- 2. NEILS HENRIK ABEL (5 AUG 1802 – 6 APRIL 1829)
- 3. HIS LIFE • He was born in a poor family in Nedstrand, Norway in 5 th august 1802 • He was the second child of Soren Georg Abel and Anne Marie Simonson • In 1815, at the age of 13 Neils Abel entered Cathredal school.
- 4. •In 1818, his Mathematics teacher, Bernt Michael Holmboe noticed Neils Abel’s talents in mathematics and encouraged him to study the subject to an advanced level • Bernt Michael Holmboe supported Neils Abel with a scholarship to remain at the school and raised money from his friends to enable him to study at the Royal Fredrick University
- 5. • Neils Abel graduated in1822. his [performance was average, except in Mathematics which was exceptionally high. • In the mid of 1823, Professor Rasmussen gave Abel a gift of 100 speciedaler, so could travel to Copenhagen and visit Ferdinand Degan and other Mathematicians there
- 6. • Abel got a government scholarship inorder to visit top Mathematicians in Germany and France • In 1823, Abel published his first article in Magazin for Naturvidenskaberne, Norway’s first scientific journal • Abel wrote a paper in French which is, “a general representation of the possibility to integrate all differential formulas”
- 7. • After studying German and French, Abel published his first notable work in 1824, “Memoir on algebraic equations in which the impossibility of solving the general equation of the fifth degree is proven” • Abel was contracted with tuberculosis and died on the 6th of April 1829 • Just two days after his death August Crelle send a letter to Abel that he has been appointed as a Professor at the University of Berlin, but it came too late
- 8. HIS CONTRIBUTIONS • Neils most famous single result is the first complete proof demonstrating the impossibility of solving the general quintic equation in radicals. This equation was one of the outstanding open problems of his days, and had been unresolved for 250 years • Neils was an innovator in the field of elliptic function
- 9. •Neils Abel did some work on Fermat’s last theorem •He showed that there is no general algebraic solution for the roots of a quintic equation or any genaral polynomial equation of degree greater than four in terms of explicit algebraic operations
- 10. • To do this he invented an extremely important branch of Mathematics known as Group Theory, which is invaluable not only in many areas of mathematics but for much of Physics as well •As a 16 year old Abel gave a proof of Binomial Theorem valid for all numbers, extending Euler’s result which had held for rationals.
- 11. • Abel wrote a fundamental work on the theory of elliptic integrals, containing the foundation of the theory of elliptic function
- 12. Abel is known for his… • Abel’s Binomial theorem • Abelian category • Abelian variety • Abelian variety of CM-type • Abel equation • Abel equation of the first kind • Abelian extension
- 13. •Abel function •Abelian group •Abel’s identity •Abel’s inequality •Abel’s irreducibility theorem • Abel- Jacobi map •Abel- Plana formula •Abel- Ruffini theorem •Abelian means
- 14. •Abel’s summation formula •Abelian and Tauberian theorems • Abel’s test • Abel’s theorem • Abel transform • Abel transformation • Abelian variety • Dual Abelian variety
- 15. Prepared by, Nandini N.L Mathematics Optional Reg.No : 13971010 K U C T E, Kumarapuram