Wittgenstein was born in Vienna to the industrialist Karl Wittgenstein. Two years later, his brother, the future philosopher Ludwig Wittgenstein was born. The household was frequently visited by prominent cultural figures, amongst them the composers Johannes Brahms, Gustav Mahler and Richard Strauss, with whom the young Paul played duets.
Paul Wittgenstein studied with Malvine Bree and later with the Polish virtuoso Theodor Leschetizky. He made his public debut in 1913 and some favourable reviews were written about him. The following year, however, World War I broke out, and he was called up for military service. He was wounded and captured by Russia during an assault on Poland, and his right arm had to be amputated. During his recovery, he resolved to continue his piano playing career using only his left hand.
Following the end of the war, Wittgenstein put this plan into action, studying intensely, arranging pieces for the left hand alone and learning new pieces composed for him by his old teacher Josef Labor (who was himself blind). He began once again to give concerts, and became well known and loved. He then approached more famous composers, asking them to write works for him to perform. Benjamin Britten, Paul Hindemith and Richard Strauss all wrote pieces for him, and Maurice Ravel wrote his Piano Concerto for the Left Hand which Wittgenstein became particularly famous for. Sergei Prokofiev also wrote a concerto for him, Prokofiev's fourth, but Wittgenstein did not like the piece, and never played it.
Many of the pieces which Wittgenstein commissioned are still frequently performed today by two-armed pianists. They have also been played by other pianists who for one reason or another have lost the use of their right hand, such as Leon Fleisher.
The Wittgenstein family had converted to Christianity three generations ago on the paternal side and two generations ago on the maternal side; nonetheless they were of mainly Jewish descent and under the Nuremberg laws were initially classed as Jews. Following the rise of the Nazi Party and the annexation of Austria, Paul tried to persuade his two sisters to leave Vienna (Ludwig had already been living in England for some years), but they demurred: they were attached to their homes there, and could not believe such a distinguished family as theirs was in real danger. Paul himself, who was no longer permitted to perform in public concerts under the Nazis, departed for the United States in 1938. From there he and Ludwig managed to use family finances (mostly held abroad) and legal connections to attain non-Jewish status for their sisters.
Paul became an American citizen in 1946. He spent the rest of his life there, mainly teaching. He died in New York City in 1961.
John Barchilon wrote a novel based on Wittgenstein's life called The Crown Prince.