He has left mathematicians enough to keep them busy for five hundred years

Vocabulary

1. Guess the meaning of these international words. Check with your teacher or a dictionary.

Astrology – astrologer, galaxy, genius, talent, cathedral, finite, binomial, amateur, fortune, periodical, transcendental, function, tuberculosis, statue, crater.

2. Key words

In spite of	Не дивлячись на
Poverty	Бідність
To spot	Помітити, побачити, розпізнати
To struggle	Докладати зусиль, долати з труднощами
To raise money	Збирати (добувати) гроші
School performance	Успішність
To confound	Бентежити, заганяти у глухий кут
To devote	Присвячувати
To show off	Подавати у вигідному світлі
To no avail	Невдало, безрезультатно
To misplace	Покласти не на те місце
To make amends	Намагатися спокутувати провину
To cut short	Обривати, зненацька припиняти
Of great promise	Той, хто подає великі надії
Commonplace	Звичайне явище
Conventionally	Звичайно
Variety	Різноманітність

Reading

I. Read the text and do the tasks 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 ax⁵ + bx⁴ + cx³ + dx² + 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.

Task 1. Decide if these statements are true or false, or the information is not given in the text

1. As a child Abel went to primary school.

2. Abel’s talent as a mathematician was perceived by his father.

3. Abel did well in all school subjects.

4. Abel’s school teacher Holmboe helped Niels Henric financially after the boy’s father’s death.

5. Abel knew mathematics better than his teachers at the age of 19.

6. Abel proved that there is no general algebraic solution for the roots of a quintic equation.

7. Abel was interested in physics as well as mathematics.

8. The great mathematicians, Abel’s contemporaries, recognized his mathematical talent.

9. The Paris Academy awarded Abel the Grand Prize posthumously.

Task 2. Find equivalents of these words or expressions in the text

1. the situation or experience of being poor

2. failure to pay proper attention to someone or something

3. to notice someone or something

4. to lose something for a short time by putting it in the wrong place

5. to do something to show you are sorry

6. a magazine, especially one about a serious or technical subject

7. to give courage or confidence to do something

8. to show publicly that someone is respected and admired

Speaking

Task 1. The adjective ‘abelian’ has become commonplace. Work in groups. Make a list of mathematical terms with this adjective. You can use a dictionary. After you have finished, compare your lists. Try to explain the terms you’ve already come across at your mathematics lessons

Task 2. Work in pairs. Discuss what impressed you most of all in Abel’s biography

Part II

Practice set 1