corollary

Imagine building with LEGOs. You carefully construct the main structure—that's your core idea or theorem. A corollary is like a smaller, neat addition you can automatically build because of how the main structure is designed. It is not the main point, but it follows logically and easily from it.

Think of it this way: if you prove that all squares are rectangles (the main rule), then a corollary is that a square has four right angles—because rectangles do. It simply has to be true once the main statement is in place. The word comes from the Latin corollarium, meaning "a flower added as an adornment" or a small gift. It's a little extra truth blossoming from a larger one. You will often hear it used in mathematics, law, or philosophy, where tight logical connections are essential.

A corollary is a proposition that follows logically and often effortlessly from another established statement, such as a theorem or axiom. It isn't the primary point being proven, but rather a direct and inevitable consequence of that proof. Think of it as a specific "if…then" situation: If this first principle is true (the theorem), then this secondary fact must also be true (the corollary).

The term originates from the Latin corollarium, which referred to a garland or "a flower added as an adornment," suggesting something naturally growing out of a larger structure. While it is most at home in formal contexts like mathematics (e.g., "as a corollary to the Pythagorean Theorem…"), it is also used more broadly to describe any natural consequence of a policy or situation.

For example, if a company decides to prioritize absolute transparency (the main policy), a corollary might be the public disclosure of all executive salaries. Or, if a new law is passed strictly limiting carbon emissions (the main rule), a corollary could be a sudden surge in the market value of electric vehicle companies.

It is important to distinguish a corollary from a mere side effect or random result. A corollary isn't just something that happens after something else; it is something that follows from it. In strict settings (like math or formal logic), it must be true if the starting statement is true. In everyday writing, the word is sometimes used a bit more loosely, but it still suggests a close, natural link—not a surprise. When you hear the word "corollary," think of an insight that blossoms from a larger idea.