Do professional physicists think in mathematical equations? Do they think in these mathematical equations first, and then come to a conclusion based on that math? Or do they think intuitively or visually about something first, then come to a conclusion, and only later prove it mathematically? Or do they think even differently? The main thing I want to know is, what comes first? The math, or non-math-based intuition? Because while looking at research papers in physics I get the idea they think in a purely mathematical way, which is strange to me. Thanks!