A mathematical sieve is a systematic method used to filter out certain elements from a set, often to identify prime numbers. One of the most famous examples is the Sieve of Eratosthenes, which efficiently finds all prime numbers up to a specified limit by iteratively marking the multiples of each prime starting from 2. In addition to prime number identification, sieves can be applied in various mathematical contexts, such as number theory and combinatorics. They help simplify complex problems by breaking them down into smaller, manageable parts, allowing mathematicians to analyze and solve them more effectively.