Academician Olli Lehto (1925–2020) – A top-level mathematician at the helm of the University

Academician Olli Lehto passed away in Helsinki on New Year’s Eve, 31 December 2020. A mathematician who reached the ripe old age of 95, Lehto established a career of exceptional scope at the University of Helsinki as a researcher, professor, dean, rector and chancellor. Alongside his international duties, Lehto distinguished himself in retirement as a non-fiction writer, also exploring the varied twists and turns his life had taken in a matter-of-fact manner, tinged with humour, in his memoirs entitled Ei yliopiston voittanutta (Otava, 1999).

Olli Erkki Lehto was born in Helsinki on 30 May 1925. His father Lauri, originally from the region of South Ostrobothnia, had a master’s degree in mathematics and worked as an insurance executive in the Suomi Mutual Life Assurance Company, while his mother Hilma (née Autio) had relocated from Vyborg to Helsinki and worked at the same company. Olli grew up in the Etu-Töölö district of Helsinki and went to the school Helsingin Suomalainen Yhteiskoulu (SYK), but his general upper secondary school studies came to a halt in the spring of 1943 when the authorities declared him a graduate without having taken the matriculation examination and called him to military service. In October, the 18-year-old youngster was sent to the front in Syväri, after which he took part in the Continuation War in Kannas and Aunus in 1944 as well as in the Lapland War against the Germans in 1945.

In spring 1945, Olli Lehto was able to enrol at the University of Helsinki with mathematics as his major subject. After progressing rapidly in his studies, Lehto received his Master of Science degree in 1947. His thesis was examined by Rolf Nevanlinna, who, after resigning from his post as rector of the University in 1945, was on a leave of absence from his professorship in mathematics, tending to a corresponding post at the University of Zurich in Switzerland. Nevanlinna arranged a scholarship in Zurich for Lehto in 1948, after which his doctoral thesis on the theory of functions was quickly completed by the summer of 1949. Lehto, who had just turned 24, had as his opponent Professor Pekka Juhana Myrberg, another function theory specialist, who was to serve as the chancellor of the University from 1952 to 1962.

Already after graduating with his master’s degree in 1947, Lehto had found employment at the cable company Suomen Kaapelitehdas Oy, gaining the opportunity to observe the construction and deployment of ESKO , the first ‘mathematical machine’ made in Finland. In the early 1960s, a memo drawn up by Lehto spurred on the electronics department of the company to invest in new information technology, laying the ground for the future success of Nokia at the end of the century. However, more important than any application was his passionate practice of science, that is, his efforts in mathematical basic research, first as an assistant to Nevanlinna in 1953–1956, who by this time had become a full-time researcher as an academician, and subsequently as the successor of P.J. Myrberg in the professorship in mathematics from 1961 to 1983.

In 1954 Olli Lehto married Eva Ekholm (1927–2020). Eva had obtained a pilot’s licence for powered flight, but as a woman she was allowed to fly only as a stewardess or a glider pilot. The couple had three children between 1955 and 1961. In the 1970s and 1980s, Eva Lehto served as the executive director of the Finnish Refugee Council, also finding a new apartment for the family on Ritarikatu close to the University. During the marriage, which spanned over 66 years, she actively contributed to the increasing academic duties of her spouse.

Olli Lehto’s central field in mathematics was the theory of functions of a complex variable, or complex analysis, a field where research was initiated in Finland by Ernst Lindelöf in the 1910s and made world-class by Rolf Nevanlinna and his student Lars Ahlfors in the 1920s and 1930s. In his memoirs, Lehto does not delve into the details pertaining to this difficult topic, but offers a good summary in an article on the history of mathematics in Finland written for Suomen tieteen historia 3 (WSOY, 2000), a work edited by Päiviö Tommila. Already in his master’s thesis, Lehto presented a constructive existence proof for Riemann’s mapping theorem, according to which a connected open set on the complex plane can be conformally mapped on the unit disk. This result can be generalised to a Riemann surface, which is composed of glued layers of the complex plane. Lehto is to thank for the revival of the function theory school which brought Finland much renown, with new insights on the properties of Riemann surfaces by Nevanlinna’s students (Ahlfors, who transferred to Harvard, and Oswald Teichmüller, who died already in 1943) as the starting point. Previously, research had been focused on conformal maps where the angles of figures are preserved. Quasiconformal mappings were an interesting novel generalisation, where the angular distortion is limited. In this case the shapes are not entirely preserved. Instead, a circle can be mapped to an ellipse. In 1958 and 1959, Lehto held a joint seminar with Professor K.I. Virtanen, and their co-authored monograph entitled Quasikonforme Abbildungen was published by Springer in 1965 in German and in 1973 in English. The publication came close to cancellation, as K.I. Virtanen (the son of Nobel laureate A.I. Virtanen) disapproved of Olli Lehto’s academic visit to the Soviet Union. In the end, the matter was resolved, and the book was established as the definitive work of a new research programme on quasiconformal mappings. Olli Lehto supervised a total of 18 doctoral theses in mathematics, and several of their authors became university professors (Jussi Väisälä, Reino Kurki-Suonio, Martti Tienari, Seppo Rickman, Kalevi Suominen, Olli Martio, Tapani Kuusalo). He held an Academy of Finland research professorship from 1970 to 1975. Study of quasiconformal mappings was continued also by Pertti Mattila, Pekka Tukia, Ilpo Laine, Kari Astala, and Matti Vuorinen. While serving as rector, Lehto was able to complete an important monograph entitled Univalent Functions and Teichmüller Spaces (Springer, 1987) before he was swept away "from a contemplative life to one of increasing activity" by his numerous elected positions. Lehto’s work as a reformer of the theory of functions continues to bear fruit in geometric analysis, a field that is currently enjoying success in Finland, with significant applications also in mathematical physics.

I can count myself as one of Olli Lehto’s students. In spring 1966, I attended his commendably lucidly structured advanced-level lectures on differential and integral calculus. In the autumn, I took an oral examination in his office, receiving the highest grade. Next spring, I continued studying the theory of real functions in Lehto’s lectures. In the end, I did not become a function theorist, but a logician and philosopher grateful for a background in mathematics. Little did I know that I would eventually follow Olli Lehto in the positions of rector and chancellor.

Lehto was nominated to the membership of the Academy of Finland in 1968, but the nomination came to nothing when President Urho Kekkonen disbanded the old Academy in the following year. In his memoirs, Lehto does not dwell on this setback, as it would later have constrained him from seizing upon the varied and diverse opportunities presented to him in his second career in the University’s leadership. In 1975, at 50 years of age, Lehto was granted the title of academician.

Olli Lehto served as the chair of the Finnish Mathematical Society in 1962–1985, dean of the Faculty of Science in 1978–1983, rector of the University in 1983–1988 and chancellor in 1988–1993. In his role as an administrator, he was punctual, conciliatory and efficient, typical of mathematicians, inspiring broad-based confidence across faculty boundaries. In his memoirs Lehto explains that he could not even begin to understand the left-wing student radicalism of the late 1960s. Indeed, when serving as the chair of the Finnish Council for Higher Education in 1967–1970, he had the opportunity to oppose the passing of the ‘one man, one vote’ principle. During Lehto’s chancellorship from 1992 onwards, an administrative reform was approved at the University of Helsinki, moving from professors having the sole power to a tripartite system. As one of the high points of his academic career, Lehto highlights in his memoirs the role of conferrer in the solemn conferment ceremony of the Faculty of Philosophy held in 1982. As rector, he adopted a novel stance to delegating duties to the two vice-rectors. As chair of a working group, he contributed to the establishment of national doctoral schools, and he also took part in the founding of the Rolf Nevanlinna Institute, a mathematical research institute, in 1987.

While serving as rector, Lehto also headed the preparations of the University’s 350th anniversary ceremony, including the hiring of Professor of History Matti Klinge, on a part-time-basis, to write the history of the University from 1640 and appointing Docent Päivi Setälä as the head marshal for the ceremony. By the anniversary in 1990, Lehto had become the chancellor, while Päiviö Tommila served as rector. Lehto succeeded in convincing the University Senate to reject a proposal to return a tall bust of Emperor Alexander I of Russia to the Great Hall of the Main Building, which was being renovated. In its place he had delivered from the chancellor’s office smaller busts of Queen Christina of Sweden and Emperor Alexander I, which were a better fit for the Great Hall, where they remain to this day.

Olli Lehto took on the challenging task of organising the International Congress of Mathematicians in Helsinki in 1978. With more than 3,000 mathematicians from 85 countries attending, it was the largest scientific conference held in Finland at the time. Lehto had the opportunity to demonstrate his versatile diplomatic skills in the executive committee of the International Mathematical Union (IMU) in 1975–1990 and as its secretary general in 1983–1990. Subsequently, he took on and completed the imposing job of writing the rich history of the IMU. The work entitled Mathematics Without Borders was published in 1998 by Springer. Lehto also served as vice-president of the International Association of Universities (IAU) in 1990–1995.

Over his career as a researcher and active member of associations, Olli Lehto visited at least a hundred universities all over the world, usually taking a butterfly net with him on his travels. His daughter's habit of catching butterflies at the family’s summer place in the 1960s was the catalyst for a hobby dear to the professor that spanned three decades, resulting in a valuable collection of butterflies, which was handed over to the Finnish Museum of Natural History Luomus in 2009. Each species and the sites where they were found have been meticulously and vividly described in the book entitled Perhosten värittämä maailmani (Otava, 2011).

After retiring from the chancellorship in 1993, Olli Lehto found a new calling as a non-fiction author. In addition to his personal memoirs (1999), Lehto produced elegant biographies of Rolf Nevanlinna (2001), the Väisälä brothers (2004), Lorenz and Ernst Lindelöf (2008) and Lars Ahlfors (2013) from the perspective of history of science. In 2009 he was awarded the State Award for Public Information for his lifetime’s achievement in information publication.

Ilkka Niiniluoto
Academician, chancellor emeritus