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Helge Tverberg

Helge Tverberg, 7 March 1935 - 28 December 2020

Helge Tverberg
Helge Tverberg
Photo:
Linn Helmich Pedersen

Helge Tverberg has been a constant presence and a part of the Maths Department for over 60 years. Tverberg grew up in the Møhlenpris quarter in Bergen and made an early mark when he won the Crown Prince's prize in the annual Norwegian mathematics competition for high school students. He then studied mathematics in Bergen where he took a Master's degree in 1958 and was soon after appointed as a university lecturer. In 1965 he became a lecturer and in 1971 he was appointed professor of Pure Mathematics. He was also a member of the Norwegian Academy of Sciences.

Tverberg was always friendly and a considerate colleague. He had a tremendous memory of people, stories and mathematical results. We especially appreciated his good anecdotes and jokes but also  the countless mathematical problems he willingly shared with all his colleagues. There was hardly anyone who was as easy to get involved in a mathematical conversation as Helge. No fear that someone might take a problem from him or continue working on it in secret. For this he needed the many small paper pieces he had in his front pocket. Tiny strips of paper could hold big mathematical problems. The smaller the notes, the bigger the mathematical problem.

He had a broad knowledge in mathematics. As a young man he had made up his mind to read all the books in the then Department library. In the age before the internet, and also after, he was therefore often used as an authority that the rest of us could go and ask.

His scientific contributions are in the field of combinatorics and convex geometry, where he has a significant international name. His main result is the so-called Tverberg's theorem which he discovered in 1965. At that time, mathematicians were trying to generalize a result about configurations of point sets in the plane, called Radon's theorem, into higher-dimensional spaces. Tverberg was visiting colleagues in Manchester and had devoted a lot of thought to this problem. One morning he woke up very early in a bitterly cold hotel room and lacked a shilling to activate the heater. He got up, just as well, and sat down to work on the problem, when the solution dawned him.

The theorem is today considered one of the fundamentals of convex geometry. Eight to ten years ago, a major international conference in discrete mathematics was held in Bergen. The main guest was Gunther Ziegler, leader of the German Mathematical Society, who gave a large overview lecture on Tverberg's theorem and the research activity it had generated and still generates.

Tverberg also liked to deepen and simplify already known results. In particular, we can mention a result in graph theory that had been already proven by Ron Graham and Henry O. Pollak. Tverberg managed to give an unusually short and simple proof. The proof has such a beauty that it was included in "Proofs from THE BOOK", a collection of the world's most beautiful mathematical proofs inspired by Paul Erdos' idea that Our Lord has such a book where all the mathematics with most beautiful proofs were collected.

As a lecturer, he was original. He did not follow the syllabus book. He would come up with his own approach to the result and used alternative sources. Own twists and unfamiliar introductions to the topic were often in focus: the students could read the syllabus books themselves, they did not need a professor to do so.

His interests extended so much beyond mathematics. He must have been one of the most faithful and eager readers of Bergens Tidende (Bergen's newspaper). Until 2005, he also had a column of math nuts in it. He shared his wife's interest in antiques and enjoyed going to second-hand markets. If there was a place you could meet him outside work, it was usually there. A lifelong interest was also jazz music.

After retiring in 2005, he still came regularly and worked in his emeritus office, as he had done for the last 60 years. The last times he came to the department, he showed his colleagues his childhood home in Olav Rye's vei, which could be seen from the department's lunch room across Nygårdsparken, symbolically closing his life cycle.

For the last few years he could no longer come to the department, and many of us missed not having him there. With his passing, an era of the institute is over. Our thoughts now go to his wife Sonja and their four children with respective families. Helge Tverberg's legacy lives on in our memories.

Colleagues at the Department of Mathematics