Mathematics is hard for mathematicians to understand too

I find it strange to compare "math" with one programming language. Mathematics is a huge and diverse field, with many subcommunities and hence also differing notation.

Your rant would be akin to this if the sides are reversed: "It's surprising how many different ways there are to describe the same thing. Eg: see all the notations for dictionaries (hash tables? associative arrays? maps?) or lists (vectors? arrays?).

You don't have "the manual" of programming languages. "

> A lot of the mathematical topics the HN crowd seems to like--things like the Collatz conjecture or Busy Beavers--are 60, 80 years old.

Do you know the reason for that? The reason is that those problems are open and easy to understand. For the rest of open problems, you need to be need expertise to even understand the problem statement.

actually a lot of minimal proof expose more intuition than older proofs people find at first. I find it usually not extremely enlightening reading the first proofs of results, counterintuitively.

> Mathematics is such an old field, older than anything except arguably philosophy

If we are already venturing outside of scientific realm with philosophy, I'm sure fields of literature or politics are older. Especially since philosophy is just a subset of literature.

It's probably a neurological artefact. When the brain just spent enough time looking at a pattern it can suddenly become obvious. You can go from blind to enlightened without the usual conscious logical effort. It's very odd.

Many ideas in math are extremely simple at heart. Some very precise definitions, maybe a clever theorem. The hard part is often: Why is this result important? How does this result generalize things I already knew? What are some concrete examples of this idea? Why are the definitions they way they are, and not something slightly different?

To use an example from functional programming, I could say:

- "A monad is basically a generalization of a parameterized container type that supports flatMap and newFromSingleValue."

- "A monad is a generalized list comprehension."

- Or, famously, "A monad is just a monoid in the category of endofunctors, what's the problem?"

The basic idea, once you get it, is trivial. But the context, the familiarity, the basic examples, and the relationships to other ideas take a while to sink in. And once they do, you ask "That's it?"

So the process of understanding monads usually isn't some sudden flash of insight, because there's barely anything there. It's more a situation where you work with the idea long enough and you see it in a few contexts, and all the connections become familiar.

(I have a long-term project to understand one of the basic things in category theory, "adjoint functors." I can read the definition just fine. But I need to find more examples that relate to things I already care about, and I need to learn why that particular abstraction is a particularly useful one. Someday, I presume I'll look at it and think, "Oh, yeah. That thing. It's why interesting things X, Y and Z are all the same thing under the hood." Everything else in category theory has been useful up until this point, so maybe this will be useful, too?)

sorry but that is a dumb quote.

Just because someone said it doesn't mean we all agree with it, fortunately.

You know the meme with the normal distribution where the far right and the far left reach the same conclusion for different reasons, and the ones in the middle have a completely different opinion?

So on the far right you have people on von Neumann who says "In mathematics we don't understand things". On the far left you have people like you who say "me no mats". Then in the middle you have people like me, who say "maths is interesting, let me do something I enjoy".