Niels Henric Abel

An astrologer in the year 1801 might have read in the stars that a new galaxy of mathematical genius was about to blaze forth the greatest century of mathematical history.

In all that galaxy of talent there was no brighter star that Niels Henric Abel, the man of whom Charles Hermite said, ‘He has left mathematicians enough to keep them busy for five hundred years.’ Abel contributed enormously to mathematics in spite of poverty and neglect by other mathematicians. Niels Henrik Abel was born in Nedstrand, Norway,on August 5, 1802. Niels Henrik and his brothers were given their first schooling by their father, a pastor, with handwritten books to read. In 1815, Niels Abel entered the Cathedral School, aged 13. His elder brother Hans joined him there a year later. They shared rooms, and had classes together. In general, Hans got better grades than Niels; however, a new mathematics teacher, Bernt Michael Holmboe, spotted Niels Henrik's talent in mathematics and encouraged him to study the subject to an advanced level. He even gave Niels private lessons after school. Niels Henrik did extremely well in mathematics, though he struggled in other subjects. At the age of 16 Abel gave a proof of the binomial theorem valid for all numbers extending Euler’s result which had only held for rationals. In 1820 Abel’s father died and Bernt Michael Holmboe supported Niels Henrik Abel with a scholarship to remain at the school and raised money from his friends to enable Abel to study at the Royal Frederick University. Holmboe had nothing more he could teach his bright pupil.

Abel entered university in 1821. He was already the most knowledgeable mathematician in Norway. He had studied all the latest mathematical literature in the University library. Abel graduated in 1822. His performance was medium, except in mathematics.

When about 20, Abel solved a problem that had confounded mathematicians for centuries: how to find the roots of ax ⁵ + bx ⁴ + cx ³ + dx ² + ex + f with a finite number of additions, subtractions, multiplications, divisions, and extractions of roots. Abel proved that the task was, in general, impossible! To do this he invented an extremely important branch of mathematics known as group theory independently from Galois. He used what little money he had to print the result himself.

Abel then received a small grant to travel in Europe. He hoped that talking to the great mathematicians would gain him entrance into mathematical circles and provide him with a good position, but he was not received well. Gauss, for example, refused to read Abel’s paper on the impossibility of solving quintic equations, believing Abel to be just another amateur.

On his two-year trip, Abel did have good fortune to meet the German mathematician A.L.Crelle, who perceived Abel’s greatness. Shortly thereafter, Crelle began publishing the first periodical in the world devoted exclusively to mathematical research ,Journal for pure and applied mathematics. The first three volumes contained 22 of Abel’s papers. Crelle showed Abel off and tried to get him a professorship at the University of Berlin, but to no avail, and Abel remained an outsider. His famous paper on transcendental functions, presented to the Paris Academy of Sciences when he was 24, was misplaced by Cauchy, almost lost, and only published 17 years later. Jacobi called it the most important mathematical discovery of the century.

Abel returned home from his trip, poor and sick with tuberculosis but still doing mathematics. In 1829, at the age of 26, he died. Two days later, a letter arrived from Crelle saying that Berlin was offering him a professorship after all. A year later, the Paris Academy of Sciences made some amends by awarding Abel the Grand Prize in Mathematics. The early death of this talented mathematician, of whom Adrien-Marie Legendre said "what a head this young Norwegian has", cut short a career of extraordinary brilliance and promise. The adjective "abelian", derived from his name, has become so commonplace in mathematical writing that it is conventionally spelled with a lower-case initial "a" (e.g., abelian variety).

Norway honors its famous son. Abel’s portrait appears on Norwegian stamps, banknotes and coins. A statue of Abel stands in Oslo, and crater Abel on the Moon was named after him. In 2002, the Abel Prize for outstanding scientific work in the field of mathematics was established in his memory.