Many clever AI systems are built on discrete mathematics, which allows for exact modelling, reasoning, and optimisation.  This essay looks at some important discrete mathematical ideas, like logic, algebraic structures, and graph theory, and shows how important they are in designing and implementing AI algorithms.  Graph-based models make it easier to describe and draw conclusions from information, and algebraic structures are the building blocks of machine learning computing systems. Logic-based inference engines also improve automatic thinking skills that are needed for smart decision-making.  The study also talks about how discrete structures have helped build neural networks and machine learning methods, which have made AI better at solving problems.