[bees_buzz]

I'm not anymore, but I used to be a research mathematician. I absolutely cannot remember how to do long division, though I was certainly competent at it at one point. I'm also terrible at mental arithmetic these days.

These things were still indispensable on my path to being a mathematician though, they just ceased to be relevant as abstraction increased.

[globular-toast]

I feel like "I can do X" always comes with an implied timescale and a degree of confidence. For example, I "can" speak Chinese, in the sense that I have no reason to believe I cannot: Chinese people do not have fundamentally different mouths or brains to me. But still, even after many years of study and practice, you might be disappointed in my ability. If I were you I would not have any confidence in my ability in Chinese.

On the other hand, if I were to hire you to perform long division I would have complete confidence in you turning in your first calculation within an hour given your research background. So I would definitely say you can do long division.

If software were a purely mechanistic task like long division then I'd have confidence in anyone being able to turn out working code within an hour too. But we can't just keep turning out new programs every time we want to change them. Even with LLMs this is prohibitively expensive. So software is really about being able to build things and maintain them over time which requires a much deeper understanding. Long division is like snakes and ladders. Software is like chess.