Ralph Tambs Lyche

Ralph Tambs Lyche: Prisoner 53, and a Herbarium

In March 1942 the professor of mathematics at Norway's Technical College was arrested and sent to Falstad concentration camp. He was given the prisoner number 53 and held until August 1943, then stripped of his chair and interned. He had been a communist, until the Hitler–Stalin pact of 1939 finished that for him. He survived, returned, and lived another forty-eight years, dying in Oslo at the age of one hundred. Along the way he wrote the textbooks that taught Norwegian mathematics for a generation and assembled the largest private plant collection in the country.

An American Birth

He was born on 6 September 1890 in Macon, Georgia. His father, Hans Tambs Lyche, was a Norwegian engineer, minister and editor; his mother, Mary Rebecca Godden, was American. The family moved to Norway in 1892, when Ralph was two. His father died while he was still young, and he was raised by his uncle, Axel Lyche, at Berg near Halden. He took his secondary examinations in 1908 and began university study in Kristiania.

Seventeen Years to a Doctorate

His training was unusually protracted, and the dates tell the story of a man supporting himself. He joined the Norwegian Institute of Technology (NTH) as an assistant in 1910, at twenty. He did not complete his cand.real. degree at the Royal Frederick University until 1916. He became a docent in 1918. And only in 1927 — seventeen years after first walking into NTH — did he obtain his doctorate, and not in Norway but from the University of Strasbourg, with a dissertation on Abel's functional equation. He was made full professor at NTH in 1937, at forty-six.

The Mathematics of Doing It Again

His research, some sixty papers across analysis, number theory, mathematics education and history, returned repeatedly to two linked themes: Abel's integral equation and the iteration of functions.

Iteration is a deceptively simple idea. Take a transformation and apply it to its own output, then again, and again. What happens? Most of mathematics is comfortable describing one application of a rule; describing the long-run behaviour of infinitely many applications is far harder, and asking what it would even mean to apply a function "half" a time — to interpolate between whole numbers of iterations — is harder still. That is the territory Abel's functional equation occupies, and it is where Tambs Lyche worked. Named for Niels Henrik Abel, Norway's founding mathematical figure, the subject also had a patriotic pull for a Norwegian analyst.

For most of the twentieth century this looked like a beautiful backwater. Then, from the 1990s, fractal geometry made iteration central to mathematics: fractals are precisely what you get when a transformation is applied over and over. Tambs Lyche's chosen corner turned out to have been the front door all along, some seventy years early.

"Over evne"

His broadest influence was not research. His three-volume *Lærebok i matematisk analyse* was the standard analysis text at NTH and Norwegian universities into the 1960s. Students nicknamed the volumes *Over evne I, II, III* — roughly, "Beyond One's Powers," a title borrowed from Bjørnson and meant as a complaint. The complaint was the point. The books deliberately raised the standard of rigour demanded of Norwegian students, and they held that raised bar for decades. He also wrote texts for secondary schools. Two generations of Norwegian engineers and mathematicians learned analysis from a man who refused to make it easy.

The Radical

He was a committed communist and socialist activist, chairing the Student Society at NTH in the spring of 1920 and helping found the cooperative business Tapir. The Hitler–Stalin pact of 1939 ended his affiliation with communism, though not his radicalism. It also, on the evidence, did nothing to protect him: German occupation forces arrested him regardless, and Falstad followed.

Fifty-Two Thousand Specimens

Botany was not a hobby he pursued lightly. Tambs Lyche published numerous articles on adventive plants — species arriving where they do not belong, carried in by ballast, trade and human traffic — and built a herbarium that by 1971 held over 52,000 specimens, the largest private collection in Norway. It is now at the Science Museum in Trondheim. He chaired the Norwegian Botanical Society from 1957 to 1959, immediately after chairing the Norwegian Mathematical Society from 1953 to 1959, and there is a certain logic to the overlap: adventive botany, like function iteration, is the study of what happens when a process runs long enough to reach somewhere unexpected.

Institutions

He was a member of the Royal Norwegian Society of Sciences and Letters from 1927 and its secretary-general from 1946 to 1950, and a member of the Norwegian Academy of Sciences from 1929. In 1950 he moved from Trondheim to the University of Oslo as professor of mathematics, holding the chair until 1961, and finished with a visiting year at the University of Colorado, Boulder, in 1961–62 — returning, at seventy-one, to the country of his birth. His wife Elsa was a pioneer of maternal hygiene work; their daughter became a noted solidarity activist.

Why Ralph Is Called a Genius

He is not, and no source examined here uses the word. Sixty papers over a long career is a modest output; his doctorate came at thirty-seven; his mathematical subject was, in his lifetime, peripheral. If the test is a theorem bearing his name, he fails it.

The quality the record does show is judgement about what is worth doing, sustained without external validation. He picked function iteration when it was unfashionable and stayed with it for decades, and the field eventually arrived where he had been standing. He wrote textbooks harder than his students wanted and was right to. He collected 52,000 plants one at a time. That is a temperament rather than a talent — the willingness to invest enormous, unglamorous effort in things whose value is not yet obvious — and it is the temperament that most actual mathematics requires.

The honest counter-case is straightforward. Tambs Lyche's contribution was cumulative, pedagogical and institutional far more than it was revolutionary. His research was specialised and his influence ran chiefly through his textbooks and his committee work. Calling him a genius would flatten what is genuinely interesting about him: that a life of stubborn, wide-ranging competence — analysis, number theory, botany, resistance to occupation, survival of a camp — is its own kind of achievement, and does not need the word.

Legacy

He died on 15 January 1991 in Oslo, having lived a hundred years and four months. The herbarium is in Trondheim. The textbooks are out of print but shaped the rigour of Norwegian mathematical education for half a century. And the subject he chose — what a transformation does when you apply it forever — is now taught to undergraduates everywhere as the foundation of fractal geometry and dynamical systems, which is a slow vindication, but a complete one.

Achievements

• Held posts at University of Oslo and Norwegian Institute of Technology