Sophus Lie: The unfortunate genius as a phenomenon in Northern European

Like his elder brother Niel Abel, Sophus Lie (1842-1899) has emerged as a phenomenon in Northern European countries in the context of the scientific background of this region was virtually unknown on the international arena. Throughout his life, he constantly came up with extremely bold ideas.

Sophus Lie is one of the big names in mathematical history, one of those visionary. He also created a new subject: Lie group mathematics, which is now developed and rooted in almost all the fields of mathematics and mathematics-physics.

Jean Dieudonné, one of the founders of the Bourbaki school, would not have been able to produce any valuable work without Lie's mathematics. Later mathematical and physical works, particularly those of Élie Cartan and Hermann Weyl, were also successful thanks to Lie's mathematical theory.

During a period of 30 years of research, Sophus Lie published works about 8,000 pages in handwritten.

The start is not perfect

Sophus Lie was born on December 17, 1842 in Nordfjordeid, a small city in the west of Norway. When Sophus was nine, his family moved to Moss, an area southeast of Oslo.

A year after reaching Moss, Sophus's mother died. This misfortune made Sophus at the age of 10 almost lose his childhood and become a serious child. From the beginning of her first year of study, Sophus enjoyed many subjects. Because the Moss school did not issue a final diploma, Lie was 15 when he went to Hartvig Nissen in the Norwegian capital. This famous school, founded by Nissen and Ole Jacob Broch, has a clear goal: to use pedagogy and modern languages ​​and to teach important sciences.

Sophus also cares a lot about Norway's educational innovation process and participates in widespread social debates. He has written many articles highlighting the need to renovate the education system in Norway and he often compares books with other education like France and Germany. He also emphasized the special importance of higher education. Although education interested him, he eventually chose science as a career path. It should be remembered that at that time, out of 560 students at the University of Oslo, only about a dozen people followed the scientific path.

Sophus Lie (1842-1899) - (Image: cache.eb.com)

The research conducted by Sophus Lie falls into three areas. The most arduous is the field of mathematics including geometry, mechanics, engineering design ... In this field, Sophus Lie's professors Broch and Carl Anton Bjerknes, the mathematician Lugwig Sylow.
In Sylow's class from 1862 to 1863, there were three highly regarded people, including Sophus, and this class involved a new discipline: the theory of algebraic equations of Abel and Galois. Sophus attracted the subject so much that he neglected other subjects such as physics and chemistry and natural history. Therefore, his diploma is not excellent as expected. In his last years, his personality became melancholy, quirky and lacked faith in his "intellectual ability". The rigor in Catholic education does not allow people to be too weak. It was this rigidity that drove Sophus into a depression.

Fortunately, he had many friends and they shared his feelings with him on weekends in the bay and the forests of Oslo. He also practices sports, riding horses. In the winter, he plays skiing and sleds. Lie is a very loyal person with friends. Ernst Motzfeldt, Nissen's classmate, became a lawyer, then high-ranking civil servants were always his friends and protected him.

Lie enjoys attending discussions about the Association réaliste organized by science students. At that time, in every science in the university there was a student association related to their field of study to provide in-depth discussions to complement the courses. Lie is one of the most active members of the Society and has made a series of talks about geometry there.

After receiving his diploma, Lie became interested in astronomy, and he began teaching and spreading the science. He taught at an observatory but did not earn the desired astronomical feet. In order to make a living, he took the position of a teacher instead of math, physics and astronomy lessons. He is a highly regarded professor.

Entering mathematics

The fitness and sports movement at that time was very developed and Sophus Lie was a well-known climber. He was also an excellent walker: on weekdays, he walked from 30 to 40 km, on sports practice, he went to 70-80 km. It is said that one day he left a book in Moss and so he took a "round trip" trip from the capital to Moss, which is about 100 kilometers a day. He walked so fast that many people thought he was a ... thief.

However, Sophus' social inclusion is very poor. This has always made him tormented and have a soul at times of peace. In March 1968, he wrote a letter to his best friend Motzfeldt: "When I said goodbye to you the day before Christmas, I thought it was far away from you forever. I always wanted to kill myself but I didn't. be brave enough. So I find ways to try to live. "

Not knowing what you want in life is a huge flaw. It was not until 1868 that Sophus Lie found his true job when he was 26 years old, after meeting Danish mathematician Hyeronymus Zeuthen. At the time Zeuthen was studying in Paris under the guidance of geologist Michel Chasles. Thanks to Zeuthen's advice, Lie searched and read avidly the treatise on photographic properties of Jean-Victor Poncelet's numbers. One of Poncelet's inventions at the time was the introduction and use of complex numbers in radial geometry. Besides this fascinating topic, Sophus is also fascinated by the works of Allemand Julius Plucker.

In the early 1869s, Lie completed his first book on realistic depictions of imaginary numbers. This 8-page article was immediately warmly welcomed by two renowned math professors Dan Manh, Broch and Bjerknes. Even in that year, the article was republished in German in the famous newspaper Journal de Crelle. Sophus Lie got a lot of attention and easily applied for scholarships to study in Berlin, Gottingen and Paris. Upon returning home, he was immediately appointed a member of the university and the following year became the university's professor.

The first trip abroad was very important for Lie. He met friends and colleagues who greatly appreciated his research. Especially in Berlin, he met Felix Klein, Alfred Clebsch in Gottingen and Gaston Darboux and Camille Jordan in Paris. Lie quickly became Klein's best friend and together they published three papers on geometry. Klein also often visits Lie and sometimes they visit Darboux and Jordan.

Unwanted hero

When the Franco-Prussian War broke out in July 1870, Klein left Paris because of a call to fight France. He crossed the border but was suddenly ill and could not join the fight. At that time, Lie decided to walk from Paris to Milan to meet the mathematician Luigi Cremona. But having just arrived at Fointainebleau, he was imprisoned on suspicion of being a German spy. Immediately, on the front page a Norwegian daily newspaper headline: Norwegian scientists imprisoned on suspicion of a German spy.

Lie later recounted: the guards at the time thought that the mathematical symbols in Lie's notebook were the spying codes. Fortunately, Darboux had connections with high-ranking military figures and he sought to free Lie. Many years later, Lie still considered that the time spent in captivity in Fontainebleau was the most peaceful period and it was during this period that he wrote the main part of his doctoral thesis. This thesis is entitled "A way of ranking geometric transformations" which he defended the following year in Oslo. In the words of E. Holst, Lie's friend and first biographer, the Norwegian jury was really just as incompetent as the French guards.

However, in Europe, this thesis is much appreciated. Darboux remarks that this is one of the most interesting discoveries of modern geometry. The Norwegian authorities, however, created the best conditions for Lie to work. In 1872, the Senate senators requested to give the title of special professor to Sophus Lie. They do not want to repeat the mistake that was once made with Abel. Thus, only 30 years old Lie became a true professor.

It was a happy time for Lie, he met and immediately fell in love with Anna Birch, then 18 years old and cousin of Motzeldt. He sent a confession letter to Anna. This letter surprised many people because few thought that he could be "brave" to get married. Anna's grandfather was uncle Abel and Sophus hoped it was a good thing. Although Anna hesitated at first because Lie's 30-year-old was "too old" for her at the time, their marriage still took place 20 months later. After his marriage, Lie's life was summed up in three stages: his years in Oslo, then the next 12 years in Leipzig and a brief return to Norway before his death.

During his years in Oslo, he worked hard, but hardly any scientific research was significant. In return, his family life is very happy: Sophus and Anna are very compatible and they have 3 children.

In 1882, Lie worked with Klein and Adolph Mayer in Leipzig and traveled to Paris for 2 consecutive months to discuss with Darboux, Jordan, Hermite, Poincaré, Picard, Halphén and Lévy. These people fully understand the importance of Lie's research. In 1884, Klein and Mayer wanted to help Lie improve his life and they sent students Friedrich Engel to guide him and help him perfect his ideas. The joint study by Engel and Lie is put together into a series of three books called Theorie der Transformationsgroppen (Theories of transforming groups), which were published in 1888, 1890 and 1893, with a total length of more 2,000 pages.

In 1886, Lie was promoted to a professor at Leipzig and replaced Klein, a very important scientific position there. He became a bright face in the European mathematical community and many students from home and abroad came to be his students. However, the work of teaching and guiding students has occupied his time. He also felt frustrated when he always had to work with many ordinary students. Leipzig did not seem to be the heaven he once wished.

Lie's failure to fully master German and the political theater and personal conflicts increasingly made him tired. He also remembered his friends and his native Norway. He wanted to work somewhere peaceful, but the relationship always forced him. Gradually, he felt he was misunderstanding and being used too much. These conflicts caused him to lose sleep and fall into depression again. At this time, he felt depressed.

In December 1889, he was transferred to a mental hospital near Hanovre. He stayed there for 7 months and was treated with opium and other sleeping pills. But it seemed that the habit of walking too much made him recover again. Even so, he absolutely could not return to being as healthy as he used to be. He came back hard to contact and was always suspicious of others. It was these that undermined his longtime friendship with the soulmate. He suffers from obsession and always denies friends who stole his ideas. His relationship with Klein completely shattered.

Unhappy genius

Lie continues his creative research. What he announced continued to be spread and appreciated increasingly. In 1892, he joined the French Academy of Sciences. In 1893, Darboux and Tannery invited him to Paris and he enjoyed seeing Élie Cartan. In April, 1993, it was found that Lie and Cartan frequented the Café de la Source. Lie said that before it is possible to use the theory of transform groups to solve differential equations, it is necessary to arrange transform group structures with a limited number of dimensions. A year later, in 1894, Élie Cartan published the paper "On the structure of finite and non-stop groups". Their studies seem to have quite similar results.

Lie was also highly valued in Norway and in 1905 the Senate changed his title to Professor of transformational group theory. He also enjoyed an almost double salary for a regular professor. In 1897, Lie received the prestigious Lobatchevski Prize for his outstanding work in geometry, particularly in geometry outside Oclit.

Unfortunately, when he returned to Norway in the summer of 1898, everyone realized that his illness was serious. He suffered from pernicious anemia, an incurable disease at the time. In the fall of that year, he was very difficult to be able to go to class, sometimes, he had to lecture from the bed. On February 18, 1899, he died.

Many people believe that his death forced him to retire from many unfinished research projects. Today, his most recognized work is on the study of differential equations and this work later became an important branch of mathematical research: Lie group theory and Lie algebras.