Paolo Ruffini

1765-1822

Italian Mathematician and Physician

The Abel-Ruffini theorem states that quintic equations, or algebraic equations greater than the fourth degree, cannot be solved using only radicals—i.e., square roots, cube roots, and other roots. It is named after Niels Henrik Abel (1802-1829) and Paolo Ruffini, whose findings Abel confirmed. Ruffini also contributed to the development of group theory, and was known for his work as a philosopher and physician.

When Ruffini was born on September 22, 1765, his hometown of Valentano was a part of the Papal States, a geopolitical entity on the Italian peninsula that had existed for a thousand years. His own lifetime, however, would witness political upheaval that brought the existence of the states to a temporary end under the invading forces of Napoleon Bonaparte. While he was a teenager, his parents—Basilio, a physician, and Maria Ippoliti Ruffini—moved the family to Modena, and Ruffini later studied mathematics, medicine, and other subjects at the city's university. Among his mathematics instructors were the geometer Luigi Fantini, and Paolo Cassiani, who taught infinitesimal calculus. Ruffini himself was such a talented student that he took over instruction of Cassiani's foundations of analysis course when the latter had to take a leave of absence in 1787.

In 1788, Ruffini earned his degrees in philosophy and medicine, and followed this with a degree in mathematics soon afterward. He became a professor teaching the foundations of analysis, but in 1791 replaced Fantini as professor for the elements of mathematics. He also began practicing medicine that year.

Napoleon's troops occupied Modena in 1796, when Ruffini was 31 years old, and Ruffini was forced to become a local representative in the junior council of the newly declared "Cisalpine Republic." Two years later, he was allowed to leave that post, but his troubles continued due to the fact that, for religious reasons, he refused to swear an oath of allegiance to the republic.

Despite the troubles of this period, intellectually it was a fruitful time for Ruffini. In 1799 he published Teoria generale delle equazioni, which contained the first statement of what became known as the Abel-Ruffini theorem. Several mathematicians initially rejected Ruffini's ideas, but Augustin-Louis Cauchy (1789-1857) was an outspoken supporter of his findings. Abel confirmed the theorem in 1824.

Ruffini is also credited with developing the theory of substitutions, vital to the theory of equations, which in turn helped lay the foundations for group theory. Additionally, he served as president of the Societa Italiana dei Quaranta, which advanced mathematical learning, but in his later years he increasingly turned his attention to the two other fields of primary interest to him, philosophy and medicine.

By 1815, Napoleon was defeated, but other challenges appeared. During the 1817-18 typhus epidemic in Italy, Ruffini contracted that disease while treating patients in Modena, and after his recovery wrote about his experiences as both a patient and a doctor. A few years later, he contracted chronic pericarditis, along with a fever, and died on May 10, 1822.

JUDSON KNIGHT