While science and literature have their Nobel Prize, mathematics has its Abel. Contrary to the legend that has been recounted a thousand times, the Swede Alfred Nobel did not remove mathematics from his prizes out of jealousy, but simply omitted it, as he did with many other disciplines. But mathematicians have their equivalent award, which was in fact proposed as a response to the omission of the Nobel Prize and which, by sheer coincidence, is similar even in name. But the history of the two awards share little else in common; while the elderly Nobel bequeathed a substantial fortune in order to establish his prizes, the tribute by the Norwegian Academy of Sciences and Letters to Niels Henrik Abel, that country’s most prominent mathematician, honours a prodigious mind who died young and destitute.

Anyone who had glanced at one of the notebooks with which Abel (5 August 1802 – 6 April 1829) received his first lessons at home, handwritten by his own father, might not have predicted a great future in mathematics for someone who learned from an addition table that read: 1 + 0 = 0. And this despite the fact that the father, a rural Protestant pastor, apparently took a markedly greater interest in the upbringing of Niels and his five brothers and sisters than their mother, who according to the Abel Prize’s own website was an alcoholic and “happiest in parties and festive company.”

## Best Mathematician in Norway at 18

It was Norway’s independence in 1814 that led Niels’s father to embark on a political career in Christiania (now known as Oslo), where the boy would set foot in a classroom for the first time, at the Cathedral School. But perhaps Abel’s immense talent for mathematics would not have been nurtured had it not been for a circumstance as fortuitous as it was tragic that placed him under the tutelage of a respected teacher and mathematician, Bernt Michael Holmboe, who was hired in 1818 after his predecessor was fired for punishing a boy so severely that he died.

Holmboe discovered the brilliant mathematician in Abel and was instrumental in guiding his career, tutoring him and orienting his reading. But this would not pave the way for an easy future for the young student; in that time and place, classical teaching was the norm, and there was no mathematics degree at the University of Christiania. And while Abel was a prodigy with numbers, the rest of his grades were mediocre.

Before he entered the Royal Frederick University in 1821, he had already begun work on what was to be his best-known contribution, the study of general solutions to quintic (fifth degree) equations. In 250 years, no one had succeeded in solving this problem, but Abel was by then the most qualified mathematician in Norway, so much so that his professors and the university itself saw the need for him to broaden his knowledge and make contacts outside the country. However, the death of his father and his dire financial situation only allowed him to travel to Copenhagen in the care of some relatives, although it turned out to be a fruitful stay: on a personal level, he met his future fiancée—Christine Kemp—and professionally, he came into contact with Carl Ferdinand Degen, the leading Nordic mathematician of his time.

The contact with the Danish mathematician was the catalyst for Abel’s main achievement. Degen was sceptical that the Norwegian student had found the general solution to the quintic equations, but could find no errors in his formulations. Instead, in response to Degen’s request for a numerical example of his method, Abel himself discovered a mistake in his paper. The corrected result would become what is known today as the Abel-Ruffini theorem, which proved the impossibility of solving the general equation of the fifth degree in radicals. But when Abel published his paper, which he had written in French, the out-of-pocket costs forced him to compress it down to six pages, the result of which being that no one understood it, which deprived the young man of the recognition he deserved. At Degen’s urging, Abel turned his work towards mathematical analysis.

## From professional success to personal tragedy

Finally, in 1825, Abel was able to embark on his great European journey, where he planned to make a stop in Göttingen to meet the distinguished Carl Friedrich Gauss—who had scorned his work at first sight—and then to settle in Paris. But instead he went to Berlin, where he established a fruitful symbiosis with August Leopold Crelle. The German mathematician was beginning to publish his new mathematical journal, which, thanks to the inclusion of Abel’s work, became one of the most reputable publications in its field. The young mathematician finally achieved his goal to live in Paris in July 1826, but things did not go as he had hoped. His work, the most productive of his career, was ignored and forgotten. And instead of applause, he received a fatal diagnosis: tuberculosis.

In May 1827, now back in Norway, disenchanted, ill and destitute, without a stable position and unable to repay his personal loans or his family’s debts, Abel continued to churn out papers at such a speed that Crelle found it difficult to keep up with the publication of his works. Meanwhile, his health deteriorated. A sleigh journey at Christmas 1828 to visit his fiancée was too much for his illness, and shortly afterwards he began to cough up blood; in the spring of 1829 he died at the age of 26. Abel was also a victim of that cruel irony which is sometimes the curse of so many great geniuses. Only two days after his death, Crelle wrote him a cheerful letter announcing that he had secured him a professorship at the University of Berlin. “As far as your future is concerned, you can now be completely at ease,” Crelle wrote. The following year, Abel’s work in Paris, rediscovered at last, earned him a posthumous Grand Prix from the French Academy of Sciences. The money was received by his alcoholic mother.

In 1899, following news of the establishment of the Nobel Prizes, the Norwegian mathematician Sophus Lie proposed to the crown that a mathematics prize be established in Abel’s honour, to which the then King of Sweden and Norway agreed. But the initiative was blocked by the subsequent dissolution of the joint monarchy in 1905, and was only revived in 2002, on the bicentenary of Abel’s birth. Today, the most prestigious mathematicians are keen to see themselves associated with the name that maths students invoke when learning abelian functions or abelian groups—a genius of numbers whose tragic fate befits a romantic poet.

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