The document summarizes the work and contributions of four important mathematicians: Niels Henrik Abel proved the impossibility of solving the general quintic equation with radicals, an outstanding problem for 350 years. Évariste Galois determined the necessary and sufficient conditions for a polynomial to be solvable by radicals. Sir Isaac Newton worked on the properties of the quadratic equation. Their groundbreaking work laid the foundation for solving polynomial equations and shaped modern scientific progress.

1. THERE WERE THREE
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2. ABEL
(5 August 1802 – 6 April 1829)

3. • Niels Henrik Abel was a Norwegian mathematician.
• He is most known for proving the impossibility of solving
the general quintic equation in radicals. A question that
was one of the outstanding open problems of his day, and
had been unresolved for 350 years.
• Ηe was largely unrecognized during his lifetime.
• He made his discoveries while living in poverty and died at
the age of 26.

4. g(x)= ax5 +bx4+cx3+dx2+ex+f ,
a 0

5. GALOIS
(25 October 1811 – 31 May 1832)

6. • Évariste Galois was a French mathematician born in
Bourg-la-Reine.
• He is most known for determining a necessary and
sufficient condition for a polynomial to be solvable by
radicals (for solving the quadratic equation).
• He died at age 20 from wounds suffered in a duel. (there
is a mystery behind his death)

7. NEWTON
(25 December 1642 – 20 March 1726/27)

8. • Sir Isaac Newton PRS was an English mathematician,
astronomer, and physicist.
• Among other things he worked on the properties of the
quadratic equation.
• He died in his sleep.

9. ax2+bx+c=0,
a 0
• P= x1x2 = c/a
• S=x1+x2 = -b/a

10. THE END...ALMOST
To sum up;
Before Abel noone had worked on the quintic equations.
He said that they could not be solved.
Then Galois took this subject even further.
He said that there are solutions but under certain conditions.
Before them Newton with his work on quadratic equations said that we
do not
need all the clues to find a solution.

11. Today many scientist based on the work of Galois
and
Αbel have made remarkable breakthroughs and we
keep
going…
These theories that were found hundreds of years
before
have shaped the world of scientific progress.