Lemma (mathematics) facts for kids

In mathematics, a lemma is like a small, helpful step in a bigger puzzle. It's a statement that is proven to be true, and then this proven statement helps to prove a much more important idea called a theorem. Think of it as a mini-proof that builds up to a larger, more complex proof.

What is a Lemma?

A lemma is a proven idea that acts as a stepping stone. It's not usually the main goal of a mathematician's work. Instead, it's a tool or a building block. Once a lemma is proven, mathematicians can use it to make proving a bigger, more important theorem much easier. It helps break down a large problem into smaller, manageable parts.

Famous Lemmas in Mathematics

Even though lemmas are often seen as small steps, some of them have become very famous and important. They might have seemed simple at first, but they turned out to be crucial for understanding big ideas in mathematics. Here are some examples:

• Bézout's lemma
• Dehn's lemma
• Euclid's lemma
• Farkas' lemma
• Fatou's lemma
• Gauss's lemma
• Greendlinger's lemma
• Itō's lemma
• Jordan's lemma
• Nakayama's lemma
• Poincaré's lemma
• Riesz's lemma
• Schur's lemma
• Schwarz's lemma
• Urysohn's lemma
• Yoneda's lemma
• Zorn's lemma

These lemmas show that even small, simple-looking ideas can have a huge impact. They are vital parts of the mathematical theories they belong to.

Images for kids

• 

  A robot for kids