Putnam's theorem

Putnam’s theorem addresses the idea of understanding when two mathematical objects—like shapes or functions—are essentially the same, even if they look different. It provides criteria to determine if two objects are equivalent based on certain properties and transformations. Essentially, it helps mathematicians recognize when two different descriptions actually represent the same underlying structure, much like realizing that a tilted square and a rotated square are the same shape viewed from different angles. The theorem offers a formal way to identify and classify these equivalences in complex mathematical contexts.