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Simple answer: Math. Linear algebra and calculus, etc are used heavily in AI. A neural network “learns” because it more or less puts points on a graph and puts a line between them, allowing it to predict if a new, unknown point is above or below the line and tell you if its in class one or its in class 2 (the networks dealing with classes are called supervised classification learning models). There are other types of networks and very many different ways to implement them, but thats the basic logic.