## 1765 – Ruffini – bio

Paolo Ruffini was born in Italy in 1765 and was a mathematician. After the cubic equation was solved in 1539 by del Ferro, Tartaglia and Cardano, and Ferrari had solved the quartic equation by 1545, mathematicians turned their attention toward attempting to solve the quintic. The previous polynomial equations (quadratic, cubic and quartic) had all been solved by finding a formula for the roots that used radicals. But the quintic had not been solved in this manner despite 250 years of attempts. Ruffini set out to prove that the quintic equation could not always be solved this way, that there were some solutions that could not be expressed using radicals. Lagrange had been trying to solve the quintic using permutations (rearrangements) and Ruffini used this as his starting place, but had to invent the basic concept of group theory by himself. Abel eventually completed Ruffini’s proof and and Galois built on the foundation to create what is now known as group theory.

PRECURSOR:

**1048 – Omar Khayyam**

**1500 – Fontana/Tartaglia**

**1501 – Cardano**

**1545 – Ars Magna** – cubic equations solved

**1707 – Euler**

CONCURRENT:

**1736 – Lagrange**

1752 – Legendre

**1789 – Cauchy**

SUBSEQUENT:

1802 – Abel

**1811 – Galois**

SEE ALSO:

**Timeline of Group Theory**