suggestions that one might need to understand category theory and similar such nonsense
It’s definitely unnecessary to understand category theory to work with monads. What is helpful, however, is having some comfort with math.
What does that mean exactly? It’s a level of comfort in working with definitions, properties, operations, special elements, proofs. People can get so frustrated because they think they don’t understand what a monad is. Like they want to hold it in their hand the way they would an apple or a tennis ball.
When you’re comfortable with math you kind of lose that need to think about an object concretely. You start to only care about the definitions, properties, axioms, laws, theorems, etc that concern a particular object. Then you just play around with a few examples and see the implications of these things. That’s all there is to it. The power comes from the abstraction. It can take time to become comfortable with abstract concepts though.
Another thing that is often missed is that we think we “understand” something when in fact we just got used to it. Even such simple concept as “number” would probably be very difficult to explain to someone (who either doesn’t know what a number is or wishes to “really understand” it).
Oh yeah. The history of numbers is long and complicated. I think today we take for granted the idea that numbers are objects (in some abstract sense). In the past, there was simply no concept of number as a thing. Numbers were used for counting or measuring, so they existed only as adjectives attached to their objects of counting/measuring, not nouns in their own rite.
Well the natural numbers are the decatigorification [1] of the category of finite sets.
I won't speak to other kinds of numbers but it's funny how category theory helps answer that question as well.
It’s definitely unnecessary to understand category theory to work with monads. What is helpful, however, is having some comfort with math.
What does that mean exactly? It’s a level of comfort in working with definitions, properties, operations, special elements, proofs. People can get so frustrated because they think they don’t understand what a monad is. Like they want to hold it in their hand the way they would an apple or a tennis ball.
When you’re comfortable with math you kind of lose that need to think about an object concretely. You start to only care about the definitions, properties, axioms, laws, theorems, etc that concern a particular object. Then you just play around with a few examples and see the implications of these things. That’s all there is to it. The power comes from the abstraction. It can take time to become comfortable with abstract concepts though.