**Henry Fine**'s parents were Mary Ely Burchard and Lambert Suydam Fine who was a Presbyterian minister of Dutch ancestry. Henry was the eldest of his parents four children, having a younger brother and two younger sisters. His brother John became the founder of the Princeton Preparatory School, while one of his sisters, May Margaret, became the founder of Miss Fine's School. Lambert Fine died in 1869 when Henry was ten years old, and his mother moved to Ogdensburg, New York, for a period and then to Winona, Minnesota, and finally in 1875 she came with her children to Princeton so they might have a good education [4]:-

She was, by all accounts, a woman of great ability and force of character and launched all her children on honourable careers.

Before coming to Princeton, life had not been too easy [4]:-

Fine's early years were those of a country boy under pioneer conditions. He was always enthusiastic about the two great rivers, the St Lawrence and the Mississippi, beside which he lived in those years and on which he learned to row. Rowing, by the way, was the only college sport in which he took an active part, though he was always keen on athletics and gave much time and energy to the direction of them up to the end of his life.

He received private coaching before entering the College of New Jersey in 1876, 130 years after it was founded. The College of New Jersey's name was changed to Princeton University in 1896. Fine entered the College with the intention of studying classics and he began to study these subjects as well as Sanskrit. However, at Princeton he came across Halsted who had studied under Sylvester at Johns Hopkins University and spent the years 1878 to 1881 as an instructor in postgraduate mathematics at Princeton. Halsted inspired Fine to turn towards mathematics.

After receiving his A.B. in 1880, Fine was appointed a fellow in experimental science at Princeton but, never happy with experimental work, he happily changed to be a tutor in mathematics in 1881. Fine then, as was the custom of the day, decided to study in Germany. He travelled to Leipzig in 1884 and there attended lectures by Klein, Carl Neumann and others. He worked for his doctorate on a topic suggested by Study, and approved by Klein, and the degree was awarded for the dissertation *On the singularities of curves of double curvature* in May 1885 by the University of Leipzig.

Fine spent the summer of 1885 in Berlin attending Kronecker's lectures on eliminants which made a strong impression on him. Returning to the United States from Berlin, he was appointed assistant professor at Princeton. On 6 September 1888 he married Philena Fobes of Syracuse, New York; they had three children. Despite great promise as a research mathematician, Fine moved into other areas. As Archibald writes in [1]:-

... Fine published a few research papers(1887-1890), and another of some importance as late as1916. But his time was mainly devoted to teaching, administration, and the logical exposition of elementary mathematics.

His first research paper was *On the singularities of curves of double curvature* which was his thesis, published in the *American Journal of Mathematics* in 1886. In the following year he published a generalisation of these results to *n* dimensions in the same journal. Two further paper *On the functions defined by differential equations with an extension of the Puiseux polygon construction to these equations,* and *Singular solutions of ordinary differential equations* appeared in 1889 and 1890 respectively. The later, rather significant, research publication refered to in the above quote was *On Newton's method of approximation* (1917).

Among the elementary texts he wrote are *Number system of algebra treated theoretically and historically* (1891), *A college algebra* (1905), *Coordinate geometry* (1909), and *Calculus* (1927).

Fine's most important contributions were to the American Mathematical Society and to Princeton University. He served the American Mathematical Society as vice-president 1992-93 and as president 1911-12. He gave his retiring address as president on *An unpublished theorem of Kronecker respecting numerical equations.*

At Princeton he was promoted to a full professorship in 1889 and in 1898 he was appointed Dod professor of mathematics. However, he moved into administration around 1903. In part this was due to his undergraduate friend Woodrow Wilson being appointed as president of Princeton. It was in 1903, shortly after becoming president, that Wilson appointed Fine as Dean of the Faculty. Together Wilson and Fine worked to lift the standards at Princeton, both by improving the curriculum and in making strong faculty appointments. After Wilson left Princeton in 1910 to move forward in his political career by becoming governor of New Jersey, Fine stood in to run the university for two years until a new president was appointed (many expected that Fine would be appointed president but it was not to be). He then resigned as dean, but accepted the appointment as Dean of the Departments of Science. He chaired the committee set up in 1925 to obtain funds for research in the sciences at Princeton. Largely due to his efforts three million dollars were raised by 1928.

Veblen describes his character [4]:-

His firmness of character and wisdom in counsel made him the pre-eminent figure among his colleagues of the faculty up to the very end. He was the man to whom they turned more than to anyone else for leadership or advice, both in public and private affairs. These qualities were widely recognized outside Princeton, for he had more than one opportunity to become a University President, and President Wilson made several efforts to induce him to take important posts in his administration. But as he said quite simply, he preferred to continue as a professor of mathematics.

His other interests are described in [1]:-

In early days Fine played the flute in the college orchestra ... His knowledge of music was extensive... He took keen interest in games and in the daily life of the undergraduates.

The end of Fine's life was tragic. His wife died in April 1928 but two of his three children had died earlier. However he visited Europe in the summer of 1928, meeing again old friends and revisiting places from his past. He returned to the United States in August, and seemed to be looking towards an active furure. Fine died after a bicycle accident while he was going to visit his brother John at the Princeton Preparatory School:-

In the uncertain evening light he was riding his bicycle on a road in the outskirts of Princeton and was struck from behind by an automobile, the driver of which failed to see that he was starting to make a left turn. He died the next morning without having recovered consciousness.

Fine Hall, home of the Princeton Mathematical Department, is a memorial which keeps his name before mathematicians at one of the most important centres of mathematics in the United States, and the world.

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