Ludwig Wittgenstein (April 26, 1889 - April 29, 1951) was the youngest of eight children, born to one of the wealthiest families in Vienna (in what was then the Austro-Hungarian Empire). His maternal cousin, born two weeks later, was Friedrich von Hayek -- who grew up to be one of the most important economists of the twentieth century, a Nobel laureate for his work on the theory of money and economic fluctuations. It's no surprise, then, that Ludwig and Friedrich came from a well-educated family. Karl Wittgenstein, Ludwig's father, was a wealthy industrialist who served as a patron of the arts, especially music. Brahms and Mahler were among the musicians who spent time in the Wittgenstein household, and the children all grew up with musical talent -- Paul Wittgenstein's career as a concert pianist continued even after he lost an arm during a tour of duty in World War I. The eldest boy, Hans, began composing his own music at age four.
However, alongside this penchant for genius was a dark side. Three of the five Wittgenstein boys committed suicide, including Hans, who took his life when Ludwig was three years old. Homeschooled before attending school with other young men, Ludwig was considered a bit of an oddball by his classmates. (Teenage Adolf Hitler, a fellow student at the Realschule in Linz, was not actually Ludwig's classmate, though the boys were the same age and had many of the same teachers over the course of their schooling; because of his education at home, Ludwig was two grades ahead of young Hitler.) He missed many of his classes, and when he did show up, he put on airs, insisting he be addressed formally by his classmates and dressing in ostentatiously formal clothes. His diction and grammar were extremely precise, even baroque, and yet his vocabulary was actually mediocre.
Oddball or not, Wittgenstein did fairly well in school, and went on to study mechanical engineering in Berlin and Manchester, before enrolling at the University of Cambridge at age 22. At Manchester, he had become interested in the foundations of mathematics, through the writings of Bertrand Russell; at Cambridge he sought Russell out, attending his lectures and studying logic, mathematics, and philosophy with him. Bit by bit, Wittgenstein felt that being surrounded by an academic environment was actually distracting him from his quest for the truth, and so rented a house in rural Norway, where he stayed while embarking on his private studies.
In the meantime his life was touched by tragedy again. Ludwig Boltzmann, a physicist he had hoped to work with, had committed suicide a few years earlier. Karl Wittgenstein died, leaving his fortune to his children. Ludwig used some of it to continue his father's patronage of the arts anonymously, donating money to Austrian poet Georg Trakl -- who committed suicide days before Ludwig was planning to meet him.
Like his brothers, Ludwig served in the Austro-Hungarian army during World War I. Having been raised Catholic by a family of Viennese Jews, some of whom had converted to Protestantism, Wittgenstein had been an atheist for most of his adult life -- but discovered religion during the war, not because of the horrors and bloodshed around him, but through the writings of Christian philosopher and novelist, the Russian Leo Tolstoy. He began to read Fyodor Dostoevsky, another Russian Christian, as well as St Augustine and Soren Kierkegaard. Logik, the book he had begun before the way, began to focus more on ethics rather than just logical analysis. On leave from the war following the death of a friend, he rewrote Logik to incorporate this new material, and produced the Tractatus Logico-Philosophicus.
The Tractatus was completed after the war, with an introduction by Russell which gnawed at Wittgenstein because he believed his professor had actually misunderstood his book entirely -- but without the introduction, he'd be unable to find a publisher. With the introduction intact, he secured both German and English publishers, and because he believed he had answered all of philosophy's questions, he retired as a scholar in his early 30s, becoming a teacher of young rural children. He wasn't suited to the job. He had been a stiff, formal student who had grown up in a cosmopolitan, education-rich environment, and he had no talent for dealing with pupils who couldn't keep up with him or weren't interested in the material. He was a good mentor to those who had already developed an interest in mathematics, but had no skill for inspiring that interest himself. Students' parents didn't like him, and he eventually left the post to work as a gardener.
When his sister asked for his help in designing her new house, he collaborated with architect Paul Engelmann, a friend from the war, producing a precisely designed modernist domicile. During that time, he was approached by the Vienna Circle, a new group of Austrian philosophers associated with the University of Vienna. The Circle was unable to get Wittgenstein interested in formally participating in their discussions, but his Tractatus had been very influential on them, and he did befriend some of them individually, and became interested again in public intellectual life. This was not without its frustrations. Like he had with Russell, Wittgenstein believed the members of the Circle misunderstood the Tractatus to varying degrees -- and they generally disdained its religious dimension. Often he refused to discuss it with them rather than respond to their inquiries, and would change the topic to some common ground, or a pet interest of his such as poetry or music.
However concerned he was with being misunderstood, Wittgenstein didn't treat the Tractatus as untouchable, and before long began to reevaluate it himself, coming to the conclusion that some of it was simply wrong. At the end of the 1920s, he returned to Cambridge, where he discovered that his fame had spread further than just Vienna -- many of England's greatest minds actually met him at the train station, unwilling to wait to seek out his company later. He had never actually completed a degree at Cambridge, so submitted the Tractatus, which was quickly accepted as sufficient to grant him a doctorate. He began working as a professor at Cambridge's Trinity College.
He returned to Norway later in the decade to work on Philosophical Investigations, a new book to correct the Tractatus. He was still a citizen of Austria, though, which as Germany expanded made him a German, and a Jew by birth. Lengthy negotiations and a great deal of money had the Wittgensteins -- including several siblings who still lived in Austria and were daily subject to the Nazis' harsh race laws -- reclassified as Mischlinge, or mixed Aryan/Jews. It was one of only twelve such reclassifications allowed that year, out of over two thousand requested, and without it it's unlikely that the Wittgenstein family would have survived the war. Nearly two tons of gold -- $50 million in today's currency -- was given to the Nazis in the negotiations.
In his intellectual life, Wittgenstein's views of mathematics had changed completely. He no longer believed that mathematics represented anything real, but instead were just a way of dealing with particular symbols -- and therefore a contradiction in a mathematical system was no reason to discard it. He left Cambridge when World War II broke out, to work in hospitals, and officially resigned from Cambridge not long after the war's conclusion, having never warmed up to the academic atmosphere. He died of prostate cancer a few years later, living most of the intervening time in the rural areas he preferred, while working on the unfinished Investigations.
