19th Century: Niels Abel’s Tragedy

November 21, 2011

In these days, when many things are disappointing, we should try to read history and think about the human progress. In the 19th century, some things had become better than the previous centuries, but many things were still really stupid and horrible. Niels Henrik Abel is one of the greatest mathematicians of the world who lived in 19th century. Abel is the most well-known Norwegian scientist/ mathematician ever, but his story is one of the most tragic stories in the history of science. Abel was a misunderstood genius marked by misfortune. Abel’s life that was dominated by poverty, is a sad and terrible example of the tragedy of global stupidity. In Men of Mathematics, Eric Temple Bell saw Abels life as a tragedy and a crime. In fact, the indifference and shortsightedness of the stupid world and the established mathematicians in 19th century caused Abels death, not merely his poverty and tuberculosis. The leading mathematicians did not make any effort to determine the worth of Abels work, but he had loyal and devoted friends, among them Holmboe and Crelle, who recognized Abels potential as one of the greatest mathematicians of all time, and they tried to bring the poor Abel to the attention of the world. In 19th century, Europeans treated Abel like how they treat Iranians in the 21st century. The current conditions in Iran and Europe have some similarities with Abel’s life in 19th century, and many things in Iran and Europe are still like 19th century, but we should not forget that many things have changed and it’s what we can call it “hope” or “progress”. Anyway, lets take a look at Abel’s life, and what happened to him in 1810s and 1820s. It’s one of the greatest tragedy of 19th century, and can show us many things.

Niels Henrik Abel was born on August 05, 1802 in Finnoy, an island near the Norwegian town of Stavanger. His father Soren Georg Abel was a Lutheran minister. Soren Abel had a degree in theology and philology. He was a nationalist who was active politically in the movement to make Norway independent. Abel’s mother, Ane Marie Simonson, was the daughter of a wealthy merchant and ship owner. She was a beautiful girl, who had grown up in relative luxurious surroundings. It said that her father was the richest person in their town, and she was a rebel. Abel was taught by his father in the vicarage until he reached the age of 13. However, these were the 13 years of economic crisis for Norway and Abel’s parents had not been able to feed their family well. Abel’s father became a drunkard and his mother, Ane Marie, was accused of having lax morals! She became alcoholic, while she had 7 children and Abel was the second of them. Abel was growing in a period when Norway was passing through a difficult period. At the end of the 18th century Norway was part of Denmark. During the Napoleonic wars Denmark decided to remain neutral. They signed a neutrality treaty in 1794. However, in 1801 England ignored this neutrality treaty and the English fleet destroyed most of the Danish fleet, but Denmark avoided wars until 1807, when England captured the whole Danish fleet. In this way Denmark joint the alliance against England, and the war led to an economic crisis in Norway. Due to war restrictions they could neither export timber nor import food grains from Denmark. There were wide spread poverty and suffering among the people. In 1813, Denmark was attacked by Sweden from the south. Following a treaty between the two countries, Denmark handed over Norway to Sweden in 1814. In this difficult time, Abel was growing up in Gjerstad in south-east Norway. At the age of 13, Abel entered the Cathedral School of Christiania (todays Oslo). The environment of the school failed to inspire Abel and he was nothing but an ordinary student with some talent for physics and mathematics. Though he had developed some liking for mathematics but his mathematics teacher was very cruel. The teacher hardly cared for the students. One day he hit a student so badly that he died a few days later. This incident proved to be a turning-point for Abel. The teacher was suspended and the Bernt Michael Holmboe replaced him in 1817. He was an inspiring and caring teacher. Holmboe saw that Abel had special skills in mathematics and he helped and supported Abel as long as he lived. After recognizing the exceptional mathematical talent of Able, Holmboe persuaded Abel to study the works of great mathematicians like Euler, Lagrange, Newton, etc. Later when asked how he had managed to make such progress in mathematics despite his youth, Abel responded, By studying the masters, not their pupils. Abel borrowed books and studied on his own. Soon he attacked problems that were unsolved at that time, such as fifth degree equations. He went deep into the mathematics but he did not do very well in the other subjects.


In 1820, tragedy struck Abels family when his father died. Abel was still in School. His fathers death left the family in dire poverty. He had to work and supported his family, i.e. his mother and her six children. Abel tutored schoolchildren, and Holmboe helped him to complete his school education. A small pension from the state allowed Abel to enter Christiania University in in 1821. But before entering the University Abel developed what he thought was the formula to solve the fifth degree equation. Abels paper was sent to Degen, a mathematician in Denmark. However, before he could send his observations, Abel himself discovered a mistake in his figures and wondered whether there was really an answer to the problem. But Degen praised Abels work. In 1823, Abel visited Copenhagen. The purpose was to be familiarized with the works of the Danish mathematicians. In those days, Norway had no good school of mathematics. His visit to Copenhagen was possible because he received financial support from Christopher Hansteen, professor of astronomy in Christiania University, who not only supported Abel financially but also encouraged him to continue his studies. Hansteens wife cared for Abel as her own son. It was at Copenhagen, Abel met Christine Kemp, with whom he became engaged. Holmboe tried hard to get funds for Abel, and finally the authorities of Christiania University provided necessary funds to Able for studying in Paris, but with a stupid condition. Abel had to remain in Christiania for two years and learned French and German to become fluent in these languages before traveling. For a genius like Abel, learning new languages was a waste of time and he did not succeed in learning German, and his French was weak. Abel began working again on quintic equations and, in 1824, he proved the impossibility of solving the general equation of the fifth degree in radicals. Abel sent this pamphlet to several mathematicians including Gauss. Finally in August 1825, Abel was given a scholarship from the government to allow him to travel abroad and, after taking a month to settle his affairs, he set out for the Continent with four friends, first visiting mathematicians in Norway and Denmark. On reaching Copenhagen, Abel found that Degen had died and he changed his mind about taking Hansteen’s advice to go directly to Paris, preferring not to travel alone and stay with his friends who were going to Berlin. As he wrote in a later letter “Now I am so constituted that I cannot endure solitude. Alone, I am depressed, I get cantankerous, and I have little inclination to work”.

As per the original plan Abel was to visit Gauss at Gottingen first and then go to Paris. However, this did not happen. The two great mathematicians never met. Gauss biographer wrote: When Niels Abel went to Germany in 1825, he was not well known. A copy of his proof of the impossibility of solving the general equation of the fifth degree had been sent to Gauss, who did not consider it very important.” Abel was angry at Gauss, and cancelled his planned visit to Gottingen. Eric Temple Bell wrote: “Gauss was the greatest mathematician of that time (and all time) and was called “Prince of Mathematics”. Just one word form Gauss was enough to secure Abel’s future, and Abel’s life could become longer.” Some say: “Abel’s paper was found unopened after Gauss’s death.” And some say: “After Abel’s death, Gauss did realize his mistake. But it was too late”. Gauss could save Abel’s life, but it didn’t happen. And until his death, Abel thought that Gauss is a stupid jerk. Abel spent most part of his grants for visiting Berlin with his friends in 1826. Some say it was not a good decision, but in Berlin Able met Crelle, who had just founded “Journal for Pure & Applied Mathematics”. The journal was popularly called Crelles Journal. Bell wrote: “In their first meeting, Abel tried to play politics, and at first he praised the latest Crelle’s article. But after a while, he forgot politics and started to criticized Crelle’s article and talked about his mistakes. Crelle was very open-minded, and instead of yelling at the arrogant young man and kicking him out of his office, he asked Abel some questions and listened to his answers carefully. Crelle was not a good mathematician and could not understand Abel’s answers or his papers, but he had enough wisdom to understand that Able is a great mathematician of the first rank. Crelle was not a good mathematician, but he was a very open-minded man”. The two became firm friends. This proved the most useful part of Abel’s whole trip. He encouraged Abel to publish his results in his Journal. The very first volume of the Journal had Abels seven papers. Abel published most of his major works in Crelles Journal. In 1826, Abel moved to Paris, where he stayed for about ten months. He could not meet leading mathematicians of France. Bell wrote: “Legendre did not have time to meet the unknown Abel, and just one time when he wanted to get into his carriage, said hello to Abel. After Abel’s death, Legendre admitted his mistake”. Abel submitted his masterpiece, a paper on elliptic functions and integrals which included Abels theorem to the French Academy of Sciences. Legendre and Cauchy were chosen by the Academy as referees to judge the papers worth. A couple of years passed and Abel heard nothing. He shared the contents of the article with Carl Jacobi. The latter wrote to Legendre in an effort to find out what had happened to the memoir. Legendre claimed he could not read Abels handwriting. He suggested that the author submit a new copy. Abel did so (new copy was only in 2 pages), but Cauchy mislaid the second version and forgot about it ! The copy was rediscovered in 1830 and was finally printed by the Academy after Abels death. Jacobi said of Abels work: It’s above my praise as it’s above my own work. Some say:” Cauchy brought the work home for reading but he promptly reported that the work was misplaced. It is said that he misplaced it intentionally, because Cauchy was much more interested in his own work and he was a little jealous of Abel “.


Crelle could not travel with Abel to Paris, and Abel therefore did not go directly to Paris, but chose to travel again with his Norwegian friends to northern Italy before crossing the Alps to France. He had doubt about having some fun, but finally he didn’t deprive himself of seeing the Alps and its beauty. And it was a very good decision, because Paris was so disappointing. He wrote back to Holmboe: “The French are much more reserved with strangers than the Germans. It is extremely difficult to gain their intimacy . Every beginner has a great deal of difficulty getting noticed here. I have just finished an extensive treatise on a certain class of transcendental functions to present it to the Institute which will be done next Monday. I showed it to Cauchy, but he scarcely deigned to glance at it [!]” Abel also added: Legendre is an exceedingly courteous man, but unfortunately as old as the stones. Cauchy is mad, and you can’t get anywhere with him, although he is the mathematician who knows at the moment how to treat mathematics.Cauchy is extremely Catholic and bigoted. A very strange thing in a mathematician. Poisson is a short man with a nice little belly. He carries himself with dignity. Likewise Fourier. On Monday I am going to be introduced to several of these gentlemen by Hachette. Otherwise I do not like the Frenchman as much as the German, the Frenchman is uncommonly reserved towards foreigners. It is difficult to make his close acquaintance. And I dare not count on such a thing. Everyone wants to teach and nobody to learn. The most absolute egotism prevails everywhere. The only things that the Frenchman seeks from foreigners are the practical [things]. With no money left and his health in a very poor state, he returned to Berlin at the end of 1826. Abel had got tuberculosis when he was in the damn Paris. While in Paris, Abel lived in miserable conditions, often unable to afford more than one small meal a day. He consulted a physician about his poor health and was diagnosed with tuberculosis. But he refused to believe it and left Paris for Berlin.In Berlin, Abel borrowed some money from Holmboe and continued working on elliptic functions. Crelle tried to persuade Abel to remain in Berlin until he could find an academic post for him and he even offered Abel the editorship of Crelle’s Journal. However, Abel wanted to get home and by this time he was heavily in debt. He reached Christiania in May 1827 and was awarded a small amount of money by the university although they made sure they had the right to deduct a corresponding amount from any future salary he earned. To make a little more money Abel tutored schoolchildren and his fiancée was employed as a governess to friends of Abel’s family in Froland. Abel failed to get the recognition that he rightly deserved. He had no appointment. A vacancy in mathematics department of the Christiana University arose but this was given to his mentor Holmboe. Holmboe wanted that the job should go to Abel. But when the university authorities threatened to give the job to a foreigner if he didn’t agree to take it, Holmboe accepted it. To increase his misery Abel was in debt and had tuberculosis. Abel could manage to survive with meager grants and support from his friends. The University sent students to him to tutor. But he still had his family to support, which left him weakened and sadly aware that he would not live much longer. However, with all difficulties Abel continued to work. He was also worried that his illness could end his life at any time. He was not deterred. He continued to work with a fervent zeal.

Abel continued to pour out high quality mathematics as his health continued to deteriorate. He spent the summer vacation of 1828 with his fiancée in Froland. Abel traveled by sled to visit his fiancée again in Froland for Christmas 1828. He became seriously ill on the sled journey and despite an improvement which allowed them to enjoy Christmas, he soon became very seriously ill again. His hemorrhaging returned and he often slipped into delirium, once shouting I will fight for my life. When he was calm, he said: “like a wounded eagle, who looks at the sky“. Crelle was alerted to the seriousness of Abels illness and redoubled his efforts to obtain an appointment for Abel in Berlin. He succeeded and wrote to Abel on the 8 April 1829 to tell him the good news. But it was too late, Abel had already died. “The weakness and cough increased and he could remain out of bed only the few minutes while it was being made. Occasionally he would attempt to work on his mathematics, but he could no longer write. Sometimes he lived in the past, talking about his poverty. But often he was kind and patient. He endured his worst agony during the night of April 5. Towards morning he became more quiet and in the forenoon, at 11 o’clock, he expired his last sigh. He cursed his God and the science of his day, which had been unable to overcome his illness (and he was really right); but his rage alternated with periods of apathy, and in quieter moments he worried about his fiancé, who would now have no one to provide for her. Abel’s fiancé nursed him in his final days and on the morning of April 6, 1829 he died, aged 27 years”, the historians say. Two days later, Crelle wrote that he had finally secured an appointment as professor of mathematics for his friend at the University of Berlin. After his death Abel became a national hero in Norway! In fact, in the past centuries, Norway, Europe, and Iran were so stupid. Many heroes became a national hero, only after their deaths ! . Anyway, Abel’s birth centenary (1902) was widely celebrated and a number of memorials were erected.