From a fascinating 2019 interview with Adam Gordon Bell — "Category Theory is in our minds? Bartosz Milewski weighs in." — as presented by John Walker, comments by Milewski:

... I think mathematics is something that is inherent to human beings. This is the only way we can deal with our environment because we have small brains. It's like, compared to the size of the universe, this is just like a tiny, tiny thing. And it evolved from apes that were trying to solve problems, like how to run away from a predator or how to kill an animal and eat it, start a fire, and so on. So the way we deal with complexity is by dividing into smaller tasks, solving them and then recombining the solutions. And that's what we do with everything. ...

and near the end:

... We always think that like we already understand 99% of stuff and there's this 1% missing. And I think this is completely wrong. We understand the 0.001% if that even makes sense, right? And there's so much stuff missing if we just ignore the stuff that we don't understand. ...

and:

... physicists are very pragmatic, you know; if it works, it works. Okay. If I can calculate something and then test it, then it's great. In this way, physicists are more like programmers. If it works let's ship it. ...

and completely separately from Bartosz Milewski's blog on 9 October 2019:

In category theory, as in life, you spend half of your time trying to forget things, and half of the time trying to recover them. A morphism, the basic building block of every category, is like a defective isomorphism. It maps the initial state to the final state, but it provides no guarantees that you can recover the original. But it seems like this lossiness is what makes morphisms useful.

There are people who can memorize mathematical formulas perfectly but have no idea what they mean. And there are those who get just the gist of it, but can derive the rest when needed. Somehow understanding is related to lossy compression.

We can't recover lost information. Once it's gone, it's gone. All we can do is to try to figure out what the original might have been like. In fact, knowing how the information was lost, we might be able to generate all possible inputs that could have led to a given output. It's the closest we can get to inverting the uninvertible. This is the main idea behind fibrations.

Let me illustrate this concept with an example. Consider the function ...

(cf Greatest Inventions (2011-06-09), Cakes, Custard, and Category Theory (2016-02-14), Category Theory Concepts (2016-04-25), Bird's-Eye View (2016-07-20), Category Theory for Programmers (2017-05-12), Ultimate Abstraction (2017-08-24), Eugenia Cheng on Thinking (2017-12-30), Yoneda Perspective (2018-10-03), Put the Vast Storehouse in Order (2017-10-04), Category Theory is like a Lighthouse (2018-12-24), Macro vs Micro (2019-02-03), Why Care about Category Theory (2019-03-03), ...) - ^z - 2019-10-11