**Raymond Brink**'s parents were Clark Mills Brink (1850-1916) and Helen Nellie Rebecca Bacon (1859-1930). Clark Brink graduated from Rochester Theological Seminary in 1882 and, after serving as a pastor in various churches, was a pastor in Roseville church, Newark at the time that his son Raymond was born. He was an instructor in Rhetoric and Oratory at Brown University, 1892-95, and then professor of English and History at Kalamazoo College until 1901. After a year at Harvard as a graduate student, he was appointed professor of English Literature at Kansas State University. He was Dean of the College from 1908 and later Assistant to the President. Clark and Helen Brink had five children Laurence Bacon Brink (1885-1970), Raymond Woodard Brink (1890-1973), the subject of this biography, Gertrude Emma Adams Brink (1892-1906), Wellington Tufts Brink (1895-1979), and Helen Marguerite Brink (1905-1905). After education in a number of cities as his family moved around, Raymond had his high school education in Manhattan, Kansas.

Brink entered Kansas State University in 1904 at the remarkably young age of fourteen. He received a B.S. degree in 1908 from Kansas State and a B.S.E.E. degree in the following year. He did not continue his studies immediately by attending graduate school but undertook teaching for a short time. He was an instructor of mathematics in Moscow, Idaho and taught at the State Preparatory School of the University of Idaho. His address at this time was 604 B street, Moscow, Idaho. When he was teaching in Moscow, Idaho, Bring met a thirteen year old schoolgirl Caroline Ryrie (1895-1981), the only child of Alexander Ryrie and Henrietta Watkins. Carol, as she was known, lost her parents at the age of eight and was being brought up by her maternal grandmother Caroline Watkins. David Bring, Raymond Brink's son, explained in [14]:-

My parents met here[Moscow, Idaho]when Mother was13and Father was19and teaching mathematics at the university and high school. And through that teaching my father decided that when she was old enough, my mother was who he wanted to marry. He was very discrete and didn't approach her until she was old enough, but on Valentine's day when she was14, he gave her her first bouquet of pink carnations and he repeated that every year after until his death.

He then entered Harvard University where his thesis advisor was G D Birkhoff. He was awarded his doctorate in 1916 for his thesis *Some Integral Tests for the Convergence and Divergence of Infinite Series*. He published the paper *A New Integral Test for the Convergence and Divergence of Infinite Series* (1918) which was based on his thesis. He writes:-

The thanks of the writer are due to Professor G D Birkhoff for many suggestions furnished by him during the preparation of this paper.

He begins the introduction as follows:-

A new sequence of integral tests for the convergence and divergence of infinite series has been developed by the author. Some of the tests of this sequence, and the principle by which they may be discovered will be set forth by him in another article. In the present paper it is his desire to give a central one of these tests, together with some of its applications. This particular integral test appears to play the same rôle when the ratio of successive terms is explicitly known, that the Maclaurin-Cauchy test plays when the individual term is explicitly known.

He also presented other results from his thesis to the American Mathematical Society in April 1916 but only worked out the proofs after that time. These he published in the paper *A New Sequence of Integral Tests for the Convergence and Divergence of Infinite Series* which appeared in the *Annals of Mathematics* in 1919.

Following the award of his doctorate Brink studied at the Collège de France and the Sorbonne in Paris spending the academic year 1916-17 financed by the prestigious Sheldon Travelling Fellowship. Brink fell in love with France and he had a passion for the country for the rest of his life. On returning to the United States, he was appointed, in 1917, to the Department of Mathematics in the College of Science, Literature, and the Arts at the University of Minnesota. In the following year he married Carol Ryrie on 12 July; they had two children, David Ryrie Brink and Nora Caroline Brink. The marriage was not without its problems for Carol's relations [14]:-

... once forbade the two to have contact and even after they became engaged refused to let them marry in the family house. But they decided they were right for each other and got married anyway.

Brink spent the academic year 1919-20 at the University of Edinburgh in Scotland where he was appointed as a lecturer in Mathematics. This led to him joining the Edinburgh Mathematical Society in December 1919. Except for two further periods of study leave spent in Paris (1924-25 and 1932-33) Brink continued to teach at the University of Minnesota. He was Chairman of the Mathematics Department from 1928 to 1932. David Brink described growing up in the Brink home [20]:-

[

David]Brink learned to appreciate words growing up in University Grove, the faculty neighbourhood near the University of Minnesota ... Dinner at the Brink house was a formal event, with conversations often focusing on spelling and grammar. Discussions between his parents would go on and on "until someone would get the dictionary to see if it was right or not,"[David]Brink said.

After a break from his Chairman role for a few years, Brink became Chairman again in 1939 and continued to lead the department until he retired in 1957. A student who studied under him in 1947 wrote:-

There were older people in the Science, Literature, and the Arts Mathematics Department who had been active at one time, but had turned their attention largely to administration, textbook writing, and teaching. These included Professor Raymond W Brink who was Chairman of the department, and had been President of the Mathematical Association of America.

As this quote indicates, Brink was much involved with the Mathematical Association of America. He served on its Board of Trustees from 1934 to 1940. After serving as vice-president of the Association he was elected President in 1940. He held this position until November 1943. These were difficult years with America entering World War II and this had, of course, a major impact on the Association and its members. One consequence was that the Association's annual meeting, which had been scheduled to be held 30-31 December 1942, in New York, had to be cancelled due to transport difficulties brought on by wartime conditions. Brink gave his retiring presidential address entitled 'College Mathematics during Reconstruction' in November 1943. He began his address with these words [4]:-

If we pause for a little while amid the turmoil of the war-training courses in order to look forward to the period just after the war, it is not because we feel that the war is over nor even that its end is hidden from us by being just around the corner. The war-training programs will doubtless be with us for a long time to come. Doubtless they will be subject to more of the sudden and arbitrary changes that we have all found so baffling. Doubtless we shall continue to be faced with shortages of staff, irregular schedules, budgetary difficulties, and elusive academic standards, as in the recent past. Yet I feel that the general pattern of training in the colleges is fairly well established or at least that we are psychologically better prepared than we were twelve months ago to meet such wartime changes as may occur. On this plateau, then, rather than summit, that we have reached I should like to pause to take stock of our gains and losses, and to look forward toward the land ahead. Perhaps it is not too early to see something of this land of college mathematics after the war is won and of the problems we shall find there. Perhaps, by looking back at the way we have come, we can find help in solving those problems.

Olmsted [17] writes that Brink's gave this address:-

... with astonishing accuracy of foresight for the years immediately following the end of World War II.

For further details see Brink's obituary in the *American Mathematical Monthly* at THIS LINK.

Finally we give some examples of Brink's papers: *A new integral test for the convergence and divergence of infinite series *(1918); *A new sequence of integral tests for the convergence and divergence of infinite series* (1919); *The May Meeting of the Minnesota Section* (1927); *Recent Publications: Reviews: Studies in the History of Statistical Method - With Special Reference to Certain Education Problems* (1929); *The May Meeting of the Minnesota Section *(1930); *A Simplified Integral Test for the Convergence of Infinite Series* (1931); *Recent Publications: Reviews: Differential Equations* (1932); *The Annual Meeting of the Minnesota Section* (1937); *College Mathematics During Reconstruction* (1944), and *A Course in Mathematics for the Purpose of General Education* (1947). We see from this list that, other than the papers which resulted from his thesis, most of Brink's papers relate to teaching, mathematical education or reports of meetings. The paper *A Simplified Integral Test for the Convergence of Infinite Series* (1931) is really a follow-up paper to his 1918 and 1919 papers. His introduction to this paper is interesting and we give a little below:-

In other papers the author has presented certain integral tests for the convergence and divergence of infinite series. Such tests are interesting not only because they can be used for testing types of series which are very difficult to examine by other methods, but also because, through the natural connection between integration and summation, they offer a simple and attractive means of unifying and establishing many tests of other kinds. Du Bois-Reymond gave the name "tests of the first kind" to series tests which make direct use of the general term of the series itself. And "tests of the second kind" are those which use the ratio of the general term to the preceding term. In this category are the d'Alembert test, which every student of Calculus knows as "the" ratio test, the first test of Raabe, and the sequence of tests of De Morgan and Bertrand. In a similar way, the familiar Maclaurin-Cauchy integral test, which requires the use of a function u(x)where u(n)is the general term of the series, may be called an "integral test of the first kind." And an "integral test of the second kind" is one in which an analogous role is played by a function r(x), where r(n)is the ratio of the nth term to the preceding term. Hitherto the most generally useful integral test of the second kind was given by the author in one of the papers mentioned. Its statement and proof are simple for convergence, but rather awkward for the divergence test. The purpose of the present paper is to give a modified form of the test - a form that is as widely applicable as the earlier one and that is simpler to state and to establish.

As to his contributions to mathematical education, we quote from *A Course in Mathematics for the Purpose of General Education* (1947):-

At the University of Minnesota in order to advance from the lower division to the upper division of the College of Science, Literature and the Arts a student must have completed certain group requirements. ... mathematics is one of the few that cannot be used in meeting the group requirements; philosophy, music, and fine arts are others. ... In order to fill this gap in the standard curriculum, the Department of Mathematics at the University of Minnesota in the fall of1941first offered a terminal course in mathematics especially addressed to the general student. Certainly the idea of such a course is nothing new among mathematicians. Even less is it a novelty to give unified courses that combine topics from several branches of elementary mathematics. A survey of approximately500colleges and universities indicated that the preponderant opinion is that the conventional introductory college course is more appropriate for specialists than for non specialists in mathematics. And many institutions have introduced new courses either in addition to the standard courses or partially to replace them.

The greatest contribution that Brink made is considered by most to be his textbooks. These were at high school or college level and you can see a list of some of these together with short extracts from some reviews at THIS LINK.

We noted above that Brink retired from the University of Minnesota in 1957. The following year, 1957-58, he spent as a Visiting Professor at the University of Miami. After this year, Brink and his wife [17]:-

... 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.

Bring died in Scripps Memorial Hospital, La Jolla, San Diego county, California from a stroke in the left carotid artery. He was cremated on 28 December at Crypress View Cemetery-Crematory San Diego.

Finally let us write a few words about Carol Ryrie Brink since, to many, she is better known than her husband. She was an author, her first novel being *Anything Can Happen on the River* (1934). She continued to write fiction such as *Caddie Woodlawn* (1935), *Mademoiselle Misfortune* (1936), and *Baby Island* (1937). In total she published 30 books but she also wrote poetry and was an excellent painter. She was awarded an honorary degree from the University of Idaho in 1965 and the university named Brink Hall after her. Various places in Moscow, Idaho, are named after Carol Ryrie Brink and the two Brink children donated portraits of both their parents to the Moscow-Latah County Public Library in 1995. David Bring said [14]:-

My mother was more well-known by the general public, but my father was very well respected in his field. We could have hung his portrait in many places, but we felt it was fitting to have them together and we felt it was fitting to have them in Moscow[Idaho]where they first met.

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