But after Theresa May's no-holds-barred speech on Tuesday, we've at last got a very good idea of what it won't look like.

It won't look like what a substantial portion of the country was hoping for: a soft, gentle nudging of Britain away from Brussels.

Instead, May sang the Rule Britannia chorus, as this plucky country sets sail into the world - and its old empire - to become a trading superpower.

Dwindling in the background is Europe: a valuable economic and anti-terrorism partner, sure, but a stagnant one, with stifling bureaucracy, interfering judges and too many migrants who don't count among the "best and brightest" that Britain actually wants.

May even had the cheek to offer some parting advice to the EU: loosen up, guys, she said. Try to celebrate your differences a bit more.

Oh, and by the way, screw us on the Brexit deal and we will shaft the entire continent by setting up the world's biggest tax haven on your doorstep, even if it costs us our entire social safety net and health system, so there.

No wonder the French and German ambassadors attending May's speech - sat next to each other by the Foreign Office in case they needed a friendly shoulder to cry on - were shaking their heads in anger by the end.

After wrestling for months with the alternatives, the government has decided to go for broke. Britain won't be a Norway or a Switzerland, swapping some rights and powers for a slice of what the EU offers.

It's out. Brexit definitely means Brexit.

The plan sounds simple - and there is no reason it's impossible.

But it presents huge, prickly problems to solve.

Central to May's plan is a free-trade agreement with the EU. Lacking that, stifling new trade barriers will rise between "global Britain" and its biggest trading partners. Even with the best will in the world (which, after that speech, there may not be), it would be remarkable if this ponderous, fractious continent could forge and strike a deal that satisfies everyone in even twice the two years that May allotted.

The EU's trade deal with Canada, literally the friendliest country in the world, was signed in October after a last-minute debacle when ornery Walloons managed to derail the whole thing for a couple of weeks and needed last-minute concessions to come to the party.

That deal took seven years from conception to signature. And it still won't come into effect until it's been passed by every European parliament.

Then there's the customs union. Britain has to be out of it, or it can't do its own trade deals. But it doesn't want to be too far out, otherwise it will add significant cost to the flow of goods and services to and from the continent.

The Prime Minister skated over the details for good reason: there's no obvious way to achieve what she wants.

And then … May surprised everyone by conceding that Parliament will get a vote on the final Brexit deal.

When pressed, she didn't say what would happen in the entirely possible scenario that a grumpy, Remain-stacked House of Lords, which can't be threatened with an election, turns it down.

Instead she affected a breezy optimism that they would wave it through.

And then there's the issue of EU citizens currently living and working in Britain. May said she wanted them to keep their rights. She didn't say what rights, but presumably she meant the rights to work and live here.

It's not hard to say, but it's a nightmare to put into practical effect within two years: more than 2 million people will need to be given a visa, or a passport, or whatever. They will have to prove their right to stay, they will have the right to appeal: those in the know simply throw up their arms and say it would be impossible, or at least stunningly expensive.

And then … and then … and then there's the Irish problem. Peace on that island was predicated on an open border between south and north. But it will now be the only land border between the UK and the EU, a line where the UK must police immigration and whatever new tariffs result from its new trade policy.

May said there would be a "practical solution". In other words, there exists some way to have a border with new, strict controls on people and goods, but that also lets them through more or less like before.

It's reminiscent of Fermat's Last Theorem - a mathematical conjecture whose creator in 1637 wrote confidently in the margin next to it, "I have discovered a truly marvelous proof of this, which this margin is too narrow to contain."

Mathematicians didn't manage to find this solution until 1995, 3½ centuries later.

Hopefully, the legal, political and practical hurdles raised by Britain's Brexit plan - of which I've hardly scratched the surface - will be jumped one by one, knocked over or otherwise dodged in considerably less than three centuries.

But, to (mis)quote another British prime minister who had to deal with angry Germans: this isn't the end, or even the beginning of the end, but only the end of the beginning.