Six numbers that failed their own arithmetic

1. A forecast with no source at all

A widely circulating figure put the semiconductor market at $1.51 trillion in 2026, up 90%, with memory surging around 250%.

The base it was implicitly growing from is this. The industry did $791.7bn in 2025 on a WSTS basis, up 25.6% from $630.5bn, a figure independently corroborated by an SEC filing.

So the claim is that the market reaches 1.91 times the actual 2025 base in a single year.

Our research found zero corroboration for it across every source checked, and it contradicts every other 2026-adjacent estimate by roughly a factor of two.

This is the rarest category here and by far the most dangerous. It is not a miscalculation. It is a number with no provenance at all, circulating because it has been repeated often enough to sound familiar. Nobody computed it wrongly. Nobody computed it.

The check for this class is not arithmetic. It is asking who published it first, and refusing to use the figure until you get an answer. A number that everyone cites and nobody sources is not a consensus, it is an orphan.

2. A share that was measuring two different things

One note stated renewables at 43% of generation and described it as structural dominance. The analysis section of the same note said renewables and nuclear together reached 43%.

Only one of those can be true, and you can settle it without leaving the document.

Per the same IEA-sourced generation mix, place 43% beside coal at 34% and gas at 21%. That is 98% before nuclear is counted at all. Add nuclear and the total exceeds 100%, which is impossible.

So the summary was wrong and the detail was right, which is the wrong way round from what everybody assumes.

When a takeaway and an analysis disagree, the arithmetic adjudicates, not the takeaway. The takeaway is what gets quoted, pasted into decks and carried into other documents, so the error travels while the correction sits three pages down.

3. A multiple that was not one

Data-centre electricity demand was described as doubling. The figures behind that description were 415 TWh rising to 945 TWh, which is 2.28 times.

Calling it a doubling understates the increase by roughly a quarter, in the direction that makes the grid problem look more manageable than it is. Anyone planning generation capacity against "doubling" is under-building.

This class survives for linguistic rather than numerical reasons. "Doubled", "tripled" and "surged" are the least-checked words in analytical writing, because they read as description. A reader scanning for numbers to verify does not stop at "doubled", and every one of those words is an arithmetic assertion wearing a narrative costume.

4. A percentage that never met its denominator

Secondary copper was given as about 20% of refined supply in one section of a note. Two other sections of the same note gave 4.5 Mt of secondary refined copper and a 27,000 kt world refined total.

Divide 4.5 by 27.0 and you get 16.7%. For 20% to hold, the refined base would have to be 22.5 Mt, a figure the note also contradicts elsewhere.

The percentage and its denominator sat several pages apart, which is exactly why nobody reconciled them. Human checking is triggered by proximity. Two numbers in the same sentence get compared automatically. Two numbers forty paragraphs apart do not.

A ratio and its base must be checked even when they never appear near each other. This is one of the two failures here that no automated check catches. It still has to be done by hand, by someone who has decided to go looking.

5. A margin that did not reconcile against its own numerator

Per BHP's own filings, its EBITDA margin was stated at 54%, printed beside EBITDA of $29,016m and revenue of $55,658m. Those two figures give 52.1%.

The likely explanation is entirely benign, and worth stating because it shows why this class is subtle rather than sloppy. The underlying-EBITDA margin almost certainly excludes third-party trading revenue, which would make the real denominator smaller and the 54% correct on its own basis.

The note never said so.

A margin whose base is unstated is not a margin. It is a claim. Until the base is named it cannot be compared with a peer, which is the only reason anyone quotes a margin. The number may well be right. It is unusable either way.

6. A decline that was a rise

Steel output was described as having fallen 0.9% from 2023, beside figures of 1,882.6 Mt and about 1,850 Mt. That pairing is a rise of 1.76%.

This one is not a magnitude error but a sign error. The stated rate and the stated tonnages pointed in opposite directions, and the sentence carried both without anybody noticing.

Magnitude errors are embarrassing. Sign errors invert conclusions, and anything built on this one would have been reasoning about a contracting industry that was in fact growing.

A coda on survey findings

One more, from a different family, because it is a category error rather than a calculation error.

A published headline stated that 12% of a named sector had reached a particular AI-deployment stage. On the survey's own base, that claim rests on roughly three respondents.

The number is not wrong. Twelve per cent of that subsample really did report it. It is simply not a finding. A percentage of a very small base describes those respondents, not the sector they were drawn from, and presenting it as a sector statistic is a different kind of mistake from getting the sum wrong. No amount of arithmetic checking catches it, because the arithmetic is fine.

The defence is to publish the base alongside every percentage, and to distrust any share quoted from a survey without one.

What the six have in common

None needed an external source to disprove. Every one was contradicted by figures already present in the same document, which is what makes them findable and what makes not finding them inexcusable.

They cluster where the sentence sounds like description. Phrases like "doubled", "fell slightly", "around a fifth" and "a mid-fifties margin" do not read as claims requiring verification. All of them are claims, and all of them are checkable in seconds once you notice.

The error direction is not random. The doubling understated a grid problem. The 43% flattered renewables. The margin rounded upward. The steel figure supported a slowdown narrative.

Numbers tend to fail in the direction of the argument they support. That is not dishonesty. A figure agreeing with your thesis produces no friction, so nothing prompts the second look, while a figure that contradicts you gets checked immediately. A figure that helps your case deserves a second check precisely because it will not get one naturally.

Distance defeats attention. The copper percentage and its denominator were pages apart. So were the steel rate and its tonnages. Proximity is what triggers a human to check, and nothing about the structure of a document guarantees it.

What now runs automatically

Four of these six are now mechanical checks rather than good habits: a stated rate of change tested against its own figures, a claimed multiple tested against the pair it describes, a set of shares tested against 100%, and every figure tested against the source it came from. That class of error now fails loudly instead of depending on the attention of whoever happens to be reading.

Two are not automatable and are still done by hand. A percentage reconciled against a denominator sitting paragraphs away, and a margin reconciled against its own stated numerator and denominator, or its base explicitly named.

A rule you can forget is worth less than a script that fails loudly. The six numbers above are the evidence for that, and four of them were ours.