Reverse mathematics is helping researchers understand why certain computational problems are hard to solve. The traveling salesperson problem exemplifies this difficulty. For decades, computer scientists have struggled to prove that no efficient solution exists, despite knowing intuitively that the problem is hard. By examining the foundations of mathematical proofs, researchers hope to uncover why they haven’t succeeded in proving these complexities. A recent paper by Lijie Chen, Jiatu Li, and Igor Oliveira takes a novel approach by flipping the traditional method of proving theorems. Instead of starting with axioms to prove a theorem, they used existing theorems as axioms to prove others, a technique called reverse mathematics. They found that the equality problem in communication complexity and the pigeonhole principle are equivalent when using a specific set of axioms known as PV1. Their findings led to the discovery of a network of equivalences among various theorems in complexity theory, including a surprising connection between the palindrome lower bound theorem and the pigeonhole principle. These equivalences reveal that some complexity lower bounds are more fundamental than they seem. However, the research also highlights the limitations of the PV1 axioms. While the results help clarify existing theorems, they raise questions about the complexity of statements that remain unproven. Researchers like Ján Pich emphasize the value of these new connections, though they caution that this approach has its limits in uncovering deeper truths about unproven problems.