Let’s say you are stuggling to understand a math concept for a while and suddendly you get it. What mechanism caused it?
Assuming you’re at an appropriate learning level, you already have all of the abstract knowledge comprehension to understand the concept, but your brain hasn’t made the connection yet. Literally.
Your neurons are firing in groups that you know relate to the concept, but somewhere else are neurons that once included in that neuron firing chain will result in a deeper understanding.
Neuroplasticity allows your neurons to form new connections and strengthen important existing ones. I can’t really answer this question, that sounds more like a cognitive/behavioral kind of thing, but physically this is what’s happening. As you put more effort into understanding a particular math problem you strengthen those connections responsible for math and become better at it. You can be wrong about it, it wouldn’t be any different than if you thought you were correct.
They are also different for each person, if I had a device that could read your mind I wouldn’t be able to make any sense of it since it’s not in English. I would have to train my interpretation software for your specific brain, and it would probably require constant calibration.
The main thing that solidifies a memory is dopamine. When you learn something new, dopamine is released by the brain and that encourages your braincells to reinforce the memories that were just made.
When you finally understand something, you have made new connections in your mind. You keep checking the connections you are making to see if they “make sense.” Once you finally develop the connections that create the logic you need, you recognize that you have the right answer, and a rush of dopamine hits your brain.
It’s trial and error with a hit of dopamine once you get it right.
Your brain is composed of a vast network or neurons. These neurons are constantly changing and making new connections. It’s how we form all cognitive functions. As we learn, those neurons become systems that are linking together to create relational networks that provide context. When something “makes sense” It’s because we have formed enough connections to provide contextual assumptions.
What gets tricky is just because we have those connections in our brains, it doesn’t mean that it’s factual or true. Its why our memories are faulty. Its why as children we are very susceptible to new information. It’s only when new experiences or knowledge challenges those perceptions, or when those connections that are no longer utilized, that we break or form new connections in our brains.