any links to the fancy maths? i don't get how a miner can give you the ability to generate a private key if he doesn't have the ability to do it himself and might already have done it.

Bitcoin addresses are created from ECDSA keypairs. Their property is that if you take two private keys and add them together (with appropriate modulo operations), the sum will map to a public key that is the same one as one would obtain by adding the two public keys corresponding to the private keys.

This means that in order to outsource vanity key generation, one can create an ECDSA keypair, store the private key safely, and give out the public key to other people. They would then proceed to generate ECDSA keypairs, summing the generated public keys to the one provided by you, and checking whether they map to the appropriate vanity address. If it does, they need only to give you the appropriate private key, which you then need to add to your secret private key in order to obtain the private key that maps itself to the vanity address.