Since, if each of 2256 public keys produce only 2160 hashes this means more than one public key produces the same public key hash.
Yes, that is correct.
Glad to know that.
I am not very good at math, but given a private key, is there any mathematical way to find other private keys that share the same public key?
two different private keys will
never share the same public key. What is implied by the above quote is that many different private keys may share the same
public key hash, which is not the same thing as the public key. I am not a cryptography expert, but I am 99% sure the answer to your question is no, if you actually meant public key hash.