I don't think there is a factual disagreement here, just a terminology issue. Mathematical jargon is not quite the same language as plain English. In the former

I don't think there is a factual disagreement here, just a terminology issue. Mathematical jargon is not quite the same language as plain English. In the former, 'solved' by default means you have found the mathematically perfect solution. In the latter, 'solved' by default just means you have found a solution good enough for practical purposes.