The son of Thomas and Annie Kline Montgomery was born on September 21, 1872, in Mahanoy City, Pennsylvania. His formal education was limited, since his father, a Methodist minister, had to frequently move from church to church, a traditional practice in the Methodist Church. He never finished high school. In 1941 the honorary Doctor of Laws degree was bestowed upon him by Dickinson College, Carlisle, Pennsylvania.
After his father's illness made it necessary, he took his first job at the age of 14. On February 4, 1889 he became an office boy for John Heins, a public accountant in Philadelphia (later the firm name was changed to Heins, Whelen, Lybrand & Co.). William M. Lybrand, T. Edward Ross and Adam Ross were already working in Mr. Hein's organization and they helped him learn accounting and auditing. He was made a partner in 1896. In 1898, he and other members of the firm founded in Philadelphia the firm now known as Coopers & Lybrand. In 1902 the firm opened an office in New York City with Mr. Montgomery assuming responsibility of the office. He received a CPA certificate in 1899 (Pennsylvania). He also practiced law for many years and was admitted to the Bar in Pennsylvania in 1900 and to the New York Bar in 1904. For many years he practiced both law and accounting in New York but eventually abandoned the law practice for accounting.
Professionally he was very active in a number of accounting, taxation, and business organizations. His professional career was involved with many of the early accounting organizations and he continually worked for the establishment of one national accounting organization. A charter member of the Pennsylvania Institute of CPAs in 1897, he later served as president. He was president of the New York State Society of CPAs in 1922 and in 1923. He was president of the AICPA from 1912 to 1914 and again from 1935 to 1937. For the International Congress of Accountants, he helped organize the first ever meeting in St. Louis (1904), represented Columbia University at the second in Amsterdam (1926), chaired the third in New York (1929), and represented the AICPA at the fourth in London (1933). He helped organize and finance The Journal of Accountancy and wrote an article for the first issue published in November, 1905. In 1949 he received the AICPA's Gold Medal Award.
He was a member of the faculty of the evening school sponsored by the Pennsylvania Institute of CPAs in 1902; he taught night classes at the University of Pennsylvania in 1904, and at New York University, beginning in the winter of 1905-06. He taught the first evening classes in accounting at Columbia University in 1910. He was appointed instructor in the Department of Business at Columbia University in 1912, was promoted to assistant professor in 1915 and to professor in 1919. He remained on the Columbia faculty until 1931, serving for a time on the Administrative Board of the Department of Business. Besides writing numerous articles for professional journals, he authored many books including the American edition of Lawrence R. Dicksee's Auditing (1904), A Practical Manual for Auditors(1905), the influential Auditing Theory and Practice (1912), now in its eleventh edition (1990), Auditing Principles with Walter A. Staub (1923), Financial Handbook, editor (1925), Auditing with Willard J. Graham (1929), Fifty Years of Accountancy (1939), his autobiography, and many other authoritative books, particularly on taxation.
During the Spanish-American War he served as an Army private in the artillery and saw service in Puerto Rico. He also served in the Pennsylvania National Guard from 1898 until 1902. Commissioned as a Lieutenant Colonel (1918) during World War I, he was generally referred to thereafter as Colonel Montgomery. He was a member of the War Department Board of Appraisers, the War Department Representative on the Price Fixing Committee of the War Industries Board, and Chief of the Price Fixing Section of the Purchase, Storage and Traffic Division of the General Staff, among other capacities. His post-war public service included a number of assignments to governmental agencies and commissions. He was often sought by governmental agencies as an expert in accounting and tax matters.
His most enjoyable hobby was horticulture, particularly conifer and tropical trees. He founded the Fairchild Tropical Garden in Coconut Grove, Florida in 1938. The Montgomery Library-Museum, made possible by a gift from the partners of Coopers & Lybrand, was established there in 1940. He also made significant contributions to the New York Botanical Garden and served on its Board of Managers (1935-53). This latter organization gave him its distinguished service award in 1951. He was a golfer and he collected old and rare accounting books. In 1926 he contributed his historical book collection from the entire world on such subjects as an account book of a slave ship and the record books of kings and queens in the 15th century to Columbia University; additions to the collection are made annually.
He married Elizabeth Adams Shaw on November 5, 1904; they had four children. Divorced from his first wife in 1927, he later married Lois Cate Gibb (January 26, 1928), and after their divorce, he married Eleanor Foster (July 26, 1934). He died on May 2, 1953 at the age of 80.