The Story of Fermat’s Last Theorem

I first learned of Fermat’s Last Theorem from a professor in an undergraduate calculus class at the University of Washington and have been interested in it ever since, partly because the problem appears so simple to prove and partly because of the mystery surrounding its origin. Fermat is alleged to have scribbled its formulation in the margin of his copy of Arithmetica, stating that he had found a wonderful little proof, but that it couldn’t fit in the space provided by the margin. That was in 1637. It wasn’t until 1995 that mathematician Andrew Wiles — after having spent 7 years working on the problem in secret — was finally able to come up with a complete proof — 358 years after its conjecture. Mathematicians now believe Fermat was mistaken in his method of proving the problem because the techniques finally used to crack it weren’t even invented until hundreds of years after Fermat’s death. Fermat’s last theorem is similar in form to the Pythagorean Theorem. In particular it posits that  a^n +b^n = c^n cannot be satisfied for any integer ‘n’ greater than two.

Because I have been interested in the problem for some time I was happy to find this documentary by Simon Singh, which I found quite entertaining and moving:

Tax Havens Aren’t So Havenous After All

I was surprised to find out the following requirement regarding tax havens after NPR’s Planet Money incorporated two companies in locations traditionally anointed that status: Belize and Delaware. You can learn more here and here.

“It turns out that despite all the big red letters advertising absolute confidentiality, I am legally required to declare these companies to the IRS. Even if, as is true in my case, the company has done absolutely nothing — just exists in some papers.”

You hear about the Cayman Islands, Bermuda and British Virgin Islands being called tax havens. That term makes it sound like if you can figure out how to get your money there, you suddenly don’t have to pay taxes. But of course that is not true. If you are an American earning income, you do have to pay taxes. And in fact the IRS wants you to report a lot about what exactly it is you are doing offshore.

In fact the required paperwork can take something on the order of 150 hours to fill out and file according to the story. There are, of course, still benefits to incorporating offshore:

So what’s the benefit of doing things offshore? Well, if you are determined to evade taxes, if that’s your goal, then creating a complex financial structure in a tax haven will certainly make it harder for the government to catch you.

Harder, but not, according to Buckley and Gottfried, impossible. An audit could trip you up, they say, and then of course there are the IRS’s usual informants.

And US corporations including Google, Facebook, Oracle, and Microsoft have setup overseas offices in order to “save” billions. I use quotation marks around the word save because, as mentioned, US citizens/corporations have to pay US taxes. What’s really going on is a deferral of taxes until the income is brought back to the US, if it is brought back. Though sometimes so-called “tax holidays” are lobbied for by these corporations. Here is a preview:

In October, Drucker reported that Google had saved $3.1 billion in taxes in the past three years by shifting the majority of its foreign profits into accounts in Ireland, the Netherlands and Bermuda using financial techniques called “the Dutch Sandwich” and “the Double Irish” arrangement. Basically, he says, Google credited its Irish office with the majority of its non-U.S. sales revenue — and then shuttled that money through various subsidiaries located in Ireland and other countries to save billions in taxes.

There is more here.

Finally, the United States is itself a type of tax haven. From Investopedia:

In terms of capital gains, non-resident aliens are subject to no U.S. capital gains tax, and no money will be withheld by the brokerage firm. This does not mean, however, that you can trade tax free – you will likely need to pay capital gains tax in your country of origin. In terms of dividends, non-resident aliens face a dividend tax rate of 30% on dividends paid out by U.S. companies. However, they are excluded from this tax if the dividends are paid by foreign companies or are interest-related dividends or short-term capital gain dividends. This 30% rate can also be lower depending on the treaty between your home country and the U.S., so it is important that you contact your brokerage firm to verify the rate.