Even for transferring knowledge, it depends a lot on what knowledge you're trying to transfer, and to whom. In scientific writing, the more pop-science the goal of the article, the more conversational the style should be, and vice-versa. In a paper by someone in my field written for other people in the field, a pop-science conversational style isn't helpful, and would increase the cognitive load. In that case, I want clarity, precision, and accuracy, which is often helped by using a more specialized language.

This has been one of the main changes in science writing from earlier centuries. If you read 17th-century mathematics, it's actually trying to explain it all in a jargon-free conversational style, written as if you were having a parlor conversation about numbers. "Consider three whole numbers, such that the sum of the square of the first two equals the third", etc. This does not scale well and is error-prone.

I wouldn't say that in conversation. I'd say something like: "consider three integers, with a squared plus b squared equals c".

And in writing, I'd go for something like: "consider a, b, c ∈ ℤ, such that a² + b² = c". Which isn't far off.