Graham's number is an extremely large number that arises in the field of mathematics, specifically in the study of Ramsey theory. It is named after mathematician Ronald Graham, who used it to solve a problem related to the coloring of edges in a hypercube. What makes Graham's number unique is that it is so large that it cannot be expressed using conventional notation, such as powers or even power towers. Instead, it is defined using a special notation called Knuth's up-arrow notation, which allows mathematicians to represent very large numbers in a manageable way.