Income inequality is one of the most important social issues of our time. There are vast gaps between the economies of different countries around the world: the poorest countries (Malawi, Burundi, Central African Republic) have GDPs per capita that are several hundred times smaller than those of the richest countries (such as Luxembourg and Norway). There are also vast disparities within individual western populations. In the US, the top 1% controls about 40% of the wealth; more than 20% is owned by the top 0.1%. Inequality on this scale is probably unprecedented in world history. In the Roman empire – a slave-owning, militaristic, undemocratic colonial power, which was the closest thing before the modern era to a globalised society – the top 1% of the Roman population probably controlled only about 16% of the empire’s riches.

What is it like to be in the wealthiest tier of society, either in ancient Rome or today? How do such people justify their own position of privilege, either to others or to themselves? In our society, the super-rich are generally not prolific writers, so we get only limited and mediated access to their state of mind. In Rome, things were different. The Roman Stoic philosopher, essayist, celebrity and dramatist Seneca was tutor, speech-writer and adviser to the emperor Nero, and he was also, not coincidentally, one of the very richest people of his age. He lived in the same period as Jesus, though he lasted longer before falling out with the authorities. Seneca was originally from Spain but he spent much of his life in Rome, except for a long convalescent sojourn in Egypt, and some years in exile on Corsica in the wake of a sex scandal. He was forced to kill himself at the age of about 60, in 65AD, under suspicion of conspiring against the emperor.

Seneca was obsessed with money and its discontents. He had a great deal of it. He came from a comfortable family background, although he was not in absolutely the top tier of the class system (being equestrian rather than senatorial in rank). He accumulated huge amounts of wealth and property in the service of Nero: we are told by the Greek historian Cassius Dio that he acquired more than 300m sestertii, a sum that put him easily in the top 0.1%. The average Roman senator was worth “only” about 5m, while the majority of the population lived on something closer to subsistence level; a single sestertius could buy two loaves of bread. Seneca was known to his contemporaries as “super-rich Seneca” (Seneca praedives, as Martial calls him). Enemies accused him of preying on affluent elderly people in the hope of being remembered in their wills, and of “sucking the provinces dry” by lending money at a steep rate of interest to those in the distant parts of the empire, including the unhappy inhabitants of Boudicca’s Britain. His bank balance was only part of his wealth: he also owned several villas around Italy with prosperous estates and vineyards attached, as well as the usual trappings of the elite, such as 500 citrus-wood tables with ivory legs, all alike – perfect for lavish dinner parties at which he could entertain 1,000 of his closest friends.

The interesting thing about Seneca’s wealth is not only how extensive it was, but how difficult it is to reconcile with his literary and philosophical discussions of riches. A central notion of Stoicism, the philosophical doctrine with which Seneca is most closely identified, was the idea that being virtuous is the only truly beneficial thing, and the only thing that can make a person truly happy: wealth, like health, freedom and status, is a merely “indifferent thing”. It is something we might rather have than not, since people generally prefer not being in abject poverty, but wealth does not make a fundamental contribution to human happiness. Other Stoic writers, however, do not spend as much time as Seneca does puzzling over the proper attitude towards riches. He worries repeatedly about the effects of consumerism on the psychological makeup of the consumer, who may become a “slave” to pleasure, and who may become so caught up in a cycle of false pleasure and unsatisfying satisfaction as to lose touch with any real needs: “Why do you have property overseas? Why more things than you’ve ever seen or known? Are you so horribly spoilt that you don’t even know your few slaves, or such a fat cat that you own more slaves than you can possibly remember?”

The Death of Seneca, c1615, by Peter Paul Rubens. Photograph: Gianni Dagli Orti/Corbis

The problem, for Seneca, is not that owning slaves is bad for the slaves, or that the rich man’s wealth might be better spent feeding the hungry than buying another ivory-legged table. The problem is rather that owning too much – whether slaves or tables – can be damaging for the owner, because he (it is always “he”) will be unable to achieve what we all really need, which is the peace of mind that comes from virtue and truth. “We would belong to ourselves if those things were not ours,” he declares. Consumerist desires are essentially insatiable, because they are desires for things we do not really need: “You see, it’s not thirst; it’s disease.”

We should not be too surprised that Seneca was unable to imagine an alternative to a society that owned slaves and depended on vast income inequality. He could not think about wealth, or rather income inequality, as a social and structural issue as opposed to a problem for the wealthy individual in particular. Such cultural blind-spots are not unusual; presumably we have our own. More striking is the way that Seneca laid himself entirely open to the charges of hypocrisy, which were indeed levelled against him by contemporaries and many readers since antiquity. His idealisation of an ascetic lifestyle and explicit denunciations of consumerism are clearly hard to reconcile with his multimillionaire status. Seneca himself mimics the accusations of his critics, who ask, “Why do you talk so much better than you live?”Perhaps, in theory, the philosophical ideal could be achieved in life. At times in his writings, Senca fantasises about the possibility that one could be wealthy, even extremely wealthy, and maintain one’s ethical integrity. There are three main criteria for this, we are told. The virtuous rich man must maintain the correct, aloof and unslavish attitude towards his wealth, owning it without needing it, and willing to give it all up whenever necessary: “He is a great man who uses clay dishes as if they were silver; but he is equally great who uses silver as if it were clay.” Secondly, he must acquire riches in morally legitimate ways, so his money is not “stained by blood”. Thirdly, he must use his riches generously, to benefit those less well-off than himself – a provision which invites comparison to the charity work practised by rich philanthropists in our own time.

But there is no evidence Seneca managed to fulfil any of these conditions. He may have been fairly moderate in the realm of food and drink, but he also owned a great deal of stuff, and he writes in a way that certainly does not suggest emotional detachment from the details of material possessions. He notices, and obsesses over, the polished furniture, the wine older than its consumer, the earrings that cost more than a house, the birdhouses and silver and ornamental trees and exotic slaves. His wealth was certainly stained by blood: it came from an emperor who killed his stepbrother and his mother, as well as a number of less prominent people. Seneca was probably generous in the sense that he used his wealth for grand parties and to buy friends and influence, but he never seems to have donated it to the very poor of Rome, and never founded anything like the Gates Foundation: philanthropy of this systematic kind did not exist in the ancient world.

We might then label Seneca a hypocrite, since he failed to be ethically rich by his own criteria. But most of us, including those who would call themselves middle class rather than fat cats, would have to say the same, if we were fully honest with ourselves. We buy things we don’t need. We get caught up in consumerist desire and lose track of what we might really want in life. We purchase clothes manufactured by children and make investments in companies whose practices are stained by blood. We give too little and we keep too much. Seneca’s hypocrisy is an extreme and therefore visible case of a moral problem of which we should all be more conscious. Seneca, fat cat though he was, is admirable for his refusal to give up on a problem that he knew he had not solved, and for his willingness to keep on stating a confusing and difficult truth. He acknowledged that he himself was unable to live up to his own ideals, but he kept on wrestling with the gap between how he was and how he wanted to be: “I am not a wise man and I never will be,” he writes. “I haven’t reached health and I never will get there. I’m alleviating my gout, not curing it.”

• Emily Wilson’s Seneca: A Life is published by Allen Lane.