Everyone here is partly right, but the disagreement is mostly semantic, not technical.

Yes, a private key can theoretically be derived from a public key. That’s basic math. The mapping is bijective — for every valid public key, there's exactly one corresponding private key, based on the elliptic curve parameters.

But — and this is the critical part — the process is computationally infeasible with today’s hardware and known algorithms. That’s the foundation of Bitcoin’s security. The elliptic curve discrete logarithm problem (ECDLP) is not mathematically impossible to reverse — it's just so hard that even a trillion computers working for a billion years wouldn’t crack a single key.

So:

 Yes — possible in theory (mathematically speaking).

 No — not feasible in practice (computationally speaking).

This is why we say Bitcoin is secure. Not because it's unbreakable in the abstract, but because it’s practically unbreakable without a major cryptographic or quantum breakthrough.

Let’s not confuse “possible” with “realistic.”