You solved the Riemann Hypothesis. Now do your taxes.

Say you’re a mathematician in Romania and one morning you finish a proof that has held out since 1859. Two years of peer review later, the Clay Mathematics Institute calls to say the million dollars is ready.

Most people would guess you keep most of it, minus some tax somewhere. The realistic number is closer to two thirds, and the reason is a treaty from 1973 that doesn’t say what everybody assumes it says.

The US takes 30% first

The Clay Institute is a US foundation. The US treats prize money from a US payer as US-source income, and it doesn’t matter where the winner lives. For a non-resident the default withholding is 30%, and it comes off before anything crosses the Atlantic. Universities that hand awards to foreign recipients describe this as close to automatic.

So $300,000 goes to the IRS. The only question worth asking is whether you can get it back.

The treaty doesn’t help

Romania and the US have had a double-taxation treaty since 1973. Every discussion of this kind of problem assumes the treaty steps in at this point. It’s worth opening the thing, because it’s public and it’s short: the text is on the IRS site.

It has 28 articles. Article 19 is Teachers, Article 20 is Students and Trainees, Article 21 is Relief from Double Taxation. There is no article for “other income”. Modern treaties nearly always have one, a catch-all that hands anything not covered elsewhere to the country where the recipient lives. The 1973 text doesn’t have it.

Article 20 is the only place an award is mentioned at all, and it exempts a grant, allowance or award received by someone “temporarily present in that other Contracting State” in order to study, train or do research. Temporarily present in the United States. Your mathematician is in Iași. Article 20 does nothing for them.

Article 4(1) then sets the default, and it’s the sentence that settles it:

A resident of one of the Contracting States may be taxed by the other Contracting State on any income from sources within that other Contracting State and only on such income, subject to any limitations set forth in this Convention.

The limitations are the other articles. None of them cover this. The US keeps the 30%.

A tax lawyer might still find something, though it would probably be an argument about whether the prize is really US-source rather than anything to do with the treaty. That’s what you’d be paying one to do. But the assumption most people start from, that the treaty protects you, isn’t in the document.

What Romania does with the rest

Romania’s Fiscal Code taxes prizes at 10%, with a symbolic 600-lei exemption and no social contributions. There’s an argument to be had about whether this even counts as a prize. The chapter defines prizes as winnings from competitions and commercial promotions, and you didn’t enter a competition, you sat in a room and thought hard for a decade. So ANAF might file it under “income from other sources” instead.

In the default case the argument barely matters. Romanian tax at 10% on a million dollars is about $100,000. You’ve already paid $300,000 in the US, and US tax credits against the Romanian bill up to the Romanian amount, so the credit covers the whole thing and ANAF collects nothing. You lose the difference. Romania doesn’t refund it and the US doesn’t give it back.

CASS is the loose end. If the award lands in “other sources” the health contribution applies, on a base capped at 24 minimum wages, which in 2026 is 97,200 lei, so the contribution tops out at 10% of that: 9,720 lei, around $2,160. CASS is a contribution rather than an income tax, so whether the US credit reaches it at all is a separate question, and not one I’d guess at.

You file either way. The payer is abroad, which makes the Declarația unică yours to submit by 25 May of the following year, converted at the National Bank’s average annual rate, even in a year when the credit means you owe nothing.

What the advice costs

Nobody handles this alone with a million dollars arriving from abroad. A Romanian tax consultant runs €150–300 an hour. A written opinion on the classification question plus the Declarația unică is somewhere around €2,000–5,000. On the US side an international tax attorney at $400–800 an hour reviews the position and prepares a W-8BEN, maybe 10–15 hours, so $5,000–10,000. Call it $8,000–15,000 if nothing goes wrong. These are market rates rather than quotes, and the spread is wide because the work is.

Going after the withheld $300,000 costs a lot more. It means a US non-resident return and an argument with the IRS, which is $15,000–40,000 of attorney time. According to Article 20, the odds aren’t good. If ANAF audits you in parallel and rejects your classification, contesting that through administrative appeal and then the fiscal courts adds another €20,000–50,000 over several years. Put a Big Four firm on top to coordinate both sides and $60,000–100,000 is a plausible bill. Romania doesn’t let you deduct any of it.

Where you land

Taking 4.5 lei to the dollar.

You accept the withholding. $300,000 to the IRS, nothing to ANAF because the credit covers it, $12,000 or so in fees. You keep about $688,000.

You fight it. Three years and $80,000 in lawyers, which is 8% of the prize. If the source argument works you claw some back. If it doesn’t, and on the treaty wording it probably doesn’t, you’re at roughly $620,000.

You give it away. US law excludes recognition awards from taxable income if you never touch the money and designate it to a qualifying institution. This one doesn’t depend on the treaty at all, which is why it works. Nothing withheld, nothing taxed, you keep zero, a research institute gets the full million. It still costs a few thousand dollars to draft the designation correctly.

Perelman. In 2010 Grigori Perelman turned down the Poincaré prize outright. No tax, no fees, no money.

Move first. Some winners of large foreign awards change tax residence to a zero-income-tax jurisdiction before the payout. It does nothing about the US withholding, which is the part that actually hurts here, and tax authorities treat conveniently timed residency changes with the suspicion they deserve.

The part I keep coming back to

The proof plays no part in any of this. What decides the number is a document signed in 1973 between the United States and what was then the Socialist Republic of Romania, drafted by people who were thinking about shipping profits and diplomatic salaries, and who left out the one article that would have mattered fifty years later.

The treaty is twelve pages. Read it before you pay anybody to tell you what’s in it.

Curiosity, not advice. I’m not a tax advisor, the fee figures are rough market estimates rather than quotes, and anyone actually expecting a million-dollar award should hire one professional in Romania and another in the US before the money moves.

Have fun with the proof. ;-)