Maybe, but I suspect that a lot of the actual things that produce the algorithm, proof, etc are not actually explicit reasoning. Q: "Why did you try that vs some other thing at this point?" A:"seemed right to do"/"kinda looks like other stuff I've seen before"/"first thing that came to mind" etc.

Why pursue this one avenue vs some other, typically its cause it seemed more promising, and the person can come up with reasons but did they explicitly verbalize a fully sound chain of thinking at the time? Probably not.

Not to say that the explicit thinking, or writing things down, isn't important. But if I examine the process by which I develop a proof or something, there's a lot of vague hunches, blind alleys, etc that come along the way. And, many of the blind alleys etc probably aren't actually that important in the end for me finding the right answer -- if you were to trim that part out of my own internal reasoning trace but left the rest intact, I'd still get the right answer because, well, it was a blind alley.