I've travelled on "Shepherd One", as the plane carrying the pope is known, and it's very clear when you're on board how keen the pope's PR men – and yes (sigh) they are all men – are on declaring a foreign trip a "triumph".

In the case of Francis' visit to Brazil, they're right. Today in Rio they're calling their famous beachfront the "Popacabana'' in tribute to the mass held there on Sunday, when three million camped on the sand to catch a glimpse of the pontiff on his first visit back to Latin America since being elected pope in March.

Virtually the worst thing that happened was when Francis's tiny Fiat Punto took a wrong turning, prompting fears for his safety. Not only did he come to no harm, but the new message of slimmed-down frugality was well and truly noted.

And it was this common touch – his ordinariness, his lack of pomposity, his humility – that we saw reflected back from Brazil; and the Catholic church will be the stronger, and more credible, for it. Perhaps at last we have a pope for the 21st century. Certainly the signals we have seen over the last few days have a whiff of modernity about them.

Even as a cardinal, Bergoglio had already clamped down on priests who refused to baptise children born out of wedlock; now he has gone further and said gay people should not be marginalised ("if a person is gay and seeks God, who am I to judge him?" he asked). On the role of women, (we're only 70 percent of the church's membership, so we really shouldn't push our luck) he said having girls as altar servers and employing a handful of senior women in the Vatican might perhaps not be quite enough. On the matter of women priests, of course, there was no debate to be had.

So we're seeing a thaw, though definitely not a revolution; a subtle but significant change of direction, yet from a man who remains deeply conservative. You don't need to be radical to be seen as a wind of change in the Catholic hierarchy (what they'd have made of Christ, one shudders to think). But as Francis is no doubt all too aware, the foreign trips are the easy bits. Because the truth is that it's in the Vatican, the smallest state on Earth, that most of his problems lie. None of his difficulties have gone away while he's been on the beach in Brazil. The fact is that by signalling a change of style, the new pope has raised expectations of a change of substance.

And there's certainly plenty there that needs tackling. The smell around the murky Vatican bank is very unpleasant in the Italian mid-summer heat; the issue of a non-celibate priesthood is crying out to be tackled; and even if giving women the chance to be priests isn't up for grabs, the church remains impoverished by failing to recognise and use its wealth of female talent. There's a sense right now that Francis is on the verge of moving on these fronts; and if his pontificate is to be a genuine triumph, and not just a PR one, these are the nettles Francis has to grasp.

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