When I was a university student, I studied mathematics. Real mathematics, as opposed to nearly everything that happens from childhood to undergrad called "math", is far more an art than a science. It's a creative exploration of pattern and logic, and holds deep beauty.

It's also difficult. Connecting abstract concepts together using the rules of whatever system you're currently operating under can require struggling and wrestling with ideas, sometimes literally:

Math traffics in abstractions — the idea, for example, that two apples and two oranges have something in common ... Early in his career, he struggled with a problem that involved waves rotating on top of one another. He wanted to come up with a moving coordinate system that would make things easier to see, something like a virtual Steadi­cam. So he lay down on the floor and rolled back and forth, trying to see it in his mind’s eye.
The Singular Mind of Terry Tao, Gareth Cook (archive)

Problems would sometimes take days or longer to solve, with incremental advancements and "a-ha's" found along the way. Often, I'd feel entirely stuck, not knowing how to make progress. That stuckness had a distinct embodied feeling: tightness in the head, feeling pushed physically and emotionally. There was certainly a cognitive narrative, but the feeling was primarily felt.

Inevitably, something would click and the path forward would become obvious. Over time, I learned to associate that exact feeling of stuckness as the feeling that occurs when I'm pushing myself: when something is indeed stretching my capacity, but will open new doors and realizations.

I learned to love this feeling. The first part of solving a problem was just to get to that point. If it never came before the solution, then that problem had nothing new to offer. But as soon as I arrived to the feeling, I knew it was possible to make real progress within myself.

Loving this feeling was the single greatest educational outcome I carried with me out of my undergrad education. I felt it again when learning type theory, and when reading philosophy. I felt it when solving hard software engineering problems.

I recently realized that this feeling is the same feeling I get during difficult physical activity. When climbing a mountain, there's a moment where I feel done. Sometimes there's a narrative ("I want to be done"), but the narrative is a result of feeling "pushed". It becomes the water that permeates all of awareness. This is the same stuckness feeling as I first learned to love in math: it's the feeling when things are hard, but pushing through opens breakthroughs.

A ultra-endurance athlete that I know once said long distance running is 100% mental. This is obviously not true, but points at something quite true: by the time a runner is doing ultra distances, they've done thousands of repetitions of getting through this stuckness. Of not quitting, when they feel like it.

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