[themodelplumber]

I like the way this is framed in terms of the comparison to a religious experience. A few years ago I had one of those "unified model revelation" experiences in a non-mathematical field, and based on that experience I think I would ask the author how the follow-on learning or application went. In my experience, the intuitive "experience of the knowledge" was much more striking than the eventual unfolding and application of the logic in that case. However in other cases, the intuitive experience of the revelation/knowledge was weak, yet the model turned out to be somewhat randomly selected by others as interesting or applicable.

I thought this was interesting--that the revelatory experience can end up being so subjective and limited in the goes-nowhere-from-here sense, yet it feels so darn amazing at the time. I wondered if it was similar to seeing a Tetris happen for the first time. An emotional reward in the sense of rewarding an organizational triumph of the mind. And seeing it with the intuition is one of those things our mind loves to count as actually seeing it in real life.

(I've also experienced this as a practicing religious person; in religion though, the subjectivity can quickly become a bummer because the question of one's worthiness or lack of discipline is nearly always up for discussion, especially when you ask why the results were disappointing or something like that)

[username90]

> In my experience, the intuitive "experience of the knowledge" was much more striking than the eventual unfolding and application of the logic in that case.

In math applications doesn't matter, just the beauty of the revelation. Understanding how everything in math is connected is the main goal of the field, so understanding more of it is never pointless.

But if we talk about applications then it is that if A and B are the same then all theorems derived for A also works for B and vice versa. This is very important since it automatically multiplies our productivity and learning rate! One such epiphany which many falters on is that x and y doesn't matter, they could be z or µ or whatever. Another which many struggles with but usually overcomes is that 10 + 30 is just as easy to compute as 1 + 3.