On September 11, 2026, Fields Medalist Terence Tao published a blog post. After personally reviewing the mathematical reasoning of several AI models, he described what he found as a "severe misalignment" — and The Economist put the same topic on its cover that same day.
What makes Tao's critique notable isn't the fact that AI gets things wrong. That much is already well known. What matters is the structure of the errors. At each individual step, the AI uses mathematically valid language — but somewhere between the steps, the logical connection breaks down. The overall path looks plausible, even though it has already gone wrong at some point along the way.
The first question this raises is whether this error pattern is unique to mathematical research, or whether it operates the same way in the calculations people hand off to AI in everyday work — taxes, fees, ratios, inventory valuation.
How AI Gets Math Reasoning Wrong
The way an AI language model handles a math problem is different from the way a calculator computes. A language model has learned, from a huge volume of text, how mathematical expressions are typically used. As a result, it's good at generating text that looks like mathematical reasoning — but whether that text actually holds up mathematically is a separate question.
This is where the misalignment Tao points to comes from. The AI writes something that looks like a mathematical argument. Each sentence follows proper mathematical notation and rules. But the logical link between one sentence and the next — the claim that B follows from A — sometimes doesn't actually hold. This is different from a typo in a formula or an arithmetic slip. The reasoning path itself is wrong, but that wrongness doesn't show up on the surface of any individual step.
In mathematical research, this is a serious problem. For a proof to be valid, the logical connection between every single step has to hold. If even one breaks, the whole proof collapses. If an AI-generated path breaks at a point where the connection isn't visibly wrong, the error goes undetected until an expert re-verifies the entire chain.
Where the Same Pattern Shows Up in Everyday Calculations
At first, it seemed reasonable to assume this error was confined to highly specialized math problems. It happens in proofs or partial differential equations — complex work — while everyday calculations are far simpler, so surely they're a different matter.
That assumption turned out to be wrong.
The most common form this pattern takes in everyday calculations is a calculation where several rates are applied in sequence. When multiple rates act one after another, the base value each one is applied to shifts — and so does the result.
Take calculating take-home revenue after both a 15% platform selling fee and 10% VAT. Ask in plain language, and the AI will dutifully calculate the fee and the tax separately — but whether the tax is based on the amount before or after the fee is deducted may not match what you actually meant. Each individual percentage calculation is correct on its own. But change the base value or the order of operations, and the final number changes. If the difference comes out to only a few percentage points, intuition alone won't catch it.
The same pattern shows up when valuing inventory under FIFO, when accounting for the fact that a loan's principal balance shrinks over the life of an installment plan, or when calculating a progressive tax with different rates applied bracket by bracket. Each individual step of the calculation isn't wrong. What changes is the connection between steps — which value the next step is built on. That's exactly the error structure Tao identified.
When the Error Goes Unnoticed
The more interesting part of Tao's post isn't the error itself — it's the question of when the error goes undetected.
If the person reviewing AI-generated reasoning doesn't have expertise in that field, it's hard to judge whether the path is sound. When each step looks plausible and the final result falls within the expected range, there's no reason to suspect anything is wrong.
In everyday calculations, this narrows down to a more specific condition: have you ever done this particular calculation by hand?
A calculation you've done by hand gives you a felt sense of roughly what range the answer should fall in — an intuition for what a similar case should produce. If AI hands you a number well outside that range, you'll question it immediately. But if it's your first time doing that calculation, you have no such intuition at all. Without knowing what range the answer should fall in, even a wrong number from AI can look perfectly plausible.
The first time you calculate self-employment income tax, the first time you work out the relationship between cost ratio and margin, the first time you sort out foreign-currency translation gains and losses — even if the AI walks you through the process in friendly detail, actually knowing whether that process is correct requires that you already understood the calculation before the explanation. The feeling of having followed and understood AI's explanation is not the same thing as verification.
A Practical Filter
The answer to the original question — whether AI's math errors show up the same way in everyday calculations — is yes. But the more useful answer is narrower.
Treating every AI calculation with suspicion defeats the point of using AI at all. A more realistic approach is to draw the line for how much to trust a result not by the type of calculation, but by the user's own prior experience with it.
For a type of calculation you have no prior experience with, doing it by hand once before handing it to AI is, practically speaking, the only real form of verification. If AI shows you the result first and explains afterward, you end up accepting the explanation to fit the result. Only when you already have a result you calculated yourself do you have something to check AI's answer against.
Asking AI first and learning the result from it, for a type of calculation you're doing for the first time, runs the order backward. In that order, AI becomes the standard, and the person simply follows along, assuming the standard is correct. Checking an AI calculation with no independent standard to check it against looks like verification, but it isn't one.
