The Hole in
the Budget

The Week the Line Crossed

You can argue with the two-year clock. Plenty of people do, and Part 2 of this series takes the argument seriously. What’s harder to argue with is the run of events that set it ticking, because most of them happened inside a single fortnight in September 2026 and all of them are on the record.

On 8 September, OpenAI announced that its agents had found a singularity in the three-dimensional Navier–Stokes equations, the mathematics that describes how fluids move. A smooth, well-behaved flow, pushed by a smooth force, can “blow up” and develop an infinity. The equations have been studied for nearly two centuries, and whether this can happen is one of the six open Millennium Prize Problems, each carrying a US$1 million reward from the Clay Mathematics Institute.^2,3

The numbers behind the result are what make economists sit up. OpenAI says the work involved “on the order of 10,000 concurrent agents” and took about 88 hours, with a further 17 hours to formalise the proof in Lean, a programming language that checks every logical step by machine.³ Quanta Magazine reported that the agents sent one another almost five million messages along the way.² The Next Web put the solving run at around 130 billion output tokens.⁴ Charles Fefferman of Princeton, who wrote the official statement of the problem, told Quanta, “I was thrilled that the problem was solved,” while crediting the human mathematicians Diego Córdoba and Luis Martínez-Zoroa, whose techniques the agents built on, as “the heroes of the story.”²

Two cautions belong here, because precision matters more than drama. OpenAI has said it won’t claim the prize, and whether a blow-up under an applied force satisfies Clay’s exact formulation is a question for mathematicians, not press releases.⁴ On air, Mostaque said OpenAI had won the prize. It hasn’t, at least not yet. The second caution: OpenAI’s Sébastien Bubeck put the computational cost at several million dollars.² This was a frontier lab throwing a mountain of hardware at one problem, not a tool anyone can buy.

Three days before the Navier–Stokes announcement, something quieter happened in a field that matters far more to governments. The Summer 2026 Metaculus Cup, a seasonal tournament for forecasting real-world events, resolved on 5 September with an AI system in first place. Bots took first, second and fifth; humans came third and fourth.⁵ The winner, a forecasting bot called Laertes, was built by Jeffrey Liang.⁶ A year earlier, an AI finishing eighth in the same tournament had been news.⁵

Here too the fine print is worth reading. The Cup’s scoring rewards forecasting on every question and updating often, which suits a tireless machine. In a controlled head-to-head run by Metaculus earlier in 2026, ten professional human forecasters still edged the ten best bots, by an average of 1.25 points per question across 99 shared questions.⁵ Back in July, after the spring tournament, Scott Alexander had already judged humans and AIs to be in “a statistical dead heat.”⁷ So the honest summary is this: AI has now won a major open forecasting tournament against the best humans, and the best humans still hold a thin lead when conditions are matched. Given the pace of the past twelve months, few people who follow these contests expect that lead to last.

Forecasting is what treasuries do. Every budget is a prediction about wages, employment, prices and growth. The thing that just started beating professional forecasters is the same thing those forecasts are failing to account for.

Where the Money Comes From

Strip a modern government back to its plumbing and you find the payslip. A person is hired; the employer withholds income tax from every pay run and sends it to the tax office; in many countries a second, dedicated tax on wages funds pensions and health care. That arrangement is so old and so reliable that it has become invisible. It works because, until now, almost all of the economy’s output needed people to produce it, and people had to be paid.

The United States collected about US$5.2 trillion in federal revenue in fiscal year 2025, more than half of it from individual income taxes.⁸ The Center on Budget and Policy Priorities breaks it down: individual income taxes 51 per cent, payroll taxes about a third, corporate income taxes about 9 per cent, and everything else, tariffs included, the remaining 7 per cent.⁹ Not all individual income tax falls on wages (capital gains and dividends are in there too), so RAND’s August 2026 estimate is the cleaner number: “About two-thirds of federal revenue comes from labor in the form of payroll taxes and federal income tax.”¹⁰

The payroll slice is the most exposed, because it is ring-fenced. US Social Security is paid from a tax on wages. The program’s retirement trust fund is already projected to run out early in the next decade; CBO now puts the date at 2032, and once it does, incoming payroll tax would cover about 77 per cent of scheduled benefits.¹¹ Those projections assume a labour market that looks roughly like today’s. Shrink the wage bill and the gap widens from both ends: fewer contributions coming in, more people relying on the system sooner.

Australia leans on wages harder still. Personal income tax has been the Commonwealth’s largest source of revenue since 1942–43, and the Parliamentary Budget Office has projected it climbing towards 54 per cent of total tax receipts by the early 2030s.¹² The 2026–27 Budget forecasts A$382.4 billion from individuals and other withholding taxes out of A$737.1 billion in total tax receipts, about 52 per cent. Company tax supplies about 21 per cent and GST about 14 per cent.¹³ The states add their own payroll taxes on top, and the retirement system is wage-linked as well: since 1 July 2025 employers have had to pay superannuation of 12 per cent on top of ordinary wages.²³ In Australia, a wage doesn’t just fund the government. It funds your old age.

The Treasury’s own long-range report says it plainly. “Salary and wages are the largest source of taxable personal income,” the 2026 Intergenerational Report notes. “Indirect taxes are projected to keep declining, which will increase the share of tax receipts from personal income taxes.”¹⁴ In other words, Australia’s plan for the next forty years is to become more dependent on taxing wages, not less.

What the Treasuries Are Counting

It would be unfair to say governments are ignoring AI. On Monday 21 September, Australia’s Treasury released the 2026 Intergenerational Report, its forty-year look at the economy and the budget, and AI ran right through it. Jim Chalmers called it “the biggest economic transformation of our lifetime.”¹⁵

Look closely at how AI enters the numbers, though. The report sets out productivity scenarios. The baseline keeps Treasury’s long-term productivity growth assumption of 1.2 per cent a year; an upside case runs at 1.5 to 2.0 per cent; a downside case assumes slow diffusion. On jobs, the report expects that “demand for labour is expected to increase in other areas,” that “many jobs will be redesigned,” and it reminds readers that after past waves of technology “the total amount of work available has not decreased.”¹⁴ Jobs and Skills Australia’s modelling, cited alongside it, puts about 4 per cent of today’s workforce at high exposure to automation and 79 per cent at low exposure.¹⁶

In that frame, AI is a tailwind. Faster productivity means a bigger economy, which means more tax collected through the existing system, which means a smaller deficit. In the material I could read, the report doesn’t model the other possibility: that AI changes who earns the income, moving it from the wage column, where Australia taxes most heavily and most reliably, into the profit and capital columns, or offshore.

The United States is further behind on paper. The Congressional Budget Office’s February 2026 ten-year outlook mentions AI as one of the factors in its projections, describing “faster productivity growth as generative artificial intelligence (AI) is more widely adopted” and AI-driven business investment.¹⁷ It doesn’t offer a separate analysis of what AI does to the labour share or to payroll tax receipts.

The people who are running those numbers sit mostly outside government. In July, the Budget Lab at Yale pushed three AI growth scenarios through the actual US tax code. Faster growth does lift revenue, by up to US$216 billion in 2030 in its rapid case. But the authors found that if AI growth skews towards capital, as many economists expect, the revenue gain is roughly half what it would be if wages kept their share. “The US taxes capital income at a lower rate than labor income,” they write, “and… large swaths of capital income (unrealized gains, retirement benefits, etc.) are excluded from the tax base.” Their conclusion is the sentence every finance minister should have pinned above the desk: “AI should not be expected to solve fiscal sustainability problems on its own, in part because it will likely not raise revenues as much as expected.”²⁰

And in September, economists at the Anthropic Institute (Anthropic is the company that makes Claude, the AI I write with) published three scenarios for the US economy to 2030. In the most extreme, AI does nearly half of today’s cognitive work, growth runs at 15 per cent a year, and the labour share of national income falls from 60 to 45 per cent.¹⁸ The authors are explicit that these are scenarios, not predictions, with no probabilities attached.¹⁹ But that 15-point drop in the wage share is precisely the variable public budgets are built on.

There’s a structural reason the official forecasts look the way they do, and it isn’t incompetence. Treasury models are built to project the economy forward from its past, and in every past technology shift the wage share bent but didn’t break. Steam, electricity and the personal computer all made workers more productive, and workers stayed the thing being paid. Forecasters are right to be cautious about assuming that this time is different. The trouble is that a forecasting method that can only see the past will be the last to notice when it is.

1. 20 Jul 2026Yale Budget Lab finds AI’s revenue boost shrinks by about half if income tilts to capital.²⁰
2. 31 Aug 2026RAND: two-thirds of US federal revenue rests on labour; AI could displace 10–15% of labour hours.¹⁰
3. 5 Sep 2026Metaculus Cup resolves with an AI forecaster in first place.⁵
4. 8 Sep 2026OpenAI announces its agents’ Navier–Stokes blow-up proof.²
5. Sep 2026Anthropic Institute publishes 2030 scenarios, up to 15% growth and a 45% labour share.¹⁸
6. 21 Sep 2026Australia’s IGR frames AI as a productivity upside for the budget.¹⁴

Figure 3 · The capability signals and the fiscal signals arrived in the same six weeks

The Sum That Won’t Close

Back in the studio, Bilyeu asked the obvious question. If the machines do the work, why not just pay everyone a basic income? Mostaque’s answer was arithmetic, not ideology. “The total tax base of America is $5 trillion,” he said, and a poverty-level basic income of roughly “$16,000 for every American” would cost about $5.1 trillion a year. “We can’t have UBI,” he concluded. “It doesn’t work.” Later he narrowed it: it’s the tax-funded version that isn’t real.¹

His breakdown of the tax base was loose (corporate tax brings in closer to half a trillion than the trillion he cited), but the headline holds. Federal revenue was US$5.2 trillion in fiscal 2025.⁸ The 2026 federal poverty guideline for one person is US$15,960.²² Multiply that by a population of roughly 340 million and you get about US$5.4 trillion. A poverty-line income for every resident would cost more than everything Washington collects, before a single soldier, road or Medicare claim is paid for.

Now add the twist that makes this a genuinely new problem. The usual answer is to tax the thing replacing the workers: a robot tax, or a levy on AI usage. Anthropic’s chief executive, Dario Amodei, floated exactly that in 2025, suggesting a slice of AI company revenue, perhaps 3 per cent, could go to government.²⁴ Mostaque’s objection is that the base keeps shrinking under the tax. Epoch AI has measured the price of reaching a fixed level of AI performance falling by between 9 and 900 times a year, depending on the task.²¹ A wage is sticky; it falls slowly, if at all. The price of machine intelligence falls like a stone. Tax a percentage of something that gets ten or a hundred times cheaper each year and you are taxing a melting ice cube.

So the problem, stated as plainly as I can:

1. The base is wages.

   Roughly two-thirds of US federal revenue and around half of Australia’s Commonwealth tax take rest on people being paid to work. Pensions and super ride on the same wage.

2. The forecasts treat AI as a bonus.

   Official projections model AI as faster productivity flowing through today’s tax system. The shift of income from wages to capital, which independent modellers flag, isn’t the central case.

3. The bill rises as the base falls.

   Every displaced worker stops paying in and may start drawing out. Payroll-funded systems feel it first.

4. The obvious replacement base deflates.

   Machine intelligence gets cheaper by orders of magnitude, and much of the compute and the profit sits in a handful of companies, often in another country.

Mostaque’s timeline is aggressive. He expects white-collar job losses above 10 per cent by around 2029, and described the coming change as “a sand pile that will start collapsing I think in two years.”¹ He may be early. People who build AI companies have every reason to think the future arrives fast, and plenty of careful economists think he is wrong. But notice that the fiscal problem doesn’t depend on him being right about the date. A tax system that rests on wages is exposed to any large, lasting shift from labour to capital, whether it takes two years or twenty. The only question the timing settles is whether governments redesign the system calmly or in a hurry.

Near the end of the conversation, Mostaque stopped talking about tokens and chips and said something simpler: that the time for these discussions is now, and that the strongest communities would get through whatever comes. The mathematician who had just watched his own discipline pass him by wasn’t arguing for panic. He was arguing for planning. It’s the one thing the budgets don’t yet contain.

Part 2 of this series asks what the shift will actually look like: why the jobs data can look healthy right up until they don’t, and what the evidence lets us predict about wages, prices and the economy that comes after.