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Mathematics is hard for mathematicians to understand too

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Re: Mathematics is hard for mathematicians to understand too

#121

Post by xigoi »

matheme wrote: post #103
gjulianm wrote: post #100

Earlier quoted context omitted.

The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.

"Can I enter your gate?" "In order to enter this gate you must know what this symbol means." "I am unfamiliar with that symbol." "Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."

Every good mathematical textbook introduces the notation it’s using.

Re: Mathematics is hard for mathematicians to understand too

#122

Post by xigoi »

kragen wrote: post #114
bmacho wrote: post #109

Earlier quoted context omitted.

Here is an online renderer and the description: https://asciimath.org/ The rules are basically the same as LaTeX, with saner symbol names, support for fractions, \ is not needed before symbols and () can be used instead of {}. > Supposing that the parentheses aren't necessary, as implied by your edit: how does AsciiMath determine that e^y isn't in the numerator in "e^y dy/dx" It seems to me that dx,dy,dz,dt behave li…

Thanks! It does better than I expected on tricky input like [0, 1/2). It seems like there are a lot of special cases, though. It does indeed remove parentheses from the output in some cases but not others. Probably figuring out how to write things in AsciiMath is more trouble than copying and pasting them from Wikipedia though. (The alt text on equation images is the LaTeX source preceded with \displaystyle.) How do…

Why would you want to manually set the sizes of parens? I always use \left \right when writing LaTeX (and having to do it is one of the reasons I hate LaTeX math notation).

Re: Mathematics is hard for mathematicians to understand too

#123

Post by kragen »

xigoi wrote: post #122
kragen wrote: post #114

Earlier quoted context omitted.

Thanks! It does better than I expected on tricky input like [0, 1/2). It seems like there are a lot of special cases, though. It does indeed remove parentheses from the output in some cases but not others. Probably figuring out how to write things in AsciiMath is more trouble than copying and pasting them from Wikipedia though. (The alt text on equation images is the LaTeX source preceded with \displaystyle.) How do…

Why would you want to manually set the sizes of parens? I always use \left \right when writing LaTeX (and having to do it is one of the reasons I hate LaTeX math notation).

Because \left( ... \right) doesn't give very readable results in cases like that; all the parens end up the same size.

Re: Mathematics is hard for mathematicians to understand too

#124

Post by xigoi »

UltraSane wrote: post #117
karmakurtisaani wrote: post #72

A lot of people here suggesting they'd be great mathematicians if only it wasn't for the pesky notation. What they are missing is that the notation is the easy part..

Not at all. Over and over I find really intimidating math notation actually represents pretty simple concepts. Sigma notation is a good example of this. Hmm, giant sigma or sum()?

Imagine how much unnecessary time would be added to a course about series if the lecturer had to write sum() instead of ∑ every time. If you find it hard to remember that ∑ means sum, math might not be for you, and that’s fine.

Re: Mathematics is hard for mathematicians to understand too

#125

Post by xigoi »

mzl wrote: post #21
borracciaBlu wrote: post #3

I was writing a small article about [Set, Set Builder Notation, and Set Comprehension]( https://adropincalm.com/blog/set-set-builder-natatio-set-com... ) and while i was investigating it surprised me how many different ways are to describe the same thing. Eg: see all the notation of a Set or a Tuple. One last rant point is that you don't have "the manual" of math in the very same way you would go on your programming…

I wrote about overlapping intervals a while ago, and used what I thought was the standard math notation for closed and half-open intervals. From comments, I learned that half-open intervals are written differently in french mathematics: https://lobste.rs/s/cireck/how_check_for_overlapping_interva...

We don’t talk about the French notation for intervals. Let it stay in France.

Re: Mathematics is hard for mathematicians to understand too

#126

Post by xigoi »

pathikrit wrote: post #51

I love math but the symbology and notations get in my way. 2 ideas: 1. Can we reinvent notation and symbology? No superscripts or subscripts or greek letters and weird symbols? Just functions with input and output? Verifiable by type systems AND human readable 2. Also, make the symbology hyperlinked i.e. if it uses a theorem or axiom that's not on the paper - hyperlink to its proof and so on..

What’s wrong with Greek letters? Would the number π be any easier to understand if it was written differently?

Re: Mathematics is hard for mathematicians to understand too

#127

Post by xigoi »

matheme wrote: post #83

> Venkatesh argued that the record on this is terrible, lamenting that “for a typical paper or talk, very few of us understand it.” > "few of us " You see, if you plebs are unable to understand our genius its solely due to your inadequacies as a person and as an intellect, but if we are unable to understand our genius, well, that's a lamentable crisis. To make Mathematics "understandable" simply requires the inclusio…

A lot of math is not about numbers, so not everything can have a numerical example.

Re: Mathematics is hard for mathematicians to understand too

#128

Post by gjulianm »

matheme wrote: post #103
gjulianm wrote: post #100

Earlier quoted context omitted.

The only thing that sentence says is that it’s impossible to understand math without understanding the language of math and how it is constructed. Not sure how that is controversial or gatekeeping. If you are annoyed at that comment saying “learn” instead of “be taught”, I think that’s a pedantic argument because the argument wasn’t about that at all.

"Can I enter your gate?" "In order to enter this gate you must know what this symbol means." "I am unfamiliar with that symbol." "Well, I expect you to learn what it means before I allow you to enter this gate. Now go away."

Again, learning notation is part of the process of learning math. No one is gatekeeping anything, at no point you need to do an exam or magically be aware of notation that you never saw. Every book and every class will define new notation at the beginning, in most cases they will do so even when there’s no new notation. I am not sure what your argument is.

Re: Mathematics is hard for mathematicians to understand too

#129

Post by auggierose »

aleph_minus_one wrote: post #37
segfaultex wrote: post #23

Earlier quoted context omitted.

Yeah, I don't want to be uncharitable, but I've noticed that a lot of stem fields make heavy use of esoteric language and syntax, and I suspect they do so as a means of gatekeeping. I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". Statis…

> I understand that some degree of formalism is required to enable the sharing of knowledge amongst people across a variety of languages, but sometimes I'll read a white paper and think "wow, this could be written a LOT more simply". OK, challenge accepted: find a way to write one of the following papers much more simply: Fabian Hebestreit, Peter Scholze; A note on higher almost ring theory https://arxiv.org/abs/2409…

These papers are actually great examples of what is problematic with mathematics, just as what is problematic with papers in any other specialised field: how do you judge if this could be ever useful to you?

If you want to understand what is going on there, what is the most effective way to build a bridge from what you know, to what is written there?

If you are in a situation where the knowledge of these papers could actually greatly help, how do you become aware of it?

I think if AI could help solve these two issues, that would be really something.

Re: Mathematics is hard for mathematicians to understand too

#130

Post by thaumasiotes »

baobun wrote: post #90
thaumasiotes wrote: post #30

Earlier quoted context omitted.

No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. The person who hears that poem in circulation and records it in his notes has created literature; an anthology is literature but an original work isn't.

> No, the argument is even dumber than that. The person who writes a poem hasn't created any literature. Sure they have, by virtue of writing it down. It becomes literature when it hits the paper (or computer screen, as it were). (Unless you mean to imply that formulating an original poem in your mind counts as "writing", in which case I guess we illustrate the overarching point of value in shared symbols and languag…

> Unless you mean to imply that formulating an original poem in your mind counts as "writing"

You're close. I'm making the point that, in modern English, no other verb is available for the act of creating a poem.

Here's a quote from the fantasy novel The Way of Kings that always appealed to me:

>> "Many of our nuatoma -- this thing, it is the same as your lighteyes, only their eyes are not light--"

>> "How can you be a lighteyes without light eyes?" Teft said with a scowl.

>> "By having dark eyes," Rock said, as if it were obvious. "We do not pick our leaders this way. Is complicated. But do not interrupt story."

For an example from reality, I am forced to tell people who ask me that the English translation of 姓 is "last name", despite the fact that the 姓 comes first.

Similarly, the word for writing a poem is "write", whether this creates a written artifact or not. And the poem is literature whether a written artifact currently exists, used to exist, or never existed.

(Though you've made me curious: if the Iliad wasn't literature until someone wrote it down, do you symmetrically believe that Sophocles' Sisyphus is no longer literature because it is no longer written down?)

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