I just provided a source showing that two plus two does not always equal four. It took considering of the fundamentals to do it. The proof is not valid in all situations. In fact, according to the link, in most models it is not valid.

Rather than invoking authority and relying solely on sooty old proofs, the fundamentals must be constantly challenged and understood. Challenges to status quo knowledge help to demonstrate its limits and flaws. This is why it is valuable to read about people who had to consider the fundamentals from the ground up. They may provide insight someone indoctrinated with an alternative educational background could not provide, and may spark a deeper understanding of the limits of a supposed truth.