Is asymmetric encryption the keys are mathematically related to one another?

In asymmetric encryption, the keys are not mathematically related in a straightforward way; rather, they are generated as a pair consisting of a public key and a private key. The public key can be shared openly and is used for encryption, while the private key, which must be kept secret, is used for decryption. The relationship between the two keys is such that data encrypted with the public key can only be decrypted with the corresponding private key, ensuring security. However, the exact mathematical relationship is complex and relies on certain mathematical problems that are difficult to solve without the private key.