But as long as there is no mathematical proof that such attack is impossible, I do not feel entirely comfortable with deterministic keys
You might have bigger problems then since ecdsa is also only assumed to be secure.
Why? My private keys are not sent to the server. so if the Electurm server turns out insecure, still nobody can steal my keys.
I think he's referring to Elliptic Curve Digital Signature Algorithm, not the Electrum server at ecdsa.org. Bitcoin keypairs, including deterministic keys, are created with ECDSA. Like most public key cryptosystems, it is never impossible to carry out an attack; it is only extremely impractical. That's (probably) why vuce is saying ECDSA is only assumed to be secure. If you need complete mathematical certainty of impossibility, there's bigger problems than just deterministic wallets.