One effective method for resolving mathematical difficulties in Java is to use recursion to find the Greatest Common Divisor (GCD). The greatest number that divides two numbers without leaving a residual is known as the GCD of those numbers. By creating a recursive function that shrinks the problem size with each use, you may implement gcd recursion in Java. The Euclidean approach, which says that gcd(a, b) = gcd(b, a % b), can be used to compute GCD via recursion in Java until b equals zero. By employing fewer iterations, Java's recursive approach to GCD reduces code complexity and boosts performance.