[ben_w]

Aye.

A decade or so ago I wondered if the reason maths was hard was the names being optimised for writing by hand. Everything's single letters if they can get away with it, so when mathematicians run out of Latin alphabet, they use Greek, bold, etc.

Even integration's ∫ is a fancy elongated s.

CS version would be e.g. integral(function=some_named_function, from=a, to=b, with_respect_to=argument_of_function), which may be longer, but is less opaque, especially when you get in so deep there's 3 other people in the world who've looked into this specific problem and you had to invent your own operations.

But that's all an outsider's perspective. I stopped with two A-levels in maths and further maths.

[ndriscoll]

Nope, math notations are optimized for reading, not writing (consider that people still use symbols on computers despite it being quite a bit more tedious to type). The conciseness makes it easier for you to see structural patterns and do symbolic manipulation in your mind's eye. Even something basic like the wave equation would become completely illegible with an expanded notation like that.

Same reason why we write 5-3, not subtract(minuend=five, subtrahend=three).

[sebmellen]

For those of us with strong verbal processing and weak symbolic/pattern processing, this makes math much more difficult to approach.

Interestingly, discrete math feels the most "verbal" of all the subfields of math I've encountered (I haven't gone very deep). I think this is because notation in discrete math is is somehow closer to compressed prose or logic, whereas other forms of math use notation to fill in for long sequences of symbolic manipulation.

Not sure if that makes sense... I'm curious whether anyone else experiences it that way.

[chongli]

No, math is difficult to approach because it's genuinely deep. Trying to verbalize what is going on is extremely difficult, because you end up saying stuff like "and then do that to all of these things, and then do it again to all of the results, and so on ad infinitum, and then take the collection of all of that, and join it with the collection of doing the same procedure as before starting with a different set of objects, and then join those to yet another set of objects and the results of their operations, ad infinitum, ad infinitum..."

People genuinely struggle to think verbally or visually once we extend beyond 3 dimensions and start talking about infinite-dimensional constructs, uncountable sets, and so on...

[sebmellen]

Of course, I understand this, and I hope that my comment didn't come across as saying that math would be easier to "do" if it were all fully verbal. Symbolic reasoning and interpretation are necessary for complex reasoning.

And math is, as you know, a deep but traversable graph. The traversal inherently requires a familiarity with the nodes you pass through when reaching a foreign or more difficult concept.

However, I'll give you an example. If I read through more complex math that I’m not comfortable with in Sage, I can build an intuition for the structure of the problem more easily than if I view the “raw” notation. In that sense, it is easier to for me to “approach” — but approaching something is very different from fluently using it — and I’m under no illusion that approaching a topic is the same as beginning to understand it.

Again, this is definition-dependent. To me, “approaching” something means beginning to glean how I might one day understand it. E.g. watching a 3B1B video feels like “approaching” a topic. Here we reach the limits of language already :)

[enedil]

At some point though, the speed of reading/writing is limiting what you can understand. Think of "not fitting the needed formulas/theorems in cache".

[umpalumpaaa]

I did study math at university for a while. Dropped out eventually. In the beginning I was super annoyed by the brevity and hated it. But after like 3 months it suddenly became natural. I also appreciate the clarity of how mathematicians introduce new ways to write things. That is sometimes even more verbose than some random API docs for a new function…

[cpill]

yes! I really find when computer science ppl start using math notation to describe algorithm very pretentious. we have programming languages in comp sci, we don't need it!

[gowld]

Look up "APL" and "J".

[8n4vidtmkvmk]

There's a reason they're not more popular...