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About this book

Sophus Lie (1842-1899) is without doubt one of Norway's greatest scientific talents. His mathematical works have made him famous around the world no less than Niels Henrik Abel. The terms Lie groups and Lie algebra are today part of the standard mathematical vocabulary.
In his comprehensive biography the author Arild Stubhaug let us come close to both the person Sophus Lie and his time. We follow him through childhood at the vicarage in Nordfjordeid, his growing up in Moss, school and studying in Christiania, travelling in Europe and his contacts with the leading mathematicians of his time. The academic and scientific career brought Lie from Christiania to Leipzig as professor, before the attempt to call him back to Norway, when she stood on the threshhold to national sovereignty, was successful.

Table of Contents

Frontmatter

The Measure of a Life

Frontmatter

Tracking Him Down: A Torrent of Stories

Abstract
According to most accounts of Sophus Lie, he was the embodiment of an archetypical character in a theatrical drama — with his forceful beard, his sparkling green-blue eyes magnified by the stout lenses of his spectacles — the blonde Nordic prototype, as it was called across Europe — the Germanic gigantic being — a primal force, a titan replete with the lust for life, with audacious goals and an indomitable will. These descriptions of his physical and mental strength also contained a subtext, an embryonic notion, not only about this brilliant man of science, the prophet who intuitively conceived new mathematical truths, but also about the colossus who, in his constant zeal for new knowledge, might push others aside, and inadvertently trample them underfoot. He was described as highly committed and richly innovative, someone with unusual physical strength, and the stamina to overcome the majority of obstacles, but also, a man who afterwards had to pay for this with correspondingly great swings of mood and temperament.
Arild Stubhaug

Family Background and Upbringing

Frontmatter

The Family Tree

Abstract
On the paternal side, Sophus Lie’s family tree stems from a certain Peder Lauridtzen of Streømsø in what is today the city of Drammen, west of Oslo. The sixty year-old Peder Lauridtzen is described in the census for 1665 as a beach dweller; in other words, he was far from being a member of the merchant bourgeoisie, and one might surmise, was a type of crofter who fished the fjord with a small boat.
Arild Stubhaug

The Priestly Family at Nordfjordeid

Abstract
Johan Lie was appointed parish vicar in July 1835, but it seems it was not until May of the following year the ecclesiastical couple, together with the infant Mathilde and their three year-old son Fredrik, left Molde and moved to the vicarage at Nordfjordeid.
Arild Stubhaug

Father’s Home in Moss

Abstract
When he was barely nine years of age, Sophus Lie left Nordfjordeid with his parents and five brothers and sisters (one more son was born to the Lies two years after the birth of Sophus). They were rowed out the fjord to Gloppen, from where they travelled by horse and cart down to Vadheim on Sognefjord. They were then transported by rowboat for several days up Sognefjord to Lærdal, then they took the old highway over the mountains of Jotunheimen to the valley of Hallingdal, and on down to Drammen and Holmestrand on the west side of Oslofjord. Here they took the steamboat across the fjord to Moss.
Arild Stubhaug

School and Education

Frontmatter

Nissen’s School. Examen Artium

Abstract
Beginning in the autumn of 1859, Sophus now lived in a bed-sitter in Christiania with his brother John Herman. The two parsons’ sons had found lodgings with a Miss Meyer, who seems to have lived somewhere in Pilestredet, one of the city’s safe and good neighbourhoods. She was probably a somewhat well-off lady; she was in any case a great lover of flowers and had so many that her houseplants even overflowed into the boys’ room, surely also in the windowsill, easily visible from the outside. In a letter home to his sister Laura in Moss, John Herman wrote that he and Sophus had nothing against all Miss Meyer’s plants, which in a way reminded them of their sister’s love of flowers. How were sister Laura’s twenty-four different sorts of acacia coming along anyway? The two boys had a standing rose, two ivy plants and a geranium in their room, and they wondered if such a love of flowers was something particularly common to womenfolk.
Arild Stubhaug

Student Life

Abstract
A short time after he had become a university student, in the fall of 1859, Sophus Lie enrolled at the Royal Fredrik’s University of Christiania. We know little about his reflections concerning the choice of studies, except that according to comments by his best friend Ernst Motzfeldt, Lie might well have been thinking of studying philology. The two friends and neophyte university students, Ernst and Sophus, had mounted a little hiking tour after the examen artium and before the start of lectures at the University. They headed west from Christiania, through Asker to Drammen, on to Kongsberg, and returned across Ringerike, north of the capital.
Arild Stubhaug

The Lack of a Calling

Abstract
Sophus Lie had taken his examinations; he had finished his education; and it worried him that he did not know in all certainty what he would use his education and his life for. His last period as a student seems to have been difficult, and when he went home to Moss at Christmas time,1865, he was depressed. His friend Motzfeldt later felt that this dejection was linked to Lie’s disappointment over not having achieved the top mark in the final examination. No doubt there were also other conditions that played a role, and most certainly the depression was worse than his friend Motzfeldt had believed. After he had been home at his father’s house in Moss for almost three months, Lie answered a letter from Motzfeldt, writing: “Thanks and again Thanks for your Letter. I regard this as a Sign that, at least You will not reject me, although You know that I am a forlorn Subject.” He continued, saying that he “in truth” had been “aimless, thoughtless, superficial, bad”, and despite all the time they had spent together in recent years, Lie wrote: “If You were to believe me, I should, when the Opportunity arises, tell You my Story.” He insistently urged Motzfeldt to go on acting as his friend, for thus could he (Lie) “perhaps, although the Probability has almost disappeared”, manage to struggle for “a Place in Society.“ Toward the end of this short letter to his friend in Christiania, as has already been mentioned above, Lie wrote:
When I bid You Farewell before Christmas, I believed that it was for Now and all Eternity; for it was my Intention to become a Suicide. But I do not have the Strength for it. So in consequence I get another Chance to try to live.
Arild Stubhaug

In Tune with the Times

Frontmatter

Into Mathematical History

Abstract
It was modern geometry that Sophus Lie now encountered with such fascination and zeal. This was an area within mathematics that stemmed mainly from Euclid’s two-thousand-year-old books, and a field that now, during the 1800s underwent a furious development. Outlooks and methods, both old and new were being combined together into integrated theories, and these theories developed and diverged more and more radically from what earlier had been understood as geometry — first and foremost perhaps as a liberation from a direct perception of the perceivable world. This modern geometry — called at the beginning astral or imaginary geometry — gradually came to be called non-Euclidean geometry. In many places during the course of the nineteenth century, it would come to engender oppositional reactions just as vehement as those that greeted Darwin’s Theory of Evolution. In England particularly, non-Euclidean geometry, Darwin, and ethical relativism were lumped together and said to represent those forces that were absolutely inimical to God. On the other hand, the theory of evolution and non-Euclidean geometry were manifestations of what, at the time, were radical new methods of thinking. Whereas established faith and methods of thinking tried to pack away every single phenomenon within one eternal framework — to define thought according to a single necessary formula, and explain human variation as a result of the existence of different types and stocks — the modern theories advanced conceptions about how scarcely anything could be seen, known or described in real, absolute terms: instead, everything must of necessity be seen and described according to known conditions, and therefore, in the final analysis, be relative. With that, the pivotal question arose about what it is that knowledge is really composed of, whether it be God-given or man-made.
Arild Stubhaug

There was a Mathematician in Him

Abstract
It seems that for Lie as well, the autumn of 1868 had been a constantly inspiring period of work. Apart from Poncelet, what brought him the first wave of inspiration, there were the books of Plücker — in any case, it was among the works of Poncelet and Plücker that he first found a conceptual apparatus, a mathematical language that he could use to express his own ideas. But besides these two mathematicians, he briefed himself on the works of Carnot, Hamilton, Cremona, Möbius, Hunyadi, Townsend, Grassmann, Salmon and others, and he borrowed various volumes of leading mathematical journals: Crelle’s Journal from Berlin, Liouville’s Journal and Comptes Rendus from Paris, and Philosophical Transactions published in London.
Arild Stubhaug

The First Tour Abroad

Abstract
One day in September, Sophus Lie left Christiania and set course for the great outside world. He had planned to travel by way of Copenhagen, but when the ship berthed at Fredrikshavn in Denmark, he disembarked and instead, journeyed down through the Jutland Peninsula to Germany and Berlin. The reason he had wanted to visit Copenhagen was that he felt he could obtain good advice there about how he could best spend his time abroad. At least this is what he expressed some while later in a letter to Professor Zeuthen in Copenhagen, where he simultaneously explained why he had not come through that city. Lie wrote, “Unfortunately I am such a wretched Sailor that when we landed in Fredrikshavn, I am ashamed to say, Matter overruled Mind, and I preferred Jutland to Copenhagen?” Were he to have continued on to Copenhagen, he would have had to board another ship. Instead, he proceeded onward by land.
Arild Stubhaug

Parliamentary Professor

Abstract
When Sophus Lie returned to Christiania in December 1870, he was immediately a great topic of conversation: the Norwegian scholar and scientist who had spent time in a French prison, mistaken for a German spy! And Lie himself was more than forthcoming about his experiences, at least at the beginning. An aura of celebrity and sensation enveloped him — the mighty conqueror of the mountain tracks and the suspected spy who was also involved in a mathematics that was incomprehensible to most people. From this period many anecdotal stories attached themselves to Sophus Lie’s name, something that he himself came to fear, would stand in the way of his significance as a mathematician in people’s eyes.
Arild Stubhaug

Professor in Christiania

Frontmatter

“My Inner Life Has Been Most Mighty”

Abstract
Anna Birch gave Sophus Lie her yes on Christmas Eve 1872, when he visited her parents’ home in Risør. Her only condition was that for a period of time their engagement must be secret — by way of justification she claimed that she thought she was too young to commit herself.
Arild Stubhaug

“My Life’s Good Fortune”

Abstract
Following their long alpine tour, Anna, Sophus and his sister Laura were back in Christiania by the middle of August. The two ladies put up at a hotel, and a few days later continued on to Moss. After a short sojourn in Moss, Anna returned to her parents in Ristør.
Arild Stubhaug

Marriage at Last

Abstract
Again, upon the next meeting between Sophus and Anna — the Christmas holidays at the home of her parents in Risør and at the home of his sister and brother-in-law in Tvedestrand — after the initial joy of reunion, this too, was an occasion marked by both harrowing disagreements and sincere love.
Arild Stubhaug

Herr Professor mit seiner Gemahlin

Abstract
Sophus and Anna married in Riør on August 11, 1874. The celebration seems to have gone as Sophus had wished “quietly and peacefully.”
Arild Stubhaug

In the Lee of “the Modern Breakthrough”

Abstract
From the autumn of 1875 Sophus and Anna’s residence was the Tandbergs’ løkke30 or summerhouse estate on Drammensveien, and they would continue to live here for over four years. They took an apartment on the second floor of the house of the Tandbergs. The husband died a couple of years later, and in the census, “Housewife Charlotte Tandberg” was redesignated as “Landlord”. The well-off citizenry owned their rows of houses and summer places out along Drammensveien, which was the main arterial road for traffic in and out of the city. Much of the new construction and expansion faced other streets and areas. This autumn was to see the first tramlines in the streets of the capital. The cars went from Homansbyen (in the region of today’s Bislet Stadium) to the downtown Stortorvet (Main Square) and on to (old) Oslo in the east, on elevated tracks. These cars were drawn by horses. The tram line concession had been granted on the understanding that they would function with horsepower, and not steam, for which also an application had been made. The tramline’s inauguration on October 6th was an event that caused a sensation, and drew a large crowd. The cars were fully loaded. During its first year the tramline conveyed one and a half million passengers. Horse trams were a step in the direction of modernity, and this improvement in communications naturally led to urban development a couple of years later, which in turn brought the population of Christiania to over one hundred thousand inhabitants.
Arild Stubhaug

A Steady Stream of Works

Abstract
Sophus and Anna had a daughter on May 22,1877. The newborn was christened Marie, and was most often called Lillemor and Maia, later Mai.
Arild Stubhaug

The Mathematical Milieu at Home and Abroad

Abstract
There is absolutely no indication in the existing documents and letters as to whether Sophus took his usual mountain tour in the summer of 1880. Perhaps he stayed home as support to Anna and Maia, who was now three, and to be near little Dadi. Anna, who seemed to have a special eye for hair, this summer clipped a lock Sophus’ head and folded it into a piece of paper. Then, on the outside, she wrote: “Sophus Lie, 38 years old”. Unlike what she had found in her own hair, there was no grey in this lock.
Arild Stubhaug

“It is Lonely, Terribly Lonely”

Abstract
According to the prospectus of lectures in the university calendar, Lie lectured in the spring term of 1883 for “two hours a week on Cartesian Space Geometry together with three hours a week on higher Geometry.”
Arild Stubhaug

Summoned to Leipzig

Abstract
Friedrich Engel arrived in Christiania in September of 1884, and he stayed for about nine months. He would later become Lie’s closest collaborator, and came to devote much of his life to working on Lie’s mathematics. It was Engel who was the driving force behind the publication of Lie’s Gesammelte Abhandlungen in seven volumes — the last volume being published in 1960, nineteen years after Engel’s own death.
Arild Stubhaug

Professor in Leipzig

Frontmatter

The Coming Period: A More Difficult Balancing Act

Abstract
Lie arrived in Leipzig with his family in the middle of April 1886. He was forty-four years old, Anna was thirty-two, and the children, nine, four and two. They moved into the ground floor of a house at Seeburgstrasse 5 — a few minutes’ walk from the university — and they were to live there for the full twelve years they stayed in Leipzig. Mrs. Anna and the children would gradually come to thrive so well there among their friends, at social events and school, that it was difficult for them to return to Norway.
Arild Stubhaug

In the Big City of Leipzig

Abstract
Lie began to lecture even before the agreed date of his inaugural lecture and official reception at the beginning of the summer semester in 1886. The university year in Leipzig was divided into a winter semester and a summer semester. The summer semester began in the middle of April and continued to the middle of August. This was followed by a two-month holiday before the winter semester started in mid-October and continued until mid-March — when again there was a one-month holiday before the new summer semester began. This was an arrangement of the teaching year that Lie quickly came to like, even though in Christiania he was, of course, used to having time off during the middle of summer — between the Norwegian spring and autumn semesters — when he would leave for the mountains in order to avoid the summer heat. But he seemed to think it was both natural and good that the teaching in Leipzig continued through the warmest part of the year: “Here in July one certainly cannot take any Summer Tour, on foot at least;” he wrote home to Motzfeldt — besides, the heat was less bothersome when one was working, and moreover, the houses in Leipzig were certainly designed such that the heat did not obtain any “real Strength”. In addition, his own house in Seeburgstrasse kept the heat out, as he reported to his friend in Christiania, adding, “Had I such a House on Drammensveien [in Christiania/Oslo], I would certainly feel fortunate?”
Arild Stubhaug

Breakdown

Abstract
Right at the beginning of his eighth semester as professor in Leipzig, Lie had a complete breakdown. He felt he had been “seized by a boundless despair” and allowed himself to be taken away to a psychiatric clinic at Ilten, near Hanover. Here he remained for a full seven months.
Arild Stubhaug

Fame

Abstract
During the summer semester of 1891, Lie was apparently in full activity again. And when the semester was over in August, he left with the whole family for Norway. Holst wrote later that Lie’s period of illness lasted until 1892.
Arild Stubhaug

Conflicts

Abstract
As a professor in Christiania, indeed, right back to the time of his engagement to marry Anna in 1873, Lie had worked with continuous groups, which would come to reveal themselves to be of such fundamental significance in formulating the basis of nature’s own laws. His work was noticed around Europe, although to a far lesser degree than he would have liked. Throughout the 1870s he had ongoing contact with Klein and Mayer in Germany, and to a certain degree as well, with mathematicians in France. In 1882, while Lie was giving lectures in Paris, a great change occurred in his relationship with the French. And it was Picard, more than anyone else, who had his eyes opened about what Lie’s theoretical interpretations could be used for.
Arild Stubhaug

Norwegian Students

Abstract
Right back to the time of Niels Henrik Abel, getting a stipend for further studies abroad was something that the most promising young Norwegian men of science could almost count on. And now, when the country’s great mathematician, Sophus Lie, was in a prestigious position abroad, Lie and Leipzig were a natural travel destinations for the coming generation of Norwegian mathematicians. At the very least, Lie could certainly give the best advice as to where it was most advantageous to go. The first out was Axel Thue.
Arild Stubhaug

Back to Norway

Abstract
It was Fridtjof Nansen who broached the subject of Lie’s discontent “down on the Leipzig plains”. Nansen had crossed Greenland on skis in 1888 — a bold and exhausting expedition that brought him much glory, and about which he wrote in a very successful book. Nansen was back from Greenland in the spring of 1889, and in the autumn he married Eva Sars, sister to Ernst and Georg Ossian Sars. Eva Sars was then a well-known concert singer. She had studied in Berlin, and her repertoire included opera, German lieder and Norwegian folksongs. Nansen received 7,000 kroner from the publishers, Aschehoug, for his voluminous manuscript on the tour across Greenland on skis, and in the spring of 1890 the book began to come out in instalments. It was simultaneously translated into English and German. In the autumn of 1890, Nansen left Norway together with his wife Eva, for a lecture tour of Germany. He had an audience with Kaiser Wilhelm II in Berlin. The Kaiser was presented with a copy of the German edition of the Greenland book, Auf Schneeschuhen durch Grönland,a book whose popularity did much to spread the sport of skiing, which in Germany and the continent was still considered something rather strange that belonged to the far north. In the course of his German lecture tour, Nansen and his wife Eva arrived in Leipzig, and perhaps Lie was among the many who listened to Nansen lecture about his Greenland expedition. In any case, Lie and Nansen met in Leipzig, and Lie invited Nansen and his wife Eva to visit him and Anna on Seeburgstrasse. The invitation was for November 16,1890, but Nansen had declined — with a short letter in which, on behalf of his wife and himself, he thanked Lie and his wife warmly for the friendship they showed by inviting the Nansens to their home that evening, and he continued: “As I told You however, my wife is completely mad about music, and since we shall only be in Leipzig for one day, she would very much like to attend the Opera here. Thus it is that I hope You will excuse us, as in such matters I am my wife’s obedient servant.”
Arild Stubhaug

At the End of the Road

Frontmatter

The Final Years

Abstract
When compared with the earlier years, the final period in Leipzig was no easier for Lie; relations to his colleagues still seem to have been coloured by mistrust and misunderstandings — “Dear Mayer! I find You incomprehensible. In private life you show me the greatest of kindness. As a colleague and scientist, You constantly affront me.” These were Lie’s words to the old colleague who continued to hold the most successful parties in the city.
Arild Stubhaug

Backmatter

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