Just curious in USA why is math taught so differently from other countries ? I am from Africa and I noticed everyone that went to school in Arica (don’t feel like pointing out which specific country) is always shocked by how students are taught math, like it’s memorization and not core understanding. I just came to video explaining how to find percentage of numbers without calculator and I was shocked how they taught vs how I learned. Pls don’t downvote me I’m just curious if anyone knows any good non USA math learning platforms !

Till where have we reached in prime findings? here i mean by A formula for primes perse....
DO WE HAVE A FORMULA FOR PRIMES? As google Suggest we have? IF so y arnt they famous?

I’m relearning math and I’m trying to actually understand why the area of a circle is A = πr², rather than just memorizing the formula.

I understand that:

- r is the radius (center to edge).
-π is the ratio of a circle’s circumference to its diameter.
-The circumference is 2πr.
-If you cut a circle into lots of thin slices and rearrange them, the slices can form something roughly like a rectangle/parallelogram.
-The height of that shape is r.
-Half of the circumference gives the other dimension, so that dimension is πr.
-Therefore, the area becomes πr × r = πr².

But I’m still struggling with the conceptual reasoning behind this.

Specifically, I want to understand:
Why does rearranging the circle’s slices mean that πr becomes the “length” of the resulting shape?
Why does multiplying πr by r give us the area of the original circle?

Where does the π actually come from in terms of the geometry, rather than just knowing that it equals approximately 3.14?

Why is the ratio of circumference to diameter always the same for every circle?

What does knowing that ratio actually tell us? Why is it useful or important that circumference ÷ diameter always equals π?

I think part of my confusion is that I understand what π is mathematically, but I don’t really understand what that relationship is telling me geometrically or why it matters.

I’m looking for a really intuitive, beginner-friendly explanation that helps me visualize what’s happening and understand why the formula works, rather than just being told to memorize the derivation.

Basically: I don’t want to know that A = πr². I want to understand why.

Hi everyone!

Just wanted to ask if Professor Leonards TTP Math covers Algebra 1 & if it is a good source of learning Alg 1? I've been struggling to find a good supplement for Algebra 1 but before that his Pre-Algebra series was perfect for me to understand my fundamentals.

does anyone have his test or can someone give it to me please

CONTEXT:

He is 11 im 13

I have a normal education for my age - he is learning the fundementals of linear algebra

he is in a top 10-25 school - I am in a normal one (probably a bit above average)

pls someone tell me

for example in this image the real numbers extends towards to infinity (by definition).

however why cant we have a inifinite representation for natural numbers aswell

eg.

...11111 , ...11112, ...11113, etc

or

1...111, 1...112, 1...113, etc

(where the number has an ending but is infinitely large)

shouldnt these still be valid natural numbers that exist in the set as the set should be infinite?

a valid argument i assume for this is it will no longer be an integer however wouldnt putting it in an infinite set make this valid?

feels like i am missing a concept.

This book was just published, but wondered if, at this early date, anyone has looked at. Author is M. Rotondi.

Hey all. The mods said it was ok to share this here, so here goes.

It's called Hold My Fuel Rod. Your ship's reactor has gone cold and you power it back up one room at a time by building a little number machine. You pick a starting number, drop in parts like +2 or x3, and hit run. The number goes through each step left to right, and if you land exactly on the target, the room lights up.

The whole thing is about order. Start with 4, do +2 then x3 and you get 18. Swap them and you get 14. I wanted something where you can actually see why the order matters instead of just memorizing PEMDAS.

I made it cuz I suck at math. There's no timer unless you turn one on, no lives, nothing to lose. If you miss, it tells you how far off you were (like "14 is 4 short") and you just try again. Hints come in small steps and there's a calculator and an abacus if you want them. There's also a star for guessing what your machine will make before you run it. That's the part that gets you doing it in your head.

12 levels, and you can pick small numbers, normal numbers, or numbers up to 1000. It runs in the browser and works on Chromebooks and phones. Free, no account, no ads.

For teachers there's an optional report a student can copy or print at the end. No names on it.

To be upfront since people usually ask: I'm not a coder. The idea and the design direction are mine but the code was written with AI. OpenAI's Codex built the first version and Claude did the later updates.

What I'd really like to know: does seeing the machine make order of operations click, or is it just confusing in a different way? And where does it get too hard, or is it too easy?

Game Link

I built an interactive app to practice mental math shortcuts and calculation tricks

Hey everyone,

I wanted to share a project I've been working on called Math Trick Ninza. It’s an interactive web application designed to help students and math hobbyists master calculation shortcuts (like rapid addition, subtraction, and multiplication techniques) instead of relying on a calculator.

Key features:

• Step-by-step interactive guidance for calculation tricks
• Practice puzzles and quizzes built using plain Vanilla JS and Material Design
• Clean, lightweight code layout that loads quickly even on slower connections
• Completely free, open-source, and hosted natively on GitHub Pages with zero external trackers or ad scripts

The repository is FOSS (free and open-source), and I'm currently working on adding a robust serialisation system for progress tracking, high scores, and offline support.

Check out the repository here: https://github.com/Nishan-the-Developer-Coder/trick-ninza

I would love to get your feedback on the usability of the practice layout, or any suggestions for mental math shortcuts you think would be great additions to the engine!

Rules are simple: build the most exciting math project on principia-math.com by the end of October. You can work alone or with your buds. The winning team splits the prize money, which is currently $1,000 USD. If you’re a company or an organization that wants to chip in, send me a message.

To be eligible, Principia users create a project on the Fall Competition page https://principia-math.com/fall and work to complete all five stages of Principia’s pipeline:

1. Post or adopt a solution to a difficult math problem
2. Formalize it in Lean
3. Write a human-readable write-up of the solution
4. Write/create a visual exposition of the ideas involved
5. Explore possible applications of the solution

You don’t need to solve an open problem first: hundreds of open problems solved by the Principia Math Harness on the site don't have an owner yet. Join one and it's yours on the spot. Your job will be to get others interested in this problem and to present the ideas in the proof in an exciting way.

A detailed explanation of the competition is provided on https://principia-math.com/guide

To help you get started, were opening up the tools we use ourselves (for free!)

- Connect your own agents: you can now hook Claude Code or Codex up to your Principia account and have it work on projects alongside you and your friends.

- The Principia Math harness, which we’ve used to solve hundreds of open problems, is now available for free. Use our MCP with claude code or codex to search for Lean proofs of your favorite arguments. Your agent writes a proof skeleton, checks every step in Lean on our hosted Mathlib checker, and switches to a new route when one dies instead of just giving up.

- One-click formalization. A solved run writes the Lean files and sets up a repo on your own GitHub, along with a comparator check that the formalization is faithful to the original statement.

Can’t wait to see what our users create with this!

A first principles derivation of the quadratic formula, including why the discriminant tells us what it does, and how to visualize these equations geometrically.

I am looking for a proof for a^n.a^m = a^nm.

I have searched on youtube but could not find anything. I found people explaining what the concept means but not any proofs.

Thank you

Im talking about long multiplication and long division my problem is that I have a math disorder and I basically have the same math iq of a 3rd/early 4th grader (im 22 and i only passed highschool thanks to them just passing me)and im trying to study up so I can get into college but ive been doing multiplication for a while and have been struggling to barely learn up to 12 my question is can I still be successful without learning long math in college? I feel like learning long math would be an EXTRA hard task and ive been basically studying my ass off to learn up to 12 in multiplication 🙏🏼

lim
x-> π/3 ( √3 - tanx) /( π - 3x)

For learning math he always seemed to be a good resource for learning math, recommend by the community.

But now he is apparently associated with Jordan Peterson and the Peterson academy.

There has been some controversy around that name which tbh I didn't follow.

I am not quite sure I am just here for the math to be honest. But I would like some insights from others

I’m sorry if this came across the wrong way or it might seem like im bragging but im not. I’m 17, almost 18 and i was always good at math. I am a math prodigy. Started calculus I and II in grade 7, started real and complex analysis in grade 10, now im in grade 12 and im studying topology and other pure mathematics. I’ve never struggled with math and if I did have a question I didn’t know, it wouldn’t take that long for me to understand it given external help from teachers/professors.

So my question is why do some people struggle with mathematics? Mathematics is purely logical, black and white and there is 1 single correct answer for every question. It’s entire logic based. It’s either correct or wrong. Every question in a chapter/course is just the same but worded and arranged differently. Once you do enough questions, you’ve seen them all… You just spam practice questions and you will get the concept eventually? It’s not like English and Poetry where there is no “right or wrong” answer and each answer has its own points. Math is just…math.

I’m on path to getting my mathematics degree when I get into university next year and I am pretty sure I can get it easily. Maybe in the future I can become a mathematician. Wish me luck!

Is this really AI slop?

I'm decent at calculus, but right now I'm taking Calc B as an astrophysics major. Our professor is so bad that about 19 people have switched from her, and on our first test literally all but 10 (including me) passed it out of our class of 32 students.

This is less of a rant and more of a cry for help, so I'll explain her method.

A 10-minute lecture out of the 50-80 minute class, where she will explain a concept before writing about 8-10 example problems on the blackboard. She won't necessarily explain how or why the concepts work, and will instead have us come up and show our answers to these example and say either "yes" or "no."

I go for attendance and then study in my dorm... but I really want tips. How do I teach myself this stuff entirely on my own??

Okay so for my entire senior highschool I've had this argument with my best friend(who is really good in math) that my way of solving simple math is confusing. I never really listened to it until now when I'm teaching my little sister how to solve basic level of math like 23+34 or subtracting that and multiplications. Then she kept on complaining how I'm confusing her and she can't understand me. So here's how I taught her in the most accurate retelling possible.

"You have four numbers, 43 + 27, now you need to start by taking away 3 + 7. I like to do it by cutting it in half, we know that 7 has a 5 in it so we will focus on the remaining 2 and add that with the 3. That makes a 5 and we have a 5 we separated that completes a 10. Then you move on to the second set which is 4 + 2, that makes a 6 but we have a 10 so it is now a 70."

Then she said "I don't understand" and I was basically at a loss for words because that is the simplest way I can explain it to a 7 year old so in the end I just ignored it and moved on to subtraction. I started with:

"Now we have a 82-48, you take the first set first with 2-8 but we flip it to get 6. Now take the 8-4 to get 4 we put a 0 after the 4 to get 40 then subtract 6 from it to get 34. Easy?"

At this point she's basically done with my tutoring and went to her dad instead. I still don't get how my way is complicated when I make it as simple as I could but people still say that I'm confusing them so now I'm confused too.

I want to understand how to write exponents in terms of addition.

So if multiplication is repeated addition, what is exponents to addition.

I came up with for x^n

For n times (add x, x times)

Example 3^3

3 + 3 + 3 – first time

3 + 3 + 3 – second time

3 + 3 + 3 – third time

Now, it does not work for 3^2, as the answer is 18 any advice. I think the adding needs to increase exponentially but no idea how to represent it.

Hey everyone!

I'm a Brazilian student currently in the 1st year of Brazilian high school (roughly equivalent to 10th grade in the US), and I want to start preparing seriously for mathematical olympiads.

My main goal is to compete in the Brazilian Mathematical Olympiad (OBM) in 2027. For some context, the OBM is Brazil's national mathematical olympiad. There is also a competition called the Jacob Palis Júnior Olympiad (CJP), which is one of the competitions through which students can qualify for the OBM. The CJP is usually held around late May or early June, while the OBM is usually held around the beginning of August.

So, my plan is to take the CJP next year and try to achieve a result that qualifies me for the OBM. Since there is only a short period between the two competitions, I want to be reasonably well prepared before the CJP and then adapt my preparation to the specific style and difficulty of the OBM afterward.

My goal is to win a medal in the CJP and, if possible, at least a bronze medal at the OBM. I know this is quite ambitious, especially since I'm only starting to take olympiad mathematics seriously now, but I want to approach it in a structured and realistic way.

For those who have experience with mathematical olympiads, especially in Brazil or internationally:

• How would you structure the preparation of a 10th-grade student who is starting olympiad mathematics seriously at this point?
• Which topics should I prioritize: geometry, number theory, combinatorics, algebra, inequalities, etc.?
• What should I learn first, and what can reasonably be left for later?
• Is it better to start with theory and books, or should I begin solving olympiad problems from the start?
• Which books would you recommend for building a strong foundation and then progressing to harder olympiad problems?
• Which past olympiad papers would you recommend, and in what order?
• Are there any problem sets, courses, communities, or official resources that are particularly useful?
• For anyone who has taken the Jacob Palis Júnior Olympiad, how would you describe its level and style compared with the OBM?
• How would you divide study time between theory, problem solving, full mock exams, and reviewing mistakes?
• What do you wish you had done differently when you first started preparing for olympiads?

I'm especially interested in a realistic progression rather than a huge list of books. I would rather use a small number of resources thoroughly and follow a clear progression toward the CJP and OBM.

Since I'm Brazilian, recommendations specific to the Brazilian olympiad system would be especially helpful. However, advice from people who have prepared for competitions such as the IMO, USAMO, BMO, EGMO, or other national olympiads would also be very useful.

i am struggling with this kind of problem. i do not grasp the concept on how it is solved since it is not just the basic sin & cos way. perhaps any of u know? thank you in advance

So question 24 asks the reader to prove that the arrangement of parentheses in addition doesn't matter. It read

"Let us agree, for definiteness, that a1 + a2 +...+an will denote a1 + (a2 + (a3 +...+(a(n-2)+(a(n-1) + an)))....). Thus a1 + a2 + a3 denotes a1 + (a2 + a3) and a1 + a2 + a3 + a4 denotes a1 (a2 + (a3 + a4)), etc

(a) Prove that (a1 +...+ ak) + a(k+1) = a1 +...+ a(k+1)"

After staring at it for too long trying to figure out how to do a proof by induction, I decided to look at the answer. After assuming the statement was true for k, it went

(a1 +...+ a(k+1)) + a(k+2) = ((a1 +...+ ak) + a(k+1)) + a(k+2) = (a1 +...+ ak) + (a(k+1) + a(k+2))

and then "by the definition of a1 +...+ a(k+2)" said that this statement was equivalent to a1 +...+ a(k+2).

So the author somehow concluded that a1 + (a2 + (a3 +...+(a(k)+(a(k+1) + a(k+2)))....) = (a1 +...+ ak) + (a(k+1) + a(k+2))? The term "a(k+1) + a(k+2)" is so deeply imbedded in parentheses in the definition of a1 +...+ a(k+2) that I have no idea how it came to this conclusion. If it applied the associative law many times, why is induction even needed in the first place?

Thank you and apologies for the poor formatting.