Ruffini, Paolo (1765–1822)

Italian mathematician, philosopher, and physician. He published a theorem stating that it was impossible to give a general solution to equations of greater than the fourth degree using only radicals (such as square roots, cube roots, and so on). This became known as the Abel–Ruffini theorem when endorsed by Norwegian mathematician Niels Abel.

Ruffini was born in Valentano, Viterbo, and studied at Modena. From 1788 he was a professor there, though when Napoleon entered Modena in 1796, Ruffini found himself appointed an official of the French republic. Two years later he refused to swear the oath of allegiance to the republic and was for a time barred from teaching.

Ruffini made a substantial contribution to the theory of equations, developing the so-called theory of substitutions, which was the forerunner of modern group theory. His work became incorporated into the general theory of the solubility of algebraic equations developed by the ill-starred French mathematician Evariste Galois.

In addition, Ruffini considered the possibility that living organisms had come into existence as the result of chance, thus anticipating more modern work on probability.