ERNST SNAPPER

Benjamin P. Cheney Professorof Mathematics

Ernst Snapper is a mathematician's mathematician.

At the outer reaches, his world is so abstract that he writes in what amounts to Mother language, even though the connective words are English. Indeed, his many professional articles carry titles incom- prehensible to those uninitiated to the arcane provinces of advanced algebra, geometry, algebraic geometry, geometric algebra and his new interest mathematical logic.

Even his recent book, Metric AffineGeometry, aims partially at an area of geometry in which "practically all ability to measure length, area, angles, etc., has been removed from Euclidean geometry."

Snapper's work of 35 years at the outer borders of algebra and geometry and in the one-time no-man's land in between has made him a champion of the movement toward integration of the two studies. To him, the traditional separation of algebra and geometry into two distinct disciplines is misleading, particularly at the secondary school level where young people often first gain their insights into mathematics.

When he talks about what he is doing in this latter area, Snapper is almost poetic, filling his spare, plain office with visions most of us can never see. After looking into the middle distance of the Hanover scene outside his office in Bradley Hall, he will turn and say in his courtly way and in tones still resonant with echoes of his youth in The Netherlands, "I am very much interested in the many beautiful bridges which span those two branches of mathematics ­ geometry and algebra. They have a much closer relationship than many realize."

Vet research is only a portion of his professional life. To Snapper a leading place is also occupied by teaching which he does deliberately across a continuum reaching from secondary school to the doctoral level. Each year, he seeks to arrange his academic program so that he teaches at least two undergraduate courses, including freshman courses, and two graduate courses. He also devotes virtually every summer to teaching at institutes for secondary school math teachers. In recent years, he as been particularly concerned with showing them those "bridges" he sees between geometry and algebra.

enjoy teaching mathematics - every second of it," Snapper says. "I look forward to every class, no matter what level. If I'm honest, I have to say the only part of academic life I don't like is the vacations because there's no teaching then."

A third and equally important area of professional concern is learning for himself ­ again a characteristic of this gravely serious yet gentle man in whom there is not an ounce of the hubris of position or seniority.

Mathematical logic is utterly different from the fields in which Snapper has been specializing. A couple of years ago, he started to learn about this new field because he became fascinated with it as a new dimension of his own understanding of mathematics.

He became drawn into this study, he recalls, because of the outstanding quality of the lectures he heard, discussions he sat in on, and papers he read by three young members of the Dartmouth mathematics department, who together comprise its faculty in mathematical logic. They are Stephen J. Garland '63, an assistant professor and faculty associate at the Kiewit Computation Center; James E. Baumgartner, also an assistant professor, and Victor Harnik, a John Wesley Research Instructor in Mathematics.

With his interest whetted, Snapper, who is old enough almost to be the father of this talented trio, has taken such courses as Math 69 taught by Garland and Math 89 taught by Harnik and received also what he terms as "innumerable private lessons from all three of our logicians."

And when he talks of their ability, he again becomes eloquent.

"It is my conviction," he says, "that here at Dartmouth we have the best educational organization in mathematical logic in the country. I can say this because I'm not part of the group, but merely profiting from their teachings. As a student of theirs, as well as a colleague, I think I can fairly say that there is no place in the country where an undergraduate can learn this field better than at Dartmouth."

When Snapper makes such a statement, he speaks from considerable experience in mathematical education across this country and abroad. Indeed, change ­ and learning ­ have been dominant themes in his life for many years.

Born in Groningen, The Netherlands, he received Holland's equivalent to a master's degree in mathematics from the University of Amsterdam, the city where he had grown up in the serenity of an academic household. But the year was 1936 and that peace was already being threatened by events in Germany, as Hitler re-occupied the Rhineland. Two years later, when Hitler showed his appetite for conquest by marching Nazi troops into Austria, young Ernst's father, Dr. Isidore Snapper, an internationally-known research physician and diagnostician, decided to accept an invitation from the Rockefeller Foundation to become director of medical research at the foundation's Peking Union Medical College in China.

Dr. Snapper knew he would be leaving one maelstrom for another, but he was eager to see his son out from the growing shadow cast then across Europe. During his trip to the United States to make final arrangements for his new assignment in the Far East, Dr. Snapper happened to visit with an American friend, Abraham Flexner, then director of the Institute for Advanced Study at Princeton, who suggested that Snapper have his son apply for graduate study at Princeton.

Ernst did, was accepted and came to the United States in 1938 fully expecting to return to Holland after completing graduate studies. But by 1939, when he received his A.M. degree from Princeton, Hitler had already taken over Czechoslovakia and Poland ­ moves that prompted John Kemeny's father to send his family out of Hungary to the United States a year later. And by 1941, when Snapper was awarded the Ph.D. in mathematics, his home country had become another of those overrun. Meanwhile his father and mother had been interned by the Japanese.

They were later released in an exchange, but, in a real sense then, Princeton was all Snapper could call home. Moreover, he had already begun his "love affair" with the United States, attracted by the "newness, freshness and informality" he found in a land where, he says, "its pains are still the developing pains of the young."

So Snapper began teaching mathematics at Princeton as an instructor, the first of three teaching stints there. The shuttle of fate also was bringing John Kemeny to Princeton as an undergraduate during this period and, although Snapper never had him in class, he did know of the young Hungarian student who took the mathematics department by storm. He remembers, for instance, how Claude Chevalley, a world-ranked mathematician with a reputation of a hard-nosed academic who rarely even talked to any but the brightest undergraduates, literally shared his personal office in Princeton's Fine Hall with the young Kemeny.

Later, after returning to Princeton as a visiting associate professor from the University of Southern California and after the former research assistant to Albert Einstein had joined the Princeton faculty, Snapper came to know Kemeny briefly as a colleague.

Years intervened, with Snapper teaching at Miami University in Oxford, Ohio, as the A. J. Buckingham Professor of Mathematics, and at Indiana University, before they met again - this time at Bowdoin College where Snapper was principal lecturer at a summer institute for college professors. The year was 1962.

In their discussions, Kemeny, by then chairman of the mathematics department at Dartmouth, suggested that Snapper should consider Dartmouth for his older son, then in high school. Snapper and his son John later visited Dartmouth, but it was the father who was recruited, joining the faculty in 1963. Son John opted for Princeton.

Snapper became the Benjamin P. Cheney Professor in 1971, succeeding Bancroft H. Brown, now retired and living in Hanover. The professorship was established in 1880 from a gift to Dartmouth by Benjamin Pierce Cheney, son of a Hillsboro, N.H., blacksmith. Although Cheney never went beyond grade school he parlayed an early job as a tee stagecoach driver to leadership golden age of railroading.

Despite the lure of the West, he retained his identification with New Hampshire and a strong interest in helping others to obtain the education he never enjoyed Both of those concerns led him to establish the Cheney Professorship in Mathematics.