The latest trend among internet billionaires – Jeff Bezos and Peter Thiel among them – is to funnel vast sums into research on how to prolong human life, perhaps even how to extend it indefinitely. The reasons why the prospect of immortality would appeal to those enjoying such enormous wealth are clear; even if they lived a thousand lifetimes, they still wouldn’t be able to spend a fraction of their billions. But if no amount of money is ever enough, what amount of time will ever be sufficient either to accumulate or enjoy it? Acquiring some kind of immortality might indeed be the only solution.

The connection between wealth and immortality is a theme often encountered in ancient Greek and Roman writers. Money itself, in the form of portable gold and silver coinage that could buy goods and services, was widely adopted for the first time in Greece in the sixth century BC as a means of exchange and store of value. It also rapidly became apparent to newly monetised societies that, unlike human life, the accumulation of wealth had no natural end.

This notion is given exuberant expression in a comic fourth century BC play of Aristophanes, Wealth. Wealth, personified as a god, comes on stage as a blind man – blind, because wealth so often stumbles unwittingly into households which don’t deserve to be visited by it. He is harangued by a master and slave, who say people know when they have a surfeit of anything, except when it comes to money. ‘One can have too much of all sorts of things,’ they say: bread, says the slave, wistfully; music, says the master; snacks, says the slave; honour, says the master (the different priorities soon become clear); cakes – manliness – figs – ambition – crusty bread – generalship – pea soup… ‘All of these,’ says the master, ‘we can have too much of, but not of wealth. If you have ten thousand drachmas you want fifteen thousand, if you have fifteen you covet fifty thousand, then if you can’t be a millionaire you might as well be dead.’ In similar terms, the rapacious businesswoman played by Demi Moore in the 1994 film Disclosure observes ‘Give a man a hundred million dollars and you make a frustrated billionaire.’

The tragedian Aeschylus (fifth century BC) compared the wealth of King Agamemnon to the vastness of the ocean: ‘the sea is there – who will ever drain it?’ If one could only become rich enough, perhaps, mortal finitude itself might seem to be transcended, in some sense, by mentally projecting one’s unlimited wealth onto one’s limited life-span. But the idea of actually living forever held uncomfortable resonances for ancient people. The great originary works of Western literary culture, Homer’s eighth century BC epics, portray a clear distinction between the life of mortals and that of the immortal gods they are called on to worship. Unlike the latter, for whom nothing needs matter (or matter for long) because they are never going to die, the life of human beings revolves around care – care for family, friends, honour and glory – because they cannot hope or expect to live forever. Arguably the sense of care created by the shadow of certain death is what makes human life and endeavour uniquely valuable and desirable: for the twentieth-century German philosopher Martin Heidegger the notion of care, Sorge, is central to his existentialist doctrine. When one’s day on earth is done, there is no prospect of living another. As the Roman first-century BC poet Catullus puts it, ‘when once the light of our lives has expired, there’s just one long night that we must sleep’ [nobis cum semel occidit brevis lux, nox est perpetua una dormienda].

Human cultures have long struggled, however, against the inevitability of dying, or at least of bodily death, by creating notions of life beyond the grave. Our bodies may be prone to fail and die, but the spirit (or psyche or anima) might be thought to have an independent existence that outlives the body’s demise. In Greece in the seventh and sixth centuries BC a number of cults arose that revolved around stories of individuals who had experienced physical death (in a sense) by descending to Hades but had returned from it alive. The myth of the minstrel Orpheus, who descended to the Underworld to rescue his beloved wife Eurydice, was one of the best known of these. It underlay the mystery religion of Orphism which, practised alongside more standard religious beliefs about the gods, held that individuals initiated into the Orphic ‘mysteries’ – a set of secret and privileged cult doctrines and activities – could learn how to obtain personal immortality.

One of those who adopted Orphic mystery practices in the sixth century BC was the philosopher-sage Pythagoras, who claimed to have memory and knowledge of various former lives. A trader and musical theorist as well as a proto-mathematician, Pythagoras recognised that money was as potentially endless as the number series. However, human beings faced a continual tension between the intractable nature of limitlessness and the desire to find order and continuity in their lives. One possible remedy was offered by Pythagoras’s insistence that the soul was reborn into new bodies, and that while he himself would live only a limited life-span, he could transcend mortality by recalling who he had been in previous lives. After all, the seeker of immortality would feel short-changed to be told their soul might live forever but that they themselves would not have any memory or enjoyment of their own continuing lives. Pythagoras gave evidence for his personal continuity by entering a temple and recognising a shield hung on the wall as belonging to him in his former life as the Trojan hero Euphorbus; when the shield was taken down from the wall, the name ‘Euphorbus’ was found written on the back. (Unfortunately for the verisimilitude of Pythagoras’s claim, we know that the Greek alphabet had not yet been invented at the time of the Trojan War).

For ancient thinkers, the problem of personal continuity was not the only drawback when thinking about immortality. Ancient myths told of unique individuals such as Heracles who had been granted eternal life by gods, but more often than not there was a terrible catch to such a gift. Homer shows awareness of one concern when in the Odyssey he has the goddess Calypso offer Odysseus not just eternal life if he stays with her (an offer the hero refuses out of longing for home and his wife Penelope) but, explicitly, agelessness as well. To become immortal without ceasing to age was a fate worse than death, as the myth of Tithonus reminded readers. Eos, the goddess of dawn, had fallen in love with the handsome youth Tithonus, and, whisking him away to heaven she had made him immortal. But Eos was careless about the question of ageing, so the wretched man grows ever older for eternity, shrinking into a continually-tinier chattering cricket constantly bemoaning his fate.

A similar lot was thought to have befallen the prophetess of Cumae in Southern Italy, the Sybil, whom the god Apollo had granted eternal life but not eternal youth, dooming her to live in misery as her body shrank. The Roman novelist Petronius, author of the Satyricon, has a character in his book make the evocative claim, famously cited by T. S. Eliot as an epigraph to The Waste Land: ‘Once I myself saw with my own eyes the Sibyl at Cumae hanging in a jar. When boys asked her “Sibyl, what do you want?” she replied “I want to die.”’

These themes are brought together in a remarkable ode (1.28, the ‘Archytas Ode’) by the first-century BC Roman poet Horace. The poem is a monologue from an unnamed drowned mariner, who begins with an address to the long-dead Archytas, a follower of Pythagoras – and therefore a believer in life after death. Ancient authors such as Homer assumed the soul of an unburied body was doomed to stay alive in a kind of limbo, which only a proper ritual burial could bring to an end. Horace gave no credence to such superstitions. He was a follower of the third-century BC philosopher Epicurus, who contended that the universe was entirely material, the immortal soul did not exist, and death was simply a dissolution of the physical body.

In the ode, the imagined drowned mariner tossing in the eternal ocean waves invokes various figures (including Tithonus, an example of the grim prospect of living for eternity) to drive home the point that, just as Archytas did, everyone dies in the end. Nonetheless he asks a passing sailor who is hurrying to increase his wealth through marine trade to stop a moment to give him a ritual burial: scatter three handfuls of sand over my watery tomb, he begs, so that my soul may be allowed to rest. The last thing he wants is the kind of immortality that, as in the case of the mythical sinner Tantalus punished by being eternally tantalised by thirst and hunger, condemns one to everlasting torment.

How can Horace be indicating both that there is actually no such thing as immortality and that, should it exist, it would be a deeply undesirable state of torment? The apparent contradiction is resolved when one recognises that Horace is indicating his belief in a kind of afterlife, albeit one that is not the survival of a soul floating in perpetual limbo. In another ode he declares ‘I will not wholly die’ suggesting that his poetry will survive his physical death.

For those words to survive requires bringing a poem, a book, or a collection to completion. That is the kind of finitude required for poetry to outlive the poet, and it is one reason Horace’s odes, crafted with consummate polish and finesse, have survived for posterity to read. In flagging up the undesirability of unbounded existence in a poem that imaginatively represents a victim of that miserable and unenviable condition, Horace himself is signalling that the prospect of his own immortalisation as a poet is both desirable and achievable. To echo in reverse the words of the poet Stevie Smith, the true speaker of Horace’s ‘Archytas ode’ is Horace himself – not drowning, but waving.