It is a measure of our times that a play first published in 1940 about a scientist born in 1564, back when people still thought the solar system was encased in crystal spheres, could still feel as fresh as if it were written yesterday. The popularity of Howard Davies’ adaptation, which just finished a sold-out four-month run at the Olivier National Theatre in London, is a testimony to its modern relevance. Yet Galileo, the play, has been an adaptable creature. Bertolt Brecht’s response to the fascist oppression of Nazi Germany was reworked several times thereafter to reflect his changing world views, while the version at the London National Theatre was based chiefly on David Hare’s more accessible 1994 adaptation. The sense of timeliness is enhanced by characters sporting modern dress and speaking in crisp vernacular.

The Olivier Theatre is a particularly apt venue: the audience, hanging in the dark, lurks over the stage like heavenly bodies peering down into the center of the universe as the concentric circles of the rotating stages move like orbiting planets or the shifting of primitive gears. The play opens with a disillusioned Galileo Galilei (Simon Russell Beale) forced to tutor bored students at the University of Padua and to invent silly gadgets to finance his independent experimentation – and his taste for good food and fine wine. When one Dutch student tells him of the latest craze in Amsterdam, a "queer tube" which magnifies things, the clever inventor quickly knocks up a vastly superior prototype and peddles it as his own invention.

Expecting only handy cash for his troubles, Galileo gets far more than he bargains for with his telescope: a clear view of the moons of Jupiter transiting in and out of view as they orbit the red giant. The conclusion is inescapable: nothing encased in a crystal sphere – as Aristotle dictated and as the Catholic Church endorsed at the time – could possibly exhibit such three-dimensional behavior. Galileo turns the telescope on the earth’s moon and the Milky Way and deduces a similar forbidden truth: that Copernicus’ theory of a heliocentric solar system is borne out by observation. These scenes of discovery are electrifying: imagine being the first person to gaze at close range upon other objects in the solar system. Imagine being the first person to prove that centuries of belief were completely wrong – imagine being the first person to prove that the earth is not the center of the universe, set there for God to keep an eye on His creation, but is instead one of millions of bodies, lost and lonely in a vast space.

When a concerned friend reminds Galileo that Copernicus’s champion Giordano Bruno was burnt at the stake for suggesting as much, the irascible, irrepressible Galileo rebuts that Bruno would not have been martyred if he’d had proper evidence for his claims. In the black-and-white world of the scientific method, which Galileo is said to have fathered, false dogma dissolves in the face of empirical truth. Here, we see the blinkered arrogance that even today doesn’t sit too well with non-scientists: the stubbornness of the sort of scientist who cannot comprehend that everyone else does not necessarily embrace rationality as a matter of course. According to Galileo’s calculus, faced with the irrefutable evidence, the Church should simply change its views. But it is not that easy – something Galileo’s friends, and the audience, can easily see.

And it comes to pass: in a wonderful scene, Galileo invites the leading scholars of Florence to peer into his telescope for the ultimate proof that Aristotle was wrong; but the men refuse to even look, instead making patronizing speeches why the telescope could not possibly show any such thing. The Church is even less impressed – though their own astronomer declares Galileo’s calculations to be correct, the Pope forbids Galileo to make the matter public. This is an interesting Church in many respects; its purveyors are scientifically educated and do not deny the evidence; they do not even force Galileo to stop his work. Instead, a bargain is struck: just don’t make a fuss, and things can go on as before. If it weren’t for constant underlying sinister presence of the Inquisition and its instruments of torture, this congenial papacy might even seem more enlightened than the one we have today.

By far the most interesting minor character is a mathematically minded monk whose impassioned scientific curiosity attracts him irresistibly to Galileo and his ideas. In a powerful and affecting scene, the monk tells Galileo why he’s swearing off astronomy forever:

As I study the phases of Venus I can visualize my parents sitting round the fire with my sister, eating their curdled cheese. I see the beams above them, blackened by hundreds of years of smoke, and I see every detail of their old worn hands and the little spoons they are holding. They are badly off, but even their misfortunes imply a certain order. There are so many cycles, ranging from washing the floor, through the seasons of the olive crop to the paying of taxes. There is a regularity about the disasters that befall them. … They draw the strength they need to carry their baskets sweating up the stony tracks, to bear children and even to eat, from the feeling of stability and necessity that comes of looking at the soil, at the annual greening of the trees and at the little church, and of listening to the bible passages read there every Sunday. They have been assured that God's eye is always on them – probingly, even anxiously – : that the whole drama of the world is constructed around them so that they, the performers, may prove themselves in their greater or lesser roles.

What would my people say if I told them that they happen to be on a small knob of stone twisting endlessly through the void round a second-rate star, just one among myriads? What would be the value or necessity then of so much patience, such understanding of their own poverty? What would be the use of Holy Scripture, which has explained and justified it all – the sweat, the patience, the hunger, the submissiveness – and now turns out to be full of errors? No: I can see their eyes wavering, I can see them letting their spoons drop, I can see how betrayed and deceived they will feel. So nobody's eye is on us, they'll say. Have we got to look after ourselves, old, uneducated and worn-out as we are? The only part anybody has devised for us is this wretched, earthly one, to be played out on a tiny star wholly dependent on others, with nothing revolving round it. Our poverty has no meaning: hunger is no trial of strength, it's merely not having eaten: effort is no virtue, it's just bending and carrying. Can you see now why I read into the Holy Congregations decree a noble motherly compassion; a vast goodness of soul?

Galileo retorts that his family is hungry because the Church does not provide for them, and that the beauty of science cannot be marred by lies – again exhibiting a scientist’s blindness to the real-world effects of his art. Producing a new mathematical proof that the moon causes the ocean’s tides, Galileo expertly exploits the monk’s curiosity to bring him back to the fold.

In the end, however, a new Pope comes to power, the Church runs out of patience and Galileo is forced to recant. The mere sight of the instruments of torture is all that is necessary for him to renounce his life’s work and publicly declare that the sun revolves around the earth. Reviled by his scientific colleagues as a traitor and a coward, and interred by the Church under house arrest, Galileo shrinks to a blind, hunchbacked wreck. In the end, confronted by a former pupil, he explains why scientific truth was in the end not as important as saving his hide. Science is not faith, we are told: you don’t need to die for your beliefs – because the truth is there whether you believe it or not.