Why it cannot count, and what to do instead

Two separate problems

People lump these together and they have different causes.

Counting characters fails because of tokenisation. The model never sees letters. Asked how many times r appears in “strawberry”, it must reason about spelling from what it has read about spelling, rather than by inspecting the word. Sometimes that works. It is not a look-up.

The same applies to reversing a word, counting words in a paragraph, producing exactly 100 words, or finding all words in a text starting with a given letter. Each asks for an operation on units the model does not perceive.

Arithmetic fails for a different reason. There is no calculator inside. Multiplication is not performed; it is predicted. And the digits of a long number are split into tokens by frequency, not by place value, so 4,871,203 might arrive as three chunks that do not align with hundreds, thousands and millions. Column arithmetic, the method every human uses, is unavailable.

The practical shape: single-digit and small sums are usually right, because they appeared constantly in the training text. Multiplying two five-digit numbers is frequently wrong, and wrong in the confident, well-formatted way. Percentages of large numbers, compound interest over many periods and unit conversions with awkward factors all sit in the danger zone.

Why the errors are so plausible

A person doing long multiplication badly produces an obviously mangled answer. A model produces an answer of the right magnitude, the right number of digits, and the right shape: wrong in the middle.

That is worse than an obvious error, because it survives a glance. If you are reviewing a document containing model-produced figures, the sanity check most people apply (does this look about right) is precisely the check this failure mode passes.

The fix, which is not a better prompt

Give the arithmetic to something that does arithmetic.

Ask for code, then run it. “Write Python that computes this” produces a short, readable program. Python does the sum exactly. You can check the program’s logic, which is a far easier review task than checking a number. Python is free, and if you have no installation, a free Google Colab notebook runs in a browser on a phone.

Use a tool-enabled assistant. Most major products now execute code or call a calculator when a question needs it. When the interface shows that a tool ran, the arithmetic is genuine. When it does not, it is predicted. Look for the difference: it is usually visible in the response.

Use a spreadsheet for anything with repeated structure. LibreOffice Calc is free and exact. Ask the model for the formula, not for the answer.

The underlying principle is worth stating on its own, because it generalises well beyond arithmetic: give the deterministic part to a program and the judgement part to the model. Deciding which figures matter, what the comparison should be, and how to present it: that is where a model helps. Computing the number is not.

Where reasoning models change the picture, and where they do not

Models trained to work through problems step by step before answering are substantially better at mathematics. They score highly on competition problems that older models failed outright. This is real progress and it is not marketing.

But two cautions. First, they are still predicting tokens; the improvement comes from doing the working in text where each step is short and well-supported, not from acquiring an arithmetic unit. Long multiplication of arbitrary large numbers remains shaky. Second, they cost more and take longer (often ten to sixty seconds) which is poor value for a task a spreadsheet does exactly and instantly.

A checklist for numbers in any model output

• Did a tool run, or was the number generated? If you cannot tell, assume generated.
• Is the magnitude plausible against something you know independently?
• Do the parts sum to the total? Model-produced tables of figures frequently do not, and this is the fastest single check available.
• Are percentages of a stated base actually that percentage of that base?
• Where a figure will be acted on, recompute it yourself once.

That last one sounds tedious and takes under a minute. It has caught errors in board papers, invoices and dosage calculations, and each of those has appeared in reporting since 2023.