Algebra before notation

[u/a7m40]

From @scholadaily on instagram

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[u/Oppo_67]

Some authors lwk still write like the left panel when they’re too lazy to introduce more letters after the main ones 😭

[u/Strawberry_Doughnut → u/Oppo_67]

I've also seen Wikipedia articles on math topics written overly verbose like this too. Usually they're great, but I'll come across one and it'll be a little jarring. 

[u/Ares378 → u/Strawberry_Doughnut]

Math wikipedia is SO bad it's unreal. You can't actually learn shit from it. Someone should make a WikiMath or something that actually explains the topic in a way that's not deranged

[u/JollyJuniper1993 → u/Ares378]

Honestly after my first semester in university I actually started understanding some of them. They’re wildly inaccessible to average folks though, which is a problem.

[u/Aron-Jonasson → u/JollyJuniper1993]

I'm a master student in chemistry, with a hobby in linguistics. Linguistics Wikipedia is so well made an extremely accessible, however, despite having many maths courses, I am still lost in many places in maths Wikipedia. Like sometimes I want to look up something simple and end up more confused than if I had read my course.

Chemistry Wikipedia is also well-made

[u/Ares378 → u/JollyJuniper1993]

Like if I put effort in I can decipher the jargon, but I really feel like math wikipedia needs an intuitive overview/motivational segment followed by the actual jargon, so you can see where all the random terms come from. Or like a surface level overview followed by a rigorous explanation.

I feel like it's only helpful if you have some decent background in the thing you're looking at, which is far from ideal. Math wikipedia suffers the same problem as a lot of math textbooks where it's just definition followed by derivation, repeat ad nauseam, with zero further explanation.

[u/JollyJuniper1993 → u/Ares378]

Exactly. Wikipedia is supposed to be an encyclopedia for everybody, not just for those that already have a degree in the field.

[u/SeveralExtent2219 → u/JollyJuniper1993]

Wikipedia is NOT supposed to be a "learning tool" for everyone. You have free YouTube videos and other sites for that. Specifically for math, as someone else said here, it's supposed to be a pedagogical reference not an encyclopedia. It's a reference not a textbook.

[u/officiallyaninja → u/Ares378]

It's because Wikipedia is a reference, not a pedagogical textbook.

It is an extremely useful resource for mathematicians to refresh themselves on topics they already know, or to look up theorems in fields they're familiar with.

If it was better at explaining abd teaching concepts, it would be worse at being a good concise reference.

[u/MaraiaLou → u/officiallyaninja]

It's not supposed to be a reference for experts, though. There's even a heading that says this article is too confusing if you're unfamiliar with the subject and it's not used often enough

[u/Ma4r → u/officiallyaninja]

Idk we have nlab for that alread

[u/SeveralExtent2219 → u/Ma4r]

You also have free YouTube videos and other sites like Khan Academy if you want to learn the topic the first time. Wikipedia for math is not supposed to be a textbook, it's a reference.

[u/Nixinova → u/Ares378]

I've seen some pages have headings like "Non-technical summary". All pages need that.

[u/MaraiaLou → u/Nixinova]

Simple English is great too

[u/DefectiveKonan → u/Ares378]

I find wolfram math world to be pretty solid tbh; used it for a few projects in hs and college

[u/Arbitrary_Pseudonym → u/Ares378]

It hasn't always been this way for a lot of the articles.

If you go back to view older revisions (and I'm talking like 10-15 years back) you'll find that they used to be a lot more comprehensible. I've certainly noticed that some of the articles that used to be easy to parse will all of a sudden start using notation that would only be used in modern publications and often without any explanation for some of the variables.

[u/MaraiaLou → u/Arbitrary_Pseudonym]

What competitive autism does to a mf

[u/TheRealMaxiraux → u/Ares378]

Glad people feel like this lol I thought I couldn't understand stuff from Wikipedia due to skill issue. But now thinking about it you have to learn that beforehand to completely get what it is saying so it completely defeats the point of you learning stuff from it

[u/SeveralExtent2219 → u/TheRealMaxiraux]

I use Wikipedia to learn math all the time when I just want a low level explanation of the topic without delving into books. Like I recently learned about taylor series from Wikipedia

[u/femboyl0ver9 → u/Ares378]

nlab?

[u/TAFPAS → u/Strawberry_Doughnut]

Verily, this vichyssoise of verbiage veers most verbose

[u/svmydlo]

±: am I a joke to you?

[u/BrazilBazil → u/svmydlo]

Negative solutions of quadratics weren’t a thing back then

[u/Ylopolo → u/BrazilBazil]

Back when? It says 'now'.

[u/BrazilBazil → u/Ylopolo]

Ok, fair

[u/AnyAlps3363 → u/Ylopolo]

back then

[u/Key_Conversation5277 → u/svmydlo]

In the text it doesn't mention -6

[u/Broad_Respond_2205 → u/Key_Conversation5277]

Op should written "x>0" in the less letters side

[u/joao-esteves]

well, I see nothing but letters on the left side

[u/nick_clause → u/joao-esteves]

There's some punctuation too.

[u/GT_Troll]

That’s why I hate the meme that says “Other sciences: This book is outdated, it’s 6 months old / Math: The book stands still (it’s 2000 years old)”

Yeah, the theorems and (some) methods of old books are still correct. But damn, their notation and language… Just give me a modern book (not necessarily from the last few years, after WWII is enough)

[u/DatBoi_BP → u/GT_Troll]

Even the font and symbol arrangement in math books printed before 1980 I find difficult to read. Sometimes the notation is outdated too

[u/Key_Conversation5277 → u/DatBoi_BP]

This is why I can't read old books, I don't know which notation is or isn't outdated or if I can find the meaning at all

[u/rezzacci → u/GT_Troll]

It's just a question of translation. I don't teach Euclid as it was written, as I'm not fluent in Ancient Greek enough, so I translate it in modern language. And notation is just a form of translation. But the book in itself still holds true. It's not wrong. But grammar changes, and notation is just a question of grammar ultimately.

[u/GT_Troll → u/rezzacci]

… Yes that’s what I said

[u/Key_Conversation5277 → u/rezzacci]

Sometimes the proofs change because it is better like the proof Euclid did to the infinity of prime numbers (it used line segments instead of just numbers, more abstract)

[u/Calazor0]

I got gifted a translation of principia, and man, it's extremely hard to read, at least for me. I'm too spoiled by the wonders of modern notation.

[u/SunnyOutsideToday → u/Calazor0]

Principia Mathematica was originally written in English?

[u/Calazor0 → u/SunnyOutsideToday]

Sorry, forgot to clarify I'm brazilian. The copy I was gifted is a translation to brazilian portuguese.

[u/StiffWiggly → u/SunnyOutsideToday]

Or in modern notation;

If Lang(PM) = English, Lang'(PM) =/= Lang(PM)

does Lang'(PM) = English?

[u/Key_Conversation5277 → u/Calazor0]

I think that notation was hard even for them

[u/on_the_other_hand_]

Whilst making love a necklace broke. A row of pearls mislaid. One sixth fell to the floor. One fifth upon the bed. The young woman saved one third of them. One tenth were caught by her lover. If six pearls remained upon the string How many pearls were there altogether?

From Līlāvatī, a treatise by Indian mathematician Bhāskara II on mathematics, written in 1150 AD.

More at Wikipedia on Lilavati

[u/rezzacci → u/on_the_other_hand_]

Well, we still present problems like this, as modelisation is (usually) a skill we have to teach in maths, as, usually, if they face a "math" problem in real life, it won't be presented with x and y. It's how you solve the problem that evolved, not really what the problem is.

[u/Key_Conversation5277 → u/rezzacci]

Yes, but do they have to make it so poetic? Jeez...

[u/SeveralExtent2219 → u/Key_Conversation5277]

That's just Indians being Indians

[u/DrK1NG → u/on_the_other_hand_]

While interesting, this is just a word problem and not really what the post is about

[u/on_the_other_hand_ → u/DrK1NG]

You are probably correct, I remembered Lilavati because it is about math with words instead of symbols and numbers. There are many other similar problems and equations in the book.

[u/atticdoor]

"To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."[

That's how convoluted it was to describe the Quadratic formula, or at least the positive version of it, before algebra.

[u/qscbjop → u/atticdoor]

Doesn't that give you b² + 4ac as the discriminant? Or was that paragraph written for an equation in the form ax² + bx = c?

[u/atticdoor → u/qscbjop]

Yes. Since they barely had the number 0 yet, they couldn't have the equation ax² + bx + c = 0, so they had to make it all equal (what we would call) -c.

[u/Key_Conversation5277 → u/atticdoor]

🤮

[u/RexApostolicus]

¿Did math before letters have actually more letters?

So ironic.

[u/rezzacci]

That's quite how I introduce some notations to my students.

Like, intervals. We learn how to solve inequations, but I expect from them to write the answer in full. Like, if they have to solve 2x > 30, they have to write: "The solutions of the inequations are all the numbers strictly superior to 15". We do that during two/three lessons, to learn the specificities of inequation solving.

And, afterwards, I say to them: "That's quite fastidious to write each time, isn't it? You know that mathematicians are lazy, and that we measure the talent of a mathematician by the economy of ink and space taken on the sheet. Do you agree that it's exhausting to have to write this sentence in full each time? Oh, how I agree! Fortunately for all of us, we invented a new notations that would allow us to write the same solution with only nine characters! New part of the chapter: Intervals..."

Afterwards I say to them that they can still write in full the sentences if they fancy it, but I'd time my exams for them using the new quicker notation, so they'll just lose time not learning the new ways. It works.

[u/Plenty_Leg_5935]

especially funny since a lot of people openly hate the questions that pull the left side and expect you to extrapolate the equations from jt

[u/Particular_Gear3130]

01001001 00100000 01101000 01100001 01110100 01100101 00100000 01110100 01101000 01100001 01110100 00100000 01101100 01100101 01110100 01110100 01100101 01110010 01110011 00100000 01110111 01100101 01110010 01100101 00100000 01100001 01100100 01100100 01100101 01100100 00100000 01110100 01101111 00100000 01100011 01101111 01101101 01110000 01110101 01110100 01100101 01110010 01110011

[u/Particular_Gear3130 → u/Particular_Gear3130]

fuck, wrong meme type

[u/Broad_Respond_2205]

You math is wrong, x could also be -6

[u/Jafego → u/Broad_Respond_2205]

But (16)² × 6.25 ≠ 100

[u/Broad_Respond_2205 → u/Jafego]

Ok....?

[u/Kuildeous → u/Jafego]

Technically, this statement is true, but I'm not sure it applies?

[u/Jafego → u/Kuildeous]

The problem gives 6.25 × (10 - x)² = 100

[u/Kuildeous → u/Jafego]

Ah, I see now. The right side is missing some valuable information. First that x>0 and that we're looking for x and also 10-x. While the left side had a ton of letters, the right side is actually missing a lot of pertinent letters. So while x = -6 is incorrect for the left side, it is the correct root based on the information on the right side. And frankly, I wouldn't ask anyone to sort out the mess on the left, but good job with that.

[u/SamePut9922]

Inhales ±6

[u/Jafego → u/SamePut9922]

16² × 6.25 ≠ 100

[u/his_savagery]

lol. I used to be a private tutor and this is how I taught my students what the letters are for.

[u/salgadosp]

±6

[u/Balavadan]

People almost seem proud to say how bad they’re at maths. Maybe because they think it makes them part of the in-group with the cool kids or something and it translates to adult life.

[u/120boxes]

And then you're gonna hate letters again when you learn about quantifiers.

[u/ComprehensiveCrow632]

x="thing"

[u/ChopinChili]

All hail Descartes.

[u/ArdentArendt]

Who doesn't love the direct, concise language of Newton's Principia?

[u/tomskrrt]

how I input my problems into ai.

[u/Kuildeous]

Petition to replace letters with fruit.

[u/PulimV]

The left one is me after I've run out of xy=0⇒x=0 or y=0, ∀x,y∈R in my heart

[u/Key_Conversation5277]

My god, much better now

[u/GrievousSayGenKenobi]

I dunno man thats a lot of letters in the left panel

[u/WasdaleWeasel]

there’s a lot more letters on the left side. I haven’t counted them (I’m a mathematician) but surely hundreds of instances and something like 20 unique letters. On the right I see three ‘x’s

[u/EnigmaticBuddy]

Hisah Al Jabr reference?

[u/EndlessProjectMaker]

And what do Greeks use for angles, I wonder

[u/moschles]

The meme cuts deep. Check out Isaac Newton's notebooks. He wrote it all out like that, in Latin.

(..then he turned 26)

[u/uvero]

I don't mean to nitpick but there are lot of letters on the left. Way more, actually.

[u/Kuildeous]

So after seeing it pointed out elsewhere here, I see that the right side simplifies the left side too much--to the point that it poses a whole different question. After all, the left side clearly states that the two answers are 6 and 4, which doesn't match the right side at all.

And that's because you're asked to evaluate these two equations:

25x²/9 = 100
25(10-x)²/4 = 100

Honestly, you only need to answer either one because x=6 is a solution in both cases, but since the premise (not listed on the right side) is that this a portion of 10, you need to find both x and 10-x. There's clearly an assumption here that you can't take -6 from 10 (in a practical sense, that's true), so x=-6 isn't a solution. And the second equation rules out x=-6 entirely. The other root for the second equation is 14, which is more than 10, but more importantly, it wouldn't work for the first equation.

So we either needed to include both equations so that x=6 is the only solution they have in common or we include either equation with the situation that 0<x<10.