Awarded a Sheldon Travelling Fellowship for postdoctoral study, Brink spent the year 1916-17 studying at the CoIIège de France and the Sorbonne in Paris, where he began a lifelong devotion to France and to the French language and culture. On two later occasions, in 1924-25 and in 1932-33, he spent sabbatical leaves studying at the Sorbonne.
In 1917 Brink joined the faculty of the Department of Mathematics in the College of Science, Literature, and the Arts at the University of Minnesota, where, except for three leaves of absence, he remained until retirement in 1957, when he was awarded the title of Professor Emeritus. During the year 1919-20 he lectured at the University of Edinburgh. He was chairman of the department at Minnesota from 1928 until his retirement, except for the period from 1932 to 1939. Briefly in 1955 he also assumed additional duties as acting assistant dean for his college.
Brink was a member of several professional organizations, principally the Mathematical Association of America, the American Mathematical Society (for whom he was an associate editor of the Transactions), the American Association for the Advancement of Science (for whom he was a chairman of Section A on mathematics and an invited speaker at a national meeting), Sigma Xi, the Edinburgh Mathematical Society, and the New York Academy of Sciences. His professional activities were mainly directed to the Association, of which he was a member since 1922. He wrote several book reviews and refereed many papers for the American Mathematical Monthly, was a member of the Board of Trustees of the Association (1934-40), and was elected vice president in 1940 and president for the period 1941-42. In addition, he was chairman of the Committee on Arrangements (for both the Association and the Society) for the summer meetings in 1931 at the University of Minnesota, and was chairman (1951) of the Association Committee on Places of Meetings. In his retiring presidential address, delivered at the twenty-seventh annual meeting of the Association in Chicago in November 1943, he spoke on "College Mathematics During Reconstruction" with astonishing accuracy of foresight for the years immediately following the end of World War II.
Raymond Brink and Carol Ryrie were married on July 12, 1918. They had two children, David Ryrie Brink and Nora Caroline Brink. Brink was an intensely loyal husband and father, and felt special pride in the considerable writing accomplishments of his wife. His son David has said, "He was Mother's original and most devoted fan and remained always her 'best friend and (occasionally) severest critic'." Brink was an avid reader and student throughout his life, but also a lover of games and contests, both mental and physical. In addition to setting high standards intellectually, Brink was always a complete gentleman and, perhaps stemming from his upbringing as son of a Baptist minister, his life served as a model not only for his family but for all those who had the good fortune to know him well.
Many mathematicians knew Brink primarily through his many successful textbooks in trigonometry, college algebra, and analytic geometry. Others have benefited either as authors or as users of books, from his exceedingly careful and painstaking work as editor of mathematical texts. From 1944 until his death he was consulting editor for the Appleton-Century Mathematics Series. As both author and editor Brink never lost his love for good language usage and le mot juste.
Shortly after retirement, during the year 1958-59, Brink was a visiting professor at the University of Miami. He then established permanent residence in La Jolla, California, where, in addition to his editorial work, be pursued his hobbies of gardening, reading, photography, and music. He was a member of the La Jolla Presbyterian Church, Friends of the University of California at San Diego Library, and of the La Jolla Symphony Association.
Survivors include his wife, son, daughter, a brother, and eight grandchildren. Inurnment was at the Brinks' Wisconsin vacation home at Lake Windigo near Hayward.