Cantor's diagonal argument is a mathematical proof that shows there are different sizes of infinity. It demonstrates that the set of all real numbers is larger than the set of natural numbers. By assuming you can list all real numbers, Cantor constructs a new number that differs from each number in the list, proving that not all real numbers can be included in any list. This argument was developed by Georg Cantor in the late 19th century. It highlights the concept of uncountable infinity, which contrasts with countable infinity, such as the set of natural numbers.