Marx edited the Rheinische Zeitung in Cologne from 1842 until Prussia banned it in 1843, having discovered while writing about the theft of firewood and the condition of Moselle winegrowers that he did not understand economics and would have to learn it. He married Jenny von Westphalen, an aristocrat's daughter who had been engaged to him for seven years against her family's wishes, and moved to Paris. There he read political economy seriously for the first time, wrote the manuscripts on alienated labour that would not be published until 1932, and in August 1844 met Engels at the Cafe de la Regence - a meeting that produced a collaboration of forty years and, quite literally, Marx's income.

France expelled him in 1845 at Prussian request. He went to Brussels, renounced his Prussian citizenship and remained stateless for the rest of his life. Belgium expelled him in 1848; he returned to Cologne to found the Neue Rheinische Zeitung with his father's inheritance, was tried for incitement and acquitted, and was expelled again when the revolutions failed. France would not have him back. In August 1849 he arrived in London, intending to stay a few months until the next revolutionary wave. He stayed thirty-four years.

Marx died in 1883 with volume one of Das Kapital published, volumes two and three in notebooks, and no organised movement of any size. Engels edited and published the remaining volumes in 1885 and 1894, and the theory was systematised into a doctrine over the following decades by people Marx never met. Lenin adapted it for a country Marx had considered too agrarian for socialist revolution, adding a vanguard party the original texts do not describe. Stalin and Mao adapted it further. The regimes that followed were responsible for tens of millions of deaths through famine, purge and camp, and by the middle of the twentieth century governed roughly a third of humanity.

How much of that belongs to Marx is the longest-running argument in modern political thought, and it is genuinely unsettled. He wrote of a dictatorship of the proletariat and endorsed revolutionary violence; he also spent his life as a journalist attacking censorship and state repression, and once remarked of a group of French followers that if that was Marxism, he was not a Marxist. The honest position is that his work is a critique of capitalism rather than a design for what replaces it, that the blueprint was written by others, and that the absence of a blueprint in a text claiming historical inevitability is itself a serious flaw rather than an alibi.

Michael Hart ranked Marx 27th on reach rather than on whether the theory holds. The Russian Revolution of 1917 and the Chinese Revolution of 1949 were both carried out by men citing him, and at the Cold War's height governments professing Marxism ruled roughly a third of the world's people. Most of those regimes are gone - the Soviet system collapsed between 1989 and 1991 - but the twentieth century is not comprehensible without them, and neither is the shape of the century that followed. Few private individuals writing alone in a library have had a comparable effect on the map.

The quieter legacy may prove the more durable. Sociology as a discipline is unimaginable without him; so is economic history, and much of the way historians now read any period. The habit of asking who owns a thing, who benefits from an arrangement, and whose interest a widely held belief happens to serve is so embedded in modern thought that it no longer registers as Marxist at all. Eleven people stood at his grave in Highgate in March 1883. Engels told them that his name and his work would endure through the ages, which was, on any reading, a considerable understatement.