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 — 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 together 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.”
Which is what I precisely wrote, is it not? People with superficial knowledge and no touch with science tend to communicate badly. They confuse even simple stuff like correlation with causation.
It is called computationally infeasible, not mathematically impossible.
It is possible.