I'm a postdoctoral researcher in STEM and I've always been a slow thinker. I need to slowly process research issues, theory or ideas with pencil & paper or on a whiteboard. I often need to have visual aids (drawings and writing) to help me think. Insights on relatively easy things, like understanding bugs in my code, come to me only the next day (after a good night's sleep). Insights into more complex theory can come to me only after weeks, months or even years... I've always had a sense that my colleagues process things faster than me.
But every once in a while I'm in a situation where I need to answer a question that requires quick thinking: at conferences, at group meetings, when having quick chats with collaborators. Those questions usually appear with the following pattern: I present a piece of a mathematical formulation that I've been developing to solve a problem and someone asks me:
But wouldn't this formulation be equivalent to XYZ?
I find that I can't answer those questions even though I know what XYZ is. It would require me to sit with a piece of paper and convince myself that indeed my formulation is equivalent to XYZ or that it's not. So I usually just answer: "I'm not sure, I'd have to think about this." Sometimes I might have a vague hunch about the answer and I answer: "I don't think so, but I'd have to think some more about this." Other question types that get me stuck are things like:
Isn't [insert name of a mathematical tool] what you need to solve your problem?
On the spot, I have no idea! Even though I've heard of the [mathematical tool] before. I have to go back to my desk and think for a day or two if this is what I need.
At least if I've never heard of these things it would be normal to answer "I don't know." Instead, this really is being hampered by my own brain's processing capabilities...
This is sometimes hurting my progress because if it's my advisor asking these questions during our weekly meetings then we often can't progress any further with the conversation. I have to go back to my desk and come back to my advisor a week later with an answer.
Although I've been doing well in research so far despite my slow processing (as long as I get enough time, I can figure stuff out in the end), I'm worried that as I progress in academia and still can't think on the spot, this will start to look unprofessional. For instance, I've been observing my advisors and they always seem to have some answer to questions that they get. I think I've never heard my advisor say "I don't know" to a conference question.
Can slow thinking start to look bad in my future academic path, say when I need to give an interview talk for a grant? What are some strategies then that slow-thinking academics use to become better at answering questions that require thinking on the spot?