The art of reasoning about the unknown with symbols — letting a letter stand for a number not yet known and stating laws true for every number rather than for one sum: the leap that turned arithmetic into a science of relationships and structure, named and systematized by al-Khwarizmi in ninth-century Baghdad and now the grammar of nearly all science.
Arithmetic answers one question at a time. Two plus three is five, and that is the end of it. Algebra does something stranger. It asks what times itself makes sixteen, and lets you call the missing number x before you know what it is. That single move — reasoning about a number you do not yet have — turned counting into a universal language of relationships. It is why a planet's orbit, a bridge's load, and a coded message can all be written as equations and solved. The word itself is Arabic, from al-jabr, the title of a book written in ninth-century Baghdad. The idea is older, and more global, than any one civilization.