Here's a little thread post with two quotes 💬 from Andrew Wiles' Abel Prize interview. Those quotes helped me better understand what research (mathematics) feels like. Here's a link to the interview
1 The dark mansion
Here's the first quote: "Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the ﬁrst room, and it’s dark, completely dark."
He goes on: "One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and ﬁnally, after six months or so, you ﬁnd the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were"
I always liked this metaphor in so many ways. First, it describes the struggle when you read an unknown concept for the first time and have no idea and try to understand it. Then, it describes this feeling of finally understanding a concept.
The partially discovered mansion is also a nice metaphor for how personal each individual's math journey is. Everyone has their personal favorite rooms to which they return again and again because something in their attracts them and they enjoy discovery.
2 The busy squirrel
The second quote is about perseverance. Towards the end of the interview, he likens solving a math problem to being a squirrel that is looking for nuts high up in one of several tall trees. Since it doesn't know which tree has the nuts, it tries one tree after another, always giving up after 30 feet and never finding anything. But if someone told it which tree is the right one, then it would just keep going on this one tree as high as necessary until it finds the nuts.
I think what he's saying with this quote is a) never give up and b) trust your intution as to which approach to take to solve a problem. But this approach obviously requires good intuition in the first place.