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@futurebird Algebra and calculus are in the curriculum for different reasons. Algebra is important as a tool for abstraction. Being able to express a general solution by abstracting over concrete values is one of the most powerful tools that we have for thinking.

Calculus is in the curriculum because of Sputnik. The USA redesigned the curriculum to produce people who could solve rocket equations to catch up with the USSR. Most of the western world copied this shift. In most cases, it is a complete waste of time. In the very few times when I have encountered a problem where the solution involved forming a differential equation, it never involved solving the equation because a computer can do that orders of magnitude faster than I can. The time I spent at school practicing these things so that I could solve one in 5 minutes instead of 30 was no help, given that I could enter on into a computer in a few tens of seconds and it could solve it in well under a second.

I would happily kill 90% of calculus in the curriculum.

Graph theory, to me, is closer to algebra. It’s not that there are specific things like A* that are useful, it’s that it’s an important way of framing problems. Once you understand graphs, you can understand finite automata. You can understand Markov chains. And you can understand how data is represented in most modern programming languages. It’s a tool for thought and the thing that gives it that property is, in part, the fact that it’s really hard to name the one thing that showcases it.