10 ms·

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 a

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..

zwnow 10mo ago
I'd love getting rid of all the weird symbols in favor of clear text functions or whatever. As someone who never learnt all the weird symbols its really preventing me from getting into math again... It is just not intuitive.
- Jensson 10mo ago
  Those are used since it makes things easier, if you write everything out basically nobody would manage to learn math, that is how it used to be and then everything got shortened and suddenly average people could learn calculus.
  - zwnow 10mo ago
    Yea because hieroglyphs are more understandable than the name of a function
    - Jensson 10mo ago
      That is exactly it, a long text is much harder to understand than a one liner, we see that time and time again in problem solving if you write the same problem as a long text many fewer students manage to solve it than if you write it as a one liner.
    - deleted 10mo ago
      [deleted]
    - SetTheorist 10mo ago
      There is an inherent complexity in a lot of mathematics. The compact notation makes it much easier (or even possible) to understand what is going on. Compare something like equals(integral(divide(exponentiate(negate(divide(square(var),2))),sqrt(multiply(2,constant_pi))),var,negate(infinity),infinity),1) vs $$\int_{-\infty}^{\infty}\frac{e^{-x^2/2}}{\sqrt{2\pi}}dx = 1$$ (imagine the actual generated mathematical formula here :-/ ) it is infinitely easier to grok what is going on using symbolic notation after a minimal amount of learning.
  - abraxas 10mo ago
    There has to be a happy medium between the tersness of the current notation systems and the verbosity of code-like expressions. We just need to rethink this so more people can learn it. Math still stands a bit like writing did in ancient culture. It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else.
    - gjulianm 10mo ago
      I wonder why so many people are under the impression that the notation is what is keeping them away and if only the notation was easier then the underlying concepts would be clear. For example, if you don't know what the pullback of a differential form is, it doesn't matter if I write it in clear text or if I write the common notation φ^* ω. > It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else. It's a domain reserved for people who want to learn it, and there's ton of resources to learn it. Expecting to understand it without learning it does not make any sense.
      - zwnow 10mo ago
        φ^* ω is just 2 weird symbols. There are tons of symbols to learn. I gave up trying to learn the Russian alphabet after a few days so why do u think I am capable of memorizing the Greek one? The theories are learnable, making sense of all the weird symbols is what's breaking my brain. I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content. Learning can be incredibly fun if it was designed fun. Math is a dry and slow process. Make it fun, make it readable and people will be capable to learn it easier.
        gjulianm 10mo ago
        > why do u think I am capable of memorizing the Greek one No one memorizes the Greek alphabet. We just learn it as we go because it’s useful to have different types of letters to refer to different types of objects. That’s it. > I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content. That sounds like you’re trying to learn a specific field without actually having any of the prerequisites to learn it. I don’t know what you’re specifically referring to when you say “set theory” as that’s an incredibly wide field, and depending on what you’re trying to learn it can be quite technical. > Learning can be incredibly fun if it was designed fun. Math is a dry and slow process. This sounds like someone complaining that getting to run a marathon is tiresome and hard. Yes, teaching mathematics can always be improved and nothing is perfect, but it will still be hard work.
- gjulianm 10mo ago
  I'm not sure that symbols are the thing actually keeping you away. Clear text functions might not be as clear, as it will be harder to scan and it will still contain names that you might not be familiar with. Those "weird symbols" are not there because people liked to make weird symbols. No one likes them, it's just that it makes things easier to understand.
kragen 10mo ago
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 orthographies like Shavian (https://en.wikipedia.org/wiki/Shavian_alphabet https://en.wikipedia.org/wiki/Shavian_alphabet) in that, however logical they may be, the audience they'd need to appeal to consists of people who have spent 50 years restructuring their brains into specialized machines to process the conventional notation. Aim t3mpted te rait qe r3st ev q1s c0m3nt 1n mai on alterned1v i6gl1c orx2grefi http://canonical.org/~kragen/alphanumerenglish http://canonical.org/~kragen/alphanumerenglish bet ai qi6k ail rez1st qe t3mpt8cen because, even though it's a much better way to spell English, nobody would understand it. 3. It's optimized for rewriting a formula many times. When you write a computer program, you only write it once, so there isn't a great burden in using a notation like (eq (deriv x (pow e y)) (mul (pow e y) (deriv x y)) 1), which takes 54 characters to say what the conventional math notation¹ says in 16 characters³. But, when you're performing algebraic transformations of a formula, you're writing the same formula over and over again in different forms, sometimes only slightly transformed; the line before that one said (eq (deriv x (pow e y)) (deriv x x) 1), for example². For this purpose, brevity is essential, and as we know from information theory, brevity is proportional to the logarithm of the number of different weird symbols you use. We could certainly improve conventional math notation, and in fact mathematicians invent new notation all the time in order to do so, but the direction you're suggesting would not be an improvement. People do make this suggestion all the time. I think it's prompted by this experience where they have always found math difficult, they've always found math notation difficult, and they infer that the former is because of the latter. This inference, although reasonable, is incorrect. Math is inherently difficult, as far as anybody knows (an observation famously attributed to Euclid) and the difficult notation actually makes it easier. Undergraduates routinely perform mental feats that defied Archimedes because of it. ______ ¹ \frac d{dx}e^y = e^y\frac{dy}{dx} = 1 ² \frac d{dx}e^y = \frac d{dx}x = 1 ³ See https://nbviewer.org/url/canonical.org/~kragen/sw/dev3/logarithm-derivative.ipynb https://nbviewer.org/url/canonical.org/~kragen/sw/dev3/logar... for a cleaned-up version of the context where I wrote this equation down on paper the other day.
youoy 10mo ago
Notation an symbology comes out of a minmax optimisation. Minimizing complexity maximizing reach. As with every local critical point, it is probably not the only state we could have ended at. For example, for your point 1: we could probably start there, but once you get familiar with the notation you dont want to keep writing a huge list of parameters, so you would probably come up with a higher level data structure parameter which is more abstract to write it as an input. And then the next generation would complain that the data structure is too abstract/takes too much effort to be comunicated to someone new to the field, because they did not live the problem that made you come with a solution first hand. And for you point 2: where do you draw the line with your hyperlinks. If you mention the real plane, do you reference the construction of the real numbers? And dimensionl? If you reason a proof by contradiction, do you reference the axioms of logic? If you say "let {xn} be a converging sequence" do you reference convergence, natural numbers and sets? Or just convergence? Its not that simple, so we came up with a minmax solution which is what everybody does now. Having said this, there are a lot of articles books that are not easy to understand. But that is probably more of an issue of them being written by someone who is bad at communicating, than because of the notation.
sfpotter 10mo ago
Go ahead. Write a math paper with your proposed new notation with hyperlinks and submit it to a journal somewhere.
hodgehog11 10mo ago
(1) I always tell my students that if they don't understand why things are done a certain way, that they should try to do it in the way most natural to them and then iterate to improve it. Eventually they will settle on something very similar to most common practice. (2) Higher-level proofs are using so many ideas simultaneously that doing this would be tantamount to writing Lean code from scratch: painful.
xigoi 10mo ago
What’s wrong with Greek letters? Would the number π be any easier to understand if it was written differently?
vjk800 10mo ago
1. I work in finance and here people sometimes write math using words as variable names. I can tell you it gets extremely cumbersome to do any significant amount of formula manipulation or writing with this notation. Keep in mind that pen and paper are still pretty much universally used in actual mathematical work and writing full words takes a lot of time compared to single Greek letters. Large part of math notation is to compress the writing so that you can actually fit a full equation in your vision. Also, something like what you want already exists, see e.g. Lean: https://lean-lang.org/doc/reference/latest/ https://lean-lang.org/doc/reference/latest/. It is used to write math for the purpose of automatically proving theorems. No-one wants to use this for actually studying math or manually proving theorems, because it looks horrible compared to conventional mathematics notation (as long as you are used to the conventional notation).

zwnow 10mo ago

I'd love getting rid of all the weird symbols in favor of clear text functions or whatever. As someone who never learnt all the weird symbols its really preventing me from getting into math again... It is just not intuitive.

Jensson 10mo ago
Those are used since it makes things easier, if you write everything out basically nobody would manage to learn math, that is how it used to be and then everything got shortened and suddenly average people could learn calculus.
- zwnow 10mo ago
  Yea because hieroglyphs are more understandable than the name of a function
  - Jensson 10mo ago
    That is exactly it, a long text is much harder to understand than a one liner, we see that time and time again in problem solving if you write the same problem as a long text many fewer students manage to solve it than if you write it as a one liner.
  - deleted 10mo ago
    [deleted]
  - SetTheorist 10mo ago
    There is an inherent complexity in a lot of mathematics. The compact notation makes it much easier (or even possible) to understand what is going on. Compare something like equals(integral(divide(exponentiate(negate(divide(square(var),2))),sqrt(multiply(2,constant_pi))),var,negate(infinity),infinity),1) vs $$\int_{-\infty}^{\infty}\frac{e^{-x^2/2}}{\sqrt{2\pi}}dx = 1$$ (imagine the actual generated mathematical formula here :-/ ) it is infinitely easier to grok what is going on using symbolic notation after a minimal amount of learning.
- abraxas 10mo ago
  There has to be a happy medium between the tersness of the current notation systems and the verbosity of code-like expressions. We just need to rethink this so more people can learn it. Math still stands a bit like writing did in ancient culture. It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else.
  - gjulianm 10mo ago
    I wonder why so many people are under the impression that the notation is what is keeping them away and if only the notation was easier then the underlying concepts would be clear. For example, if you don't know what the pullback of a differential form is, it doesn't matter if I write it in clear text or if I write the common notation φ^* ω. > It's a domain reserved for a few high priests inducted into the craft and completely inaccessible to everyone else. It's a domain reserved for people who want to learn it, and there's ton of resources to learn it. Expecting to understand it without learning it does not make any sense.
    - zwnow 10mo ago
      φ^* ω is just 2 weird symbols. There are tons of symbols to learn. I gave up trying to learn the Russian alphabet after a few days so why do u think I am capable of memorizing the Greek one? The theories are learnable, making sense of all the weird symbols is what's breaking my brain. I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content. Learning can be incredibly fun if it was designed fun. Math is a dry and slow process. Make it fun, make it readable and people will be capable to learn it easier.
      - gjulianm 10mo ago
        > why do u think I am capable of memorizing the Greek one No one memorizes the Greek alphabet. We just learn it as we go because it’s useful to have different types of letters to refer to different types of objects. That’s it. > I tried to get into set theory thrice now, not happening with all the math lingo, hieroglyphs and dry ass content. That sounds like you’re trying to learn a specific field without actually having any of the prerequisites to learn it. I don’t know what you’re specifically referring to when you say “set theory” as that’s an incredibly wide field, and depending on what you’re trying to learn it can be quite technical. > Learning can be incredibly fun if it was designed fun. Math is a dry and slow process. This sounds like someone complaining that getting to run a marathon is tiresome and hard. Yes, teaching mathematics can always be improved and nothing is perfect, but it will still be hard work.
gjulianm 10mo ago
I'm not sure that symbols are the thing actually keeping you away. Clear text functions might not be as clear, as it will be harder to scan and it will still contain names that you might not be familiar with. Those "weird symbols" are not there because people liked to make weird symbols. No one likes them, it's just that it makes things easier to understand.

kragen 10mo ago

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 orthographies like Shavian (https://en.wikipedia.org/wiki/Shavian_alphabet https://en.wikipedia.org/wiki/Shavian_alphabet) in that, however logical they may be, the audience they'd need to appeal to consists of people who have spent 50 years restructuring their brains into specialized machines to process the conventional notation. Aim t3mpted te rait qe r3st ev q1s c0m3nt 1n mai on alterned1v i6gl1c orx2grefi http://canonical.org/~kragen/alphanumerenglish http://canonical.org/~kragen/alphanumerenglish bet ai qi6k ail rez1st qe t3mpt8cen because, even though it's a much better way to spell English, nobody would understand it. 3. It's optimized for rewriting a formula many times. When you write a computer program, you only write it once, so there isn't a great burden in using a notation like (eq (deriv x (pow e y)) (mul (pow e y) (deriv x y)) 1), which takes 54 characters to say what the conventional math notation¹ says in 16 characters³. But, when you're performing algebraic transformations of a formula, you're writing the same formula over and over again in different forms, sometimes only slightly transformed; the line before that one said (eq (deriv x (pow e y)) (deriv x x) 1), for example². For this purpose, brevity is essential, and as we know from information theory, brevity is proportional to the logarithm of the number of different weird symbols you use. We could certainly improve conventional math notation, and in fact mathematicians invent new notation all the time in order to do so, but the direction you're suggesting would not be an improvement. People do make this suggestion all the time. I think it's prompted by this experience where they have always found math difficult, they've always found math notation difficult, and they infer that the former is because of the latter. This inference, although reasonable, is incorrect. Math is inherently difficult, as far as anybody knows (an observation famously attributed to Euclid) and the difficult notation actually makes it easier. Undergraduates routinely perform mental feats that defied Archimedes because of it. ______ ¹ \frac d{dx}e^y = e^y\frac{dy}{dx} = 1 ² \frac d{dx}e^y = \frac d{dx}x = 1 ³ See https://nbviewer.org/url/canonical.org/~kragen/sw/dev3/logarithm-derivative.ipynb https://nbviewer.org/url/canonical.org/~kragen/sw/dev3/logar... for a cleaned-up version of the context where I wrote this equation down on paper the other day.

youoy 10mo ago

Notation an symbology comes out of a minmax optimisation. Minimizing complexity maximizing reach. As with every local critical point, it is probably not the only state we could have ended at. For example, for your point 1: we could probably start there, but once you get familiar with the notation you dont want to keep writing a huge list of parameters, so you would probably come up with a higher level data structure parameter which is more abstract to write it as an input. And then the next generation would complain that the data structure is too abstract/takes too much effort to be comunicated to someone new to the field, because they did not live the problem that made you come with a solution first hand. And for you point 2: where do you draw the line with your hyperlinks. If you mention the real plane, do you reference the construction of the real numbers? And dimensionl? If you reason a proof by contradiction, do you reference the axioms of logic? If you say "let {xn} be a converging sequence" do you reference convergence, natural numbers and sets? Or just convergence? Its not that simple, so we came up with a minmax solution which is what everybody does now. Having said this, there are a lot of articles books that are not easy to understand. But that is probably more of an issue of them being written by someone who is bad at communicating, than because of the notation.

sfpotter 10mo ago

Go ahead. Write a math paper with your proposed new notation with hyperlinks and submit it to a journal somewhere.

hodgehog11 10mo ago

(1) I always tell my students that if they don't understand why things are done a certain way, that they should try to do it in the way most natural to them and then iterate to improve it. Eventually they will settle on something very similar to most common practice. (2) Higher-level proofs are using so many ideas simultaneously that doing this would be tantamount to writing Lean code from scratch: painful.

xigoi 10mo ago

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

vjk800 10mo ago

1. I work in finance and here people sometimes write math using words as variable names. I can tell you it gets extremely cumbersome to do any significant amount of formula manipulation or writing with this notation. Keep in mind that pen and paper are still pretty much universally used in actual mathematical work and writing full words takes a lot of time compared to single Greek letters. Large part of math notation is to compress the writing so that you can actually fit a full equation in your vision. Also, something like what you want already exists, see e.g. Lean: https://lean-lang.org/doc/reference/latest/ https://lean-lang.org/doc/reference/latest/. It is used to write math for the purpose of automatically proving theorems. No-one wants to use this for actually studying math or manually proving theorems, because it looks horrible compared to conventional mathematics notation (as long as you are used to the conventional notation).