Real math or science doesn't come with answers in the back of the book. A researcher might work for years without knowing whether their efforts are leading them down a blind alley. The exquisite feeling you get when you've solved a really hard problem is why people become physicists, mathematicians, and engineers. It's the feeling of having eyes where once you couldn't see.
Having her self-confidence assaulted by every problem set in grad school was a challenge for "K", the applied physics Ph.D. I wrote about in Part 2. But there was that one problem set in high school that stumped everyone else in the class, but which she solved. Once you've tasted that success, you don't forget it.
There are a lot of ways to get to the bottom of any slope. Some people like to do traverses. Some people go straight down. My method was to swallow the sheer terror, point my skis downhill, and power through some turns and some slides. I've never been a great skier so I'd get half way down and land on my butt. Gradually, I figured out how to avoid falling.
This is apparently a typical male's approach to skiing. A touch of reckless self confidence lends itself to this approach. Just watch some teenage boys on a ski slope if you doubt it.
K realized that she didn't have to ski like the guys. The part of skiing she enjoyed was carving turns. To carve a good turn, you have to put your weight downhill, which at first feels insecure, but in practice gives you more control. And having good technique gives you real confidence.
Realizing that she could approach problem sets her way really helped K get through those difficult problem sets. It was OK that she felt like she had no idea what to do while many of her male colleagues just pretended to know how to do them. There was nothing wrong with focusing on skills and carving away the difficulty. And not break anything.