Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Mathematics is hard for mathematicians to understand too

science.org

Post reply on HN
Print view View original

91–100 of 152 posts

Re: Mathematics is hard for mathematicians to understand too

#91

Post by bmacho »

kragen wrote: post #65
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..

Probably not. The conventional math notation has three major advantages over the "[n]o superscripts or subscripts or [G]reek letters and weird symbols" you're proposing: 1. It's more human-readable. The superscripts and subscripts and weird symbols permit preattentive processing of formula structures, accelerating pattern recognition. 2. It's familiar. Novel math notations face the same problem as alternative English…

AsciiMath makes easy equations read easy.

1 and 2 would be

  1) d/dx e^y = e^y dy/dx = 1
  2) d/dx e^y = d/dx x = 1
edit: edited, first got them wrong

Re: Mathematics is hard for mathematicians to understand too

#93

Post by gjulianm »

matheme wrote: post #87
voidhorse wrote: post #60

Earlier quoted context omitted.

Precisely. Think of mathematics like a game. Players of magic the gathering will say a creature "has flying" by which they mean "it can only be blocked by other creatures with reach or flying". Newcomers obviously need to learn this jargon, but once they do, communication is greatly facilitated by not having to spell out the definition. Just like games, the definitions in mathematics are ethereal and purely formal as…

My entire being is anthithetical to this type of gatekeeping. > You expect the players of the game to learn the rules before they play. TFA is literally from a 'player' who has 'learned the rules' complaining that the papers remain indecipherable. > You expect the players of the game to learn the rules before they play. Actually, I expect to have to teach rules to new players before they play. We are different.

The article does not complain about notation. It describes how the different fields of mathematics are so deep and so abstract that it’s hard to understand them as a professional mathematician in a different field. That’s a hard problem worthy of discussion, but as the article says, it’s not as much a problem of notation or of explanations, rather than it’s just intrinsically difficult and complex because these are abstract and deep fields.

It’s not gatekeeping. It’s just hard.

Re: Mathematics is hard for mathematicians to understand too

#94

Post by matheme »

assemblyman wrote: post #89

I find software engineers spend too much time focused on notation. Maybe they are right to do so and notation definitely can be helpful or a hindrance, but the goal of any mathematical field is understanding. It's not even to prove theorems. Proving theorems is useful (a) because it identifies what is true and under what circumstances, and (b) the act of proving forces one to build a deep understanding of the phenome…

> If the idea is that the right notation will make getting insights easier, that's a futile path to go down on.

I agree whole heartedly.

What I want to see is mathematicians employ the same rigor of journalists using abbreviations: define (numerically) your notation, or terminology, the first time you use it, then feel free to use it as notation or jargon for the remainder of the paper.

Re: Mathematics is hard for mathematicians to understand too

#95

Post by gjulianm »

matheme wrote: post #88
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..

> What they are missing is that the notation is the easy part. This is so wrong it can only come from a place of inexperience and ignorance. Mathematics is flush with inconsistent, abbreviated, and overloaded notation. Show a child a matrix numerically and they can understand it, show them Ax+s=b, and watch the confusion.

Well, obviously they will be confused because you jumped from a square of numbers to a bunch of operations. They’d be equally confused if you presented those operations numerically. I am not sure what it is you want to prove with that example. I am also not sure that a child can actually understand what a matrix is if you just show them some numbers (i.e., will they actually understand that a matrix is a linear transformer of vectors and the properties it has just by showing them some numbers?)

Re: Mathematics is hard for mathematicians to understand too

#96

Post by matheme »

gjulianm wrote: post #93
matheme wrote: post #87

Earlier quoted context omitted.

My entire being is anthithetical to this type of gatekeeping. > You expect the players of the game to learn the rules before they play. TFA is literally from a 'player' who has 'learned the rules' complaining that the papers remain indecipherable. > You expect the players of the game to learn the rules before they play. Actually, I expect to have to teach rules to new players before they play. We are different.

The article does not complain about notation. It describes how the different fields of mathematics are so deep and so abstract that it’s hard to understand them as a professional mathematician in a different field. That’s a hard problem worthy of discussion, but as the article says, it’s not as much a problem of notation or of explanations, rather than it’s just intrinsically difficult and complex because these are a…

I was calling you a gatekeeper rather than notation, but feel free to keep stuffing that man with your straw.

The sentence I called out, independent of the article's content: "You expect the players of the game to learn the rules before they play."

Is you explicitly stating your goal is gatekeeping.

Re: Mathematics is hard for mathematicians to understand too

#97

Post by matheme »

gjulianm wrote: post #95
matheme wrote: post #88

Earlier quoted context omitted.

> What they are missing is that the notation is the easy part. This is so wrong it can only come from a place of inexperience and ignorance. Mathematics is flush with inconsistent, abbreviated, and overloaded notation. Show a child a matrix numerically and they can understand it, show them Ax+s=b, and watch the confusion.

Well, obviously they will be confused because you jumped from a square of numbers to a bunch of operations. They’d be equally confused if you presented those operations numerically. I am not sure what it is you want to prove with that example. I am also not sure that a child can actually understand what a matrix is if you just show them some numbers (i.e., will they actually understand that a matrix is a linear trans…

> a bunch of operations.

Sorry, the notation is bit confusing. The 'A' here is a matrix.

Re: Mathematics is hard for mathematicians to understand too

#98

Post by gjulianm »

matheme wrote: post #97
gjulianm wrote: post #95

Earlier quoted context omitted.

Well, obviously they will be confused because you jumped from a square of numbers to a bunch of operations. They’d be equally confused if you presented those operations numerically. I am not sure what it is you want to prove with that example. I am also not sure that a child can actually understand what a matrix is if you just show them some numbers (i.e., will they actually understand that a matrix is a linear trans…

> a bunch of operations. Sorry, the notation is bit confusing. The 'A' here is a matrix.

I know it is a matrix, the notation is not confusing at all. I am saying that the concept of a matrix as a set of numbers arranged in a rectangles and the concept of operations on a matrix are very different things, the confusion will not come from notation.

Re: Mathematics is hard for mathematicians to understand too

#99

Post by matheme »

gjulianm wrote: post #98
matheme wrote: post #97

Earlier quoted context omitted.

> a bunch of operations. Sorry, the notation is bit confusing. The 'A' here is a matrix.

I know it is a matrix, the notation is not confusing at all. I am saying that the concept of a matrix as a set of numbers arranged in a rectangles and the concept of operations on a matrix are very different things, the confusion will not come from notation.

You must be correct, because this interaction is completely devoid of any confusion between the two people attempting to communicate clearly.

Re: Mathematics is hard for mathematicians to understand too

#100

Post by gjulianm »

matheme wrote: post #96
gjulianm wrote: post #93

Earlier quoted context omitted.

The article does not complain about notation. It describes how the different fields of mathematics are so deep and so abstract that it’s hard to understand them as a professional mathematician in a different field. That’s a hard problem worthy of discussion, but as the article says, it’s not as much a problem of notation or of explanations, rather than it’s just intrinsically difficult and complex because these are a…

I was calling you a gatekeeper rather than notation, but feel free to keep stuffing that man with your straw. The sentence I called out, independent of the article's content: "You expect the players of the game to learn the rules before they play." Is you explicitly stating your goal is gatekeeping.

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.
Post reply on HN