How Claude works, without a single equation
One mechanism sits underneath every strange thing you have noticed, and you can understand it in five minutes without meeting a formula or a diagram.
Nobody needs the maths. What people need, when they ask how Claude AI works, is an explanation accurate enough to cover the things they keep noticing: the reply that changed when they asked the same question twice, the confident detail about a company that turned out not to exist, the way it forgot everything overnight. All of that comes from one mechanism, and the mechanism is less mysterious than the vocabulary around it.
It predicts a plausible continuation
Claude does not look an answer up. It produces text a piece at a time, and each piece is chosen because it is a plausible continuation of everything that has come before it, including your question. Stack enough plausible continuations together and you get a paragraph that reads as though someone sat down and thought about it. Everything odd you have noticed about Claude follows from that one fact.
Ask the same thing twice and you will often get two different replies, which unnerves people expecting a calculator. If the system is choosing a plausible next piece instead of fetching a stored one, more than one continuation qualifies, and it does not always take the same route. Anthropic's published advice on cutting down errors suggests running a prompt more than once and comparing what comes back.
Two different kinds of knowing
There is a distinction here that clears up more confusion than anything else I teach. What Claude absorbed during training is one thing: an enormous quantity of text, taken in once and fixed, with no way for the model to consult or check it. What it can see right now is a separate thing: the context window, meaning everything present in the current conversation, your messages, any documents you have uploaded, results from tools, and its own reply as it is being written.
Training is what it learned. The context window is what it can currently see. Nothing from the second carries into the next conversation, which is why a fresh chat starts blank and why pasting the brief again is not a failure on your part. A larger window is also not a licence to tip everything in, since more material is not automatically better material. If you want that idea in detail, what a context window holds is where the real limits live.
Why it cannot check a fact on its own
Left to itself, Claude has no way of verifying anything. It cannot open your contract, ring the supplier, or read this morning's announcement. Give it a search tool or an uploaded file and it can, because the material is then in front of it. Without one, a question about a specific fact gets a plausible-sounding answer, and plausible is not the same thing as correct.
The practical rule that falls out of this is unglamorous. If accuracy matters, supply the source. Do not ask what the renewal terms are; paste the agreement and ask what the renewal clause says. Skipping that step is where most confident mistakes begin.
What this changes about your working week
Once the mechanism is clear, the habits follow without much argument: supply the material rather than assuming it is known, expect some variation between runs, start a fresh conversation when the subject changes, and read anything carrying a number or a name yourself. None of that is difficult. It is just not what people do when they meet a chat box for the first time.
This is the least commercially useful thing I teach, because a team that understands it properly needs me for a good deal less.