The mathematical system in current math is quite simply broken

The mathematical system in current math is quite simply broken.

First of all across many math textbooks there is inconsistency of syntax such that a student learning from different math books come across different answers.

Furthermore the syntax to mathematical language taught in schools is riddled with wats, gotchyas, and general faffing about which cause students to produce more errors than necessary. Even basic syntactic structures like PEMDAS which were aimed to add more control to math have actually cause students to struggle further thus preventing them from attaining higher maths.

Furthermore most math notation is not general purpose until calculus level. In algebra all the basic pieces are taught in order to achieve basic computing only that a few pieces are left mussing such that a student can not write a general purpose program and compute it by hand without including english into their problem. The need for using words to describe math problems is a weakness, not a strength. It hinders students from understanding the full breadth of what logic and math can do when combined.

A new notation is necessary not only to make math more consistent, but to reduce errors and to allow students to progress further into mathematics with less struggle.

The true answer to this problem is the lambda calculus proposed by alfonso church.

Using polish notation such as this:

(+ 2 2 (- 3 3)) is not only unambiguous but allows for faster computation by pencil and is less error prone.

The fact that we continue to teach students antiquated notations is a side effect from the "boy's club" of university that persists in making students jump through hoops rather than innovating.

It's just plain dense.

Even reverse polish notation arguably provides a better more complete mathematical system than infix notation.

All math is just a set of variables with axioms telling you how to use them. You can literally make up any bullshit you want (people do every day) and call it "math" so long as you adhere to your axioms.

>First of all across many math textbooks there is inconsistency of syntax such that a student learning from different math books come across different answers.
If everyone were smart enough to use the objectively superior French syntax, this would not be a problem.

>Even basic syntactic structures like PEMDAS which were aimed to add more control to math have actually cause students to struggle further thus preventing them from attaining higher maths.
PEMDAS is as simple and unambiguous as it gets unless you still fall for 2008 baits from /b/.

>In algebra all the basic pieces are taught in order to achieve basic computing only that a few pieces are left mussing such that a student can not write a general purpose program and compute it by hand without including english into their problem.
If you think 100%-symbolic proofs are readable, you have a problem. There is a reason Donald Knuth included dotted lists, tables and paragraphs in [math]\rm\LaTeX[/math].

>A new notation is necessary not only to make math more consistent, but to reduce errors and to allow students to progress further into mathematics with less struggle.
Introducing thousands of new symbols will make things worse, especially in middle school where most students can't even tell an adverb from an adjective.

>The true answer to this problem is the lambda calculus proposed by alfonso church.
λ-calculus is for computation, not notation.

>(+ 2 2 (- 3 3)) is not only unambiguous but-
Ass-unreadable. Lisp is easy to parse, but only a newfa/g/ would think it's anywhere legible. Besides, the brackets here make it even more complicated since it hides the fact [math]\left( \mathbf Z,\, +\right)[/math] is a group (no brackets needed).

Take your Reddit-spaced Lisp FizzBuzz circlejerk back to

>PEMDAS is as simple and unambiguous
PEMDAS is inaccurate and may yield multiple possible results in certain edge cases. It, and the way it's taught, are why I ditched formalized mathematics for ten years. I developed other, non directly numerical ways of computing logarithms, renormalization, certain geometrical and temporal relationships. I'm fairly biased towards thinking mechanically to begin with.

Mathematics are in general, terribly taught. There are reasons for this in the US that can be attributed to large scale intellectual purges, and movements to limit mathematical literacy in the general population. "The common man need only be able to count money and pay his taxes. He has no need nor capacity for such things as geometry, or algebra." Faculty were generally removed after being framed as communists, or communist sympathizers. Further down the chain, present day, these artifacts and their effects are still ticking away.

But that's really irrelevant. I just didn't like being told I was wrong, and didn't care to learn other people's junk hackjob little systems constantly. I didn't know the history, see the connections, and I did not properly see its relationship with nature and the underlying logic of the universe. There is no desire or attempt to speak of such pretentious philosophical things. No mention of Lepponicus and Democritus when introducing atomic theory, no mention of void and the big debate in Greece about the nature of change. No mention of Babylonian mathematics, base 60, and all the ways it's used everyday.

Nothin'. There's nothin' but junk and iterative repetition to clumsily patch all the ways the high level heuristic gets it wrong.

Fuck PEMDAS. PEMDAS is trash.

are you a highschooler who just failed an algebra I test because you couldn't follow PEMDAS or something?

>follow PEMDAS
2^3^2 = ?

Oh look another undergrad with a plan to fix all of mathematics!

64, what is your point?

wrong, it's 512
top-down is not covered by PEMDAS

woops I see what you mean now, i'm a dolt.

All effective syntactic systems are equal up to isomorphism.

Instead of trying to force everyone to speak exactly the same language (which has NEVER worked out in practice), your efforts would be better spent in equipping math students with the skills to be effective translators, capable of recognizing the common underlying structure between seemingly-unrelated presentations of the same object, while allowing them to design a personalized syntax that best reflects their mental models.

I'm 23. Learning algebra from its foundations, on and off.

lmao who gives a shit
students won't care about math more just because you make the syntax better
and no one really wants to change conventions, too much effort

you know parentheses exist, right? and that you're supposed to use them for several reasons, one of which is ambiguous statements like thst

>anime image
>several references to "school"
>basically complaints about how math is written
OP is a massive faggot.

Learn some basic formal languages and parsing theory.

PEMDAS isn't syntax, it's actually a notational convention that allows one to omit a ton of parenthesis that appear in the actual syntax.

lambda calculus is not what you think it is.

Polish notation has the same problems, you just don't see them.

You are literally retarded and the opinions you're spouting aren't wrong because we disagree with them, they're wrong because you don't understand the things you're talking about.

PEMDAS is operation precedence, not associativity.

Also, ^ is right-associative.

>write a coherent post
>use an anime picture
>post becomes worthless

>inconsistency of syntax
Read any differential geometry textbook if you want to learn fuck ton of inconsistent notations. What you're complaining about is retarded and you should just kill yourself

Also
>reddit spacing

>reddit spacing
Is it really that bad? My prior hypothesis is that it makes the post more readable, so consider this a test post:

The mathematical system in current math is quite simply broken.
First of all across many math textbooks there is inconsistency of syntax such that a student learning from different math books come across different answers.
Furthermore the syntax to mathematical language taught in schools is riddled with wats, gotchyas, and general faffing about which cause students to produce more errors than necessary. Even basic syntactic structures like PEMDAS which were aimed to add more control to math have actually cause students to struggle further thus preventing them from attaining higher maths.
Furthermore most math notation is not general purpose until calculus level. In algebra all the basic pieces are taught in order to achieve basic computing only that a few pieces are left mussing such that a student can not write a general purpose program and compute it by hand without including english into their problem. The need for using words to describe math problems is a weakness, not a strength. It hinders students from understanding the full breadth of what logic and math can do when combined.
A new notation is necessary not only to make math more consistent, but to reduce errors and to allow students to progress further into mathematics with less struggle.
The true answer to this problem is the lambda calculus proposed by alfonso church.
Using polish notation such as this:
(+ 2 2 (- 3 3)) is not only unambiguous but allows for faster computation by pencil and is less error prone.
The fact that we continue to teach students antiquated notations is a side effect from the "boy's club" of university that persists in making students jump through hoops rather than innovating.
It's just plain dense.
Even reverse polish notation arguably provides a better more complete mathematical system than infix notation.

Well shit, that didn't turn out as bad as I expected.
One more test:

>First of all across many math textbooks there is inconsistency of syntax such that a student learning from different math books come across different answers.
If everyone were smart enough to use the objectively superior French syntax, this would not be a problem.
>Even basic syntactic structures like PEMDAS which were aimed to add more control to math have actually cause students to struggle further thus preventing them from attaining higher maths.
PEMDAS is as simple and unambiguous as it gets unless you still fall for 2008 baits from /b/.
>In algebra all the basic pieces are taught in order to achieve basic computing only that a few pieces are left mussing such that a student can not write a general purpose program and compute it by hand without including english into their problem.
If you think 100%-symbolic proofs are readable, you have a problem. There is a reason Donald Knuth included dotted lists, tables and paragraphs in LATEXLATEX.
>A new notation is necessary not only to make math more consistent, but to reduce errors and to allow students to progress further into mathematics with less struggle.
Introducing thousands of new symbols will make things worse, especially in middle school where most students can't even tell an adverb from an adjective.
>The true answer to this problem is the lambda calculus proposed by alfonso church.
λ-calculus is for computation, not notation.
>(+ 2 2 (- 3 3)) is not only unambiguous but-
Ass-unreadable. Lisp is easy to parse, but only a newfa/g/ would think it's anywhere legible. Besides, the brackets here make it even more complicated since it hides the fact [math]\left( \mathbf Z,\, +\right)[math] is a group (no brackets needed).
Take your Reddit-spaced Lisp FizzBuzz circlejerk back to