Hillclimbing is a mathematical optimization technique used to find the best solution to a problem by iteratively making small changes. It starts with an initial solution and evaluates neighboring solutions to determine if they are better. If a better solution is found, the algorithm moves to that solution and continues the process until no better neighbors are available. This method is often used in fields like artificial intelligence and operations research. However, it can get stuck in local optima, which are solutions that are better than their neighbors but not the best overall. To overcome this, variations like simulated annealing may be employed.