Neils Henrik Abel was a renowned Norwegian mathematician born in 1802 in Norway. He showed exceptional talent in mathematics from a young age. He received support and scholarships to study mathematics further and traveled to Copenhagen and universities in Germany and France to study under other mathematicians. Abel made several influential contributions to mathematics, most notably the first complete proof that the general quintic equation cannot be solved algebraically using radicals. He also invented group theory and made important advances in elliptic functions and Fermat's last theorem. Unfortunately, Abel died of tuberculosis at a young age in 1829, just before being appointed professor at the University of Berlin.

1. A GREAT
MATHEMATICIAN

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