Explore the intricacies of mathematical problem-solving and computational complexity in this 56-minute AMS-MAA Invited Address delivered by Karen Lange from Wellesley College at the Joint Mathematics Meetings 2020 in Denver, CO. Delve into the fascinating world of "Different Problems, Common Threads" as Lange examines the difficulty of computing mathematical problems. Journey through key concepts such as mathematical theorems, computability, the Halting Problem, and the Tree Theorem. Investigate the Prime Ideal Theorem and its algorithmic handling, and gain insights into the foundational crisis of mathematics and reverse mathematics. Conclude with a thought-provoking exploration of "The Big Five" and engage in a stimulating Q&A session.