Einstein formulated GR "happiest thought of his life" intuition... Newton intuitively grasped the essense of inertia and later step by step formulated it into his law..
The old distinction (or something like it) between context of discovery and context of justification may be relevant here. Where do hypotheses come from? Insight, intuition, and the like (and of course deductions therefrom); that is the so-called context of discovery. It may be a "new" discovery or revelation that something follows from something else but it isn't yet a new discovery of something empirical prior to empirical confirmation, which is the so-called context of justification. For physics, intuitive thought (in certain senses), rightly or wrongly, is held to be absent from the context of justification.
https://www.mpiwg-berlin.mpg.de/research/projects/DeptII_AufrechtMonica_History
Sure, you can listen to the Popper based response the other poster argued, and it may make sense. There is some truth to it; still, things are rarely that simple.
Intuition is a key driver of the advancement of all fields alike, and physics is not special in that regard. But intuition as a process is dirty and vague and just as fuzzy as it is powerful. The sad truth is that some academics have sought to adorn their own standing by portraying their disciplines as shinning beacons of unbreakable rigor. If you scratch the surface, however, what you'll find are... well... humans, with boundless biases, prejudices, and religious dogmas informing their acceptance or denial of whatever comes across their minds.
Einstein rejected Quantum Physics, after all, because it undermined his deity: God does not play dice. And Newton was an alchemist and an astrologer. Now, someone could argue that these are extreme cases, but I'd bet the farm that they are not, that they are closer to the rule than to being exceptions.
Humans thought is not logical or mathematical. These are tools. Your thinking can become more logical or mathematical if you bother to learn logic or mathematics and then practice applying these tools in your everyday thinking. But this isn't a natural occurrence, and thinking using logic or mathematics will never be the majority of someone's thought regardless of how often they practice.
To admit this fact simply isn't elegant.
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