I had never heard of "tropical algebra" so I have no idea of its utility here. I'm only commenting on the distinction between learning about something and learning something.
The former enables you to direct your learning towards learning the thing itself when you realize it's applicable (JIT for learning) if that's your role. And if you're in a leadership position it helps you to recognize the insights those you are in charge of are bringing to you and their relative applicability, or to direct them towards a line of work that may be useful. (Of course, there's a level of incompetent awareness that often happens as well, and that's how SAFe shops are born.)
The former enables you to direct your learning towards learning the thing itself when you realize it's applicable (JIT for learning) if that's your role. And if you're in a leadership position it helps you to recognize the insights those you are in charge of are bringing to you and their relative applicability, or to direct them towards a line of work that may be useful. (Of course, there's a level of incompetent awareness that often happens as well, and that's how SAFe shops are born.)