Ask HN: How did you learn math notation?

Millions of programmers that work hard and for a long time to master their trade are just dumb for not learning it instantly, like you. Poor bastards, deluding themselves they do somehow advance the field, while in reality programmers are just doing "tabs vs spaces" over and over again, and any kind of advancement is given to them by our benevolent mathematical overlords.

No. We've worked for decades to make programming this simple. You're driving an obviously overpowered car in a race, but choose to conveniently forget about its specs once you win.

> Mathematicians have written plenty of such cheat sheets, you can find them everywhere just by Googling. Here is one for physics

Sure they were created. I never said they weren't, so please stop insinuating that. I (not GGP) said specifically:

> It has literally nothing to do with explaining the syntax *close to where it's used*.

And that is not being done, so I really don't understand how the rest of the paragraph has anything to do with me.

> say that nobody cares about your woes because that python documentation was in fact not easy enough for you to read!

So? What's wrong with that? Are you telling me I'm dumb? Is it really all you can do?

Well, it's either that I'm simply an uneducated idiot, or that the documentation indeed could be better. You seem to default to the former. Well, I feel differently about that.

You just said they don't because it's not worth it. So which is it in the end?

> In programming you learn an instruction set, and then you use those instructions to compose programs, therefore learning that instruction set is relatively easy.

Yeah, sure. Elementary arithmetic, like 22 and so on, is also not that hard to learn. What you're saying is barely scratching the surface of what programming is, then misrepresent it as the whole truth.

It's not that programming is easy. It's just that you can still earn a very good salary without ever touching the harder and more complex parts. People who knew how to do 22 were also well-paid at some point in the past, yet Euclid still managed to write his Elements. You're like an actuary (working under a Pharaoh to count the cattle, let's say) who says that writing Elements is as easy as his current job (you could do it yourself, but you're too busy right now, so maybe later).

> For example, when learning programming you have to learn about arithmetics, pointers, functions and structs.

And then you try to write a JIT for a dynamic (and concurrent, let's say, as Erlang succeeded in this in the last release) language and, with just "arithmetics, pointers, functions and structs", it becomes obvious it's not nearly enough. Then you start reading books and papers and soon you realize that 5 years have just passed. And JITs are not really that complex!

> Programming however becomes the art of expressing everything using these very simple instructions.

Programming is an art of creating new instructions, both out of thin air and out of already existing instructions. The fact that you seem to think "the instruction set" (meaning concepts that have to be understood, I think?) is constant suggests to me that you you're not very interested in history of the field.

And now you're telling me that Mathematica, Maple and the like don't exist. Yeah, we can't express the concepts directly, but if we're very good at one thing, it would be emulation.

> How would you express that?

Like this:

    >>> from sympy import *
    >>> i, n, m = symbols('i n m', integer=True)
    >>> # For example, lets say you want to sum 1/N^2 for N from 1 to infinity. 
    >>> Sum(1 / n ** 2, (n, 1, oo))
      ∞
     ____
     ╲
      ╲   1
       ╲  ──
       ╱   2
      ╱   n
     ╱
     ‾‾‾‾
    n = 1

You said:

> because programs can't work without being specified.

.. what I think you may have meant was "can't work without being implemented", because your subsequent comments are all about implementation.

> Undefined behavior isn't a feature

Yes it is, it's a feature of the C specification.

This is where a whole load of pain and insecurity comes from, because as you say the implementations must do something when encountering undefined behavior, and people learn what usually happens, then an improvement is made to the optimizer which changes the implementation.

For example, when you write a sum in python then the computer will sum the values and do the work for you. But when you write an infinite sum like that, you the human still has to do all the math work figuring out what to do with it, so you didn't circumvent the need to do math at all. The computer doesn't understand the sum. You can program simple simple rules for it to try to simplify it, but it still isn't nearly as versatile as a skilled human. For example this problem is a basic problem from a first year course, it makes sense that someone programmed in the human derived solution for it, but they haven't actually programmed the logic for infinite sums into the computer.