Arthur Cayley was a really smart man who lived a long time ago. He was born in 1821 and lived until 1895. He was a mathematician, which means he was really good at math. He did lots of important work in math, and he is known for some big ideas called "group theory" and "matrix theory."
Group theory is all about things that can be moved or changed around in specific ways. This might sound a little bit like something you would do when you play with toys or building blocks. Matrix theory is all about using numbers in special ways to solve problems. It's kind of like solving puzzles or riddles.
Arthur Cayley was a really important mathematician because he worked on things that were really hard to understand. He also taught other people about math, and helped others learn things that they might not have been able to learn on their own.
Even though Arthur Cayley was really smart, he was also a regular person. He had a family, and he liked to do things like take walks and read books. He just happened to be really good at math, which made him a special person in the world of math and science.