“Here’s to the crazy ones. The misfits. The rebels. The troublemakers. The round pegs in the square holes. The ones who see things differently. They’re not fond of rules. And they have no respect for the status quo,” ran the eulogy of Apple’s Think Different television advertisement in 1997. In the same spirit, here’s to Margrethe Vestager.

The EU competition commissioner insists she is not deliberately making trouble by deciding this week that Ireland should levy €13bn in taxes that it allowed the company to underpay over a decade. “No rules have been changed - not one,” she retorted to the accusation that she is ripping up international tax treaties and diverting US tax revenues to Europe. She looked unperturbed by the rumpus.

Ms Vestager seems to have taken lessons from Apple about presentation. Her original 2014 complaint against the company was jammed with details. This week’s update was pared down and clean, making the argument simply. Steve Jobs might have appreciated the elegant Danish design, although the content infuriated the US and Irish governments - and Tim Cook, Jobs’s successor as Apple chief executive.

Its simplicity is both a weakness and a strength. The weakness is that it is hard to believe it will hold up in court, where the argument is heading. There is something a bit too neat about the way Ms Vestager sliced through the Gordian knot of transfer pricing and tax residency with one stroke by declaring Apple’s three-decade-old arrangements with Ireland invalid.

Corporate tax is a complex matter: intellectual property can be moved to offshore locations and exploited at arm’s length according to intricate related-party formulas; sales in one country can become revenues in another; US companies can invert themselves to somewhere else. If any tax arrangement that beats others can be outlawed as selective state aid, a lot of tax lawyers are out of work.

Enter Ms Vestager, with her plan to make Ireland retrieve €13bn, and to let other EU countries stake their own claims to the money …Her boldness will change the rules of global taxation if it survives

the legal challenges

Ms Vestager’s strength is that none of that makes much sense, or feels justifiable, to individual taxpayers. “If my effective tax rate would be 0.05pc, falling to 0.005pc, I would have felt that maybe I should have a second look at my tax bill,” she said. Apple insists that it paid $400m in taxes in Ireland in 2014, but her rhetoric was powerful.

Apple sounded quite flustered as it protested that things are not as they appear. On tax matters, it resembles the nerdy PC character in its ‘Get a Mac’ campaign in the 2000s, with Ms Vestager as the cool, cocksure Mac. The more it explains that it has deferred taxation, not avoided it, the more conventionally corporate it looks.

Its tax challenge is straightforward enough, and is common to a lot of US companies. It produces most of its value - its intellectual property and distinct approach to technology and design - in California. Under existing global tax treaties, it could legitimately channel most profits from around the world back to the US through royalty fees on overseas sales.

It does not want to do this because that would involve paying up to 35 per cent tax in the US on the profits compared with Ireland’s 12.5pc rate. The simple answer, as Ms Vestager points out, would be to pay the latter instead; Apple is structured so it could easily do so. Its Irish subsidiaries hold royalty rights for European sales and most profits flow there.

But Ireland used to offer a twist: the right to form companies that were not tax resident there or in the US. Rather than pay taxes immediately, Apple could defer them under US tax law. Hence its anger about being accused of tax dodging: where others see billions in unpaid Irish taxes, Apple and the US government see future US ones. Apple is not, overall, an aggressive tax avoider: it paid $19.1bn in taxes last year.

It is not quite so simple, though. Apple has made provisions for deferred US taxes on about half of the $215bn in cash and equivalents it held overseas in 2015. It is waiting for the US tax rate to fall before it repatriates this money to shareholders, but this could be a long time. It may never send back the rest: US companies often reinvest overseas cash in growth or acquisitions.

US corporate taxation is especially peculiar and hard to grasp and is painfully dysfunctional. The US government keeps on trying to pass tax reforms, and the details of Apple’s Irish tax structures first emerged publicly during a Senate committee investigation three years ago. The Senate identified US companies’ overseas cash as a tax target for the US not the EU.

Enter Ms Vestager, with her plan to make Ireland retrieve €13bn, and to let other EU countries stake their own claims to the money. Since no one else moved, she gained first mover advantage, and state aid law has given her extraordinary legal powers. It is an audacious, revolutionary and surprising move, but that was Jobs’s style too.

Her boldness will change the rules of global taxation if it survives the legal challenges. Bill Gates, Microsoft co-founder, used to get irritated that Apple was hipper than his own company but arguing with public opinion got him nowhere. In Ms Vestager, Apple faces a cool opponent.

john.gapper@ft.com

Published in Dawn, Business & Finance weekly, September 5th, 2016