also retired from his professorship at the University of Michigan, the university he had been associated with for fifty-two years. On his retiral he was made Professor Emeritus.... he was awarded the Decoration for Exceptional Civilian Service, the highest decoration given to a civilian by the Air Force in peace time.

There is one final story that we should tell since it says much about Carver. When he retired in 1961 he decided that he would move to the place in the United States that had the best climate. How did he go about finding what that place was? Perhaps not surprisingly, given his passion for statistics, he chose the criteria that he believed would give him the answer, such as average temperature, maximum temperature, minimum temperature, total rainfall, number of sunny days etc. When he put into his model the data from as many sites in the USA that he could find, his system told him that Santa Barbara, California, had the ideal climate. He moved there, but did not cut his ties with his colleagues in Ann Arbor and he also kept his contacts with the Air Force. These Air Force contacts allowed him to continue to fly, even to make a flight over the North Pole. His health, however, began to deteriorate and when he reached the age of 75 he gave up flying and when he reached the age of 80 he gave up driving cars. By 1976 he had reached the age of 85 and, now in quite poor health, he returned to Ann Arbor to be close to his two daughters. He died in January of the following year.

From the events of Carver's life that we have recounted above, the reader will have gained a fairly good idea as to his personality. However, we end this biography with Cecil C Craig's description [3]:-

Carver was an unusually gifted and, in some ways, almost an eccentric person. His diet consisted principally of milk and crackers, and he neither drank nor smoked. He had a real zest for living; he worked hard and effectively at whatever he found interesting and, as a rule, he did not persist long at anything that became boring. He had a warm personality, and he took a very sympathetic interest in his students. Few of his students ever forgot the experience of having a course with him. He was a unique and very valuable contributor to his university and to the science of statistics

**Article by:** *J J O'Connor* and *E F Robertson*

**List of References** (10 books/articles)

**Mathematicians born in the same country**

**Additional Material in MacTutor**

**Other Web sites**