Stephen Hawking is widely spoken of as a genius. He was also lots of fun, with cameo appearances in popular comedies like The Big Bang Theory. For the (few) readers who haven't seen it, it's a hoot. TBBT revolves around the life and loves of four scientists, one of them, Sheldon Cooper, is the archetypal nerd – ferociously intelligent, a creature of pure reason (Mr Spock is his hero) and more than a little weird.

TBBT is not kind to religion and Sheldon's mother's Christian fundamentalism is regularly mocked. A scene from a recent spin-off, Young Sheldon, has been widely shared: it shows the precocious wunderkind taking on his pastor during a service, to his family's mortification. Things come to a head when Pastor Jeff asks, 'So you don't think science and religion can go hand in hand?' 'Science is fact, religion is faith. I prefer facts,' says Sheldon.

Pastor Jeff: 'Here's a cool fact for you. A lot of famous scientists believed in God. Isaac Newton; Albert Einstein; even Charles Darwin.'

Sheldon: 'So Darwin was right about God and wrong about evolution?'

Pastor Jeff: 'Now you're getting it...'

At the root of TBBT's philosophy, and of Stephen Hawking's, is that there is no need to invoke God in order to account for the universe, and that therefore there's no reason to believe in him.

It's the sort of thing that gives conservative Christians conniptions – and that drives many, particularly in the US, to espouse the full-blown young-earth creationism so much mocked by TBBT. If the Big Bang Theory (first put forward in its modern form, incidentally, by a Catholic priest) is true, what place is there for God in the world?

It's an argument that seems to have persuaded Hawking. He said that if there were a God, and he didn't think there was, he 'does not break the laws of science' – in other words, there are no miracles or divine interventions. Furthermore, as he wrote in The Grand Design (2010): 'Because there is a law such as gravity, the universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the universe exists, why we exist. It is not necessary to invoke God to light the blue touch paper and set the universe going.'

Is he right? At one level, of course: in the end, it's the job of scientists to try to account for absolutely everything in the physical world. For religious believers to carve out territory that can only be accounted for by divine intervention is an enterprise doomed to failure. The trouble with the 'God of the gaps' approach is that the gaps keep getting filled in, leaving less and less space for God.

This isn't a new problem. Famously, the Marquis de Laplace, another scientific genius and France's answer to Isaac Newton, was once asked by Napoleon why he hadn't mentioned God in his latest work. 'Sir, I had no need of that hypothesis,' Laplace is said to have replied. Like many such tales, however, it turns out not to be quite true: Laplace, it's thought, was challenging Newton, who had speculated that God needed to intervene from time to time to keep the universe on track. Not so, he said; it works very well as it is. And Hawking said in 1999 in a lecture entitled, Does God Play Dice?: 'I don't think that Laplace was claiming that God does not exist. It's just that he doesn't intervene, to break the laws of science. That must be the position of every scientist. A scientific law is not a scientific law, if it only holds when some supernatural being decides to let things run, and not intervene.'

That lecture, however, is an argument against what Laplace believed, that the universe was predictable and deterministic: 'If you knew the state of the universe at some time in the past, you could predict it in the future.' Because of quantum mechanics and black holes, however, that's not true. There's an element of randomness in how the universe works. As Hawking concludes: 'Thus, the future of the universe is not completely determined by the laws of science, and its present state, as Laplace thought. God still has a few tricks up his sleeve.'

So it might be thought Hawking is rather undercutting his own argument, though certainly he didn't see it like that himself. According to David Wilkinson, for instance, a theologian and astrophysicist, it's this quantum nature of reality that allows us still to believe in a God who works miracles. In a little book entitled, When I pray, what does God do? he says there's plenty of room for God to act in the world without breaking his own rules. He can push an electron here or there and radically affect outcomes. He cites 'chaos theory', which Hawking also invokes, whereby the flap of a butterfly's wing in Brazil might set off a tornado in Texas, saying that chaos 'might give God space to work in unusual and specific ways within the scientific description of the world'.

So ordinary Christian believers who don't, if we are honest, really grasp much of what Stephen Hawking was talking about, can take heart: unlike Pastor Jeff's Darwin, we might say he was right about the science but wrong about God.

And we should, as well, do all we can to bring to an end the phoney war between science and religion. It's not a choice: you can believe science offers – or might do one day – a complete understanding of the universe we live in, and still believe in a God who is 'over all and through all and in all' (Ephesians 4:6).

After all, we don't believe in God because of the things we don't understand; we believe in him because of the things we do understand. Not everything we know can be proved, and God still has a few tricks up his sleeve.

Follow Mark Woods on Twitter: @RevMarkWoods.