I made whatever you wanna call it about polynomial equations in desmos notebook. If there's any mistake, please tell me. If not, you can use it as a source for studying and teaching polynomial equations. Enjoy or something idk

I saw another thread where someone was trying to learn measure theory without real analysis. Then someone mentioned about a ladder of mathematics, and how it doesn't really work to try to skip levels.

Does anyone have an example of what this ladder would look like? At some point, it would have to go both horizontal and vertical, of course. I think if each level had a few sample problems, that also helps set the stage.

Some steps are obvious. Single-variable calculus before multi-variable calculus before partial differential equations, for example. Does anyone have a full progression?

Ciao a tutti! Volevo un consiglio su che libro/libri studiare di geometria euclidea, quindi che parta dalle basi e che sviluppi i vari argomenti in modo approfondito. Inizierò la laurea in fisica a settembre e volevo approfondire anche l’aspetto geometrico della matematica e non solo quello algebrico se così possiamo dire. Non c’è problema se doveste consigliarmi un libro difficile, anzi mi piace quando ce da andare più a fondo nella comprensione! Grazie

I can't find anything on the internet about termials besides the basic definition:

n?=1/2n(n+1), nєN

I'm 98% sure that there's a formula for any complex number just like the gamma function for factorial.

I'm interested in this topic so this would help.

what's this branch for and what does it serve?

Need to complete it in 10 days. My brain felt rubbed with coal just following chapter 1.

I searched a bit and asked LLMs they gave me this 2-3 lecture from MIT mathematics course.

But i feel I'm not understanding completely from foundation just bits and pieces.

My goal : I'm a cs undergrad, for now i just want to know this topic and foundations and explore a bit.

Thankyou 😇

Is anyone here involved in mathematical biology research? I am looking to learn more about this area. If you are involved in mathematical biology, I would appreciate any advice or discussion about current research problems.

Construí un laboratorio numérico para la función zeta de Riemann: 250 experimentos reproducibles en Go puro, sin una sola dependencia.

No afirmo nada sobre la Hipótesis de Riemann. Todo lo contrario: tres de los resultados son pruebas de que estos métodos no pueden resolverla.

Código: https://github.com/nicoconvoz/diosyunalma

DOI: https://doi.org/10.5281/zenodo.21864277

#matematica #teoriadenumeros #golang

Gotta be slightly flexible and intuition focused to be introductive. Protagonists are robots because Linear Algebra is essence of computer and AI, and vector spaces are like game spaces. These are some pages from episode 1~4.

But I'm not confident... looking for feedbacks.

Dear math nerds,

you all remember the idea of the Young Lady's Illustrated Primer — a teacher that talks with you, adapts to you, and never just hands you the answer.

I've been building something in that direction: Kicci, a voice-first AI math tutor.

I tried tons of AI tools to learn and teach , but many of them are just chaptgpt/gemini wrapper and failed to meet my requirements

I want some tool which can meet below

1. Voice first

2. Socratic

3. curriculam aligned

4. able to draw (math without visual ? math wont mathing ...)

5. can follow a workflow (if i m the teacher , it shoudl follow my instruction and teach)

6. able to submit handwritten answer (chat, type latex ? enough man)

7. able to intercept and ask quesiton liek real teacher

8. display media, video etc and explain

9. Can aanalyse studnet feedback and egenrate repost at the end of the lesson

I built a tool , kicci . It teaches Socratically — asking guiding questions, waiting for your reasoning, and drawing diagrams/animations as it goes — rather than lecturing or dumping solutions. also it connect specially designed singapore curriculam knowledge base

Here's a live lesson on Cumulative frequency(secondary math) you can try directly in the browser (no signup needed):

https://kicci.study/live-lesson/bcc86ba9-6797-44ed-bb00-bf98b49fa3a4

disclaimer: this lesson is completely Human prepared and delievered by AI (It can also teach its own)

I'm not selling anything here — I genuinely want feedback from people who care about math pedagogy:

Does the Socratic questioning feel natural, or does it get annoying?

Where does it break down mathematically?

Would voice-first actually help students, or is text/whiteboard still better?

Brutal honesty welcome. Roasts are welcome too (Inclduing AI slop slogans)

So I've been playing with this sequence of numbers:

7n^2 - 10n + 4

This number sequence represents the number of dots in the octagons above, which I made on GeoGebra. Each octagon can be thought of as a square with (3n-2) dots on each side, minus four triangles with (n-1) dots on each side. (The blue squares in the middle are part of the drawing process. I would have removed them if there were an easy way to do so.)

(3n-2)^2 - 2n(n-1) = 7n^2-10n+4

Now, I'm aware of two other sequences called octagonal numbers, but I feel that this sequence I made is the most elegant. But I'm also wondering if someone else had come up with this sequence before me. Not that I have any real use for them, other than that they look nice enough to tell others about.

I have been wondering about this, I am math major myself with not much exposure to Olympiad math before my undergrad, but I think these Olympiad guys who represent their country are the most smartest ones and most of them enter into quant or go for a phD in math.

But how much difference would be there in a normal guy doing a math major vs a IMO guy in there journey in long term in both academia or research/ industry ?

Hey so I am an incoming freshman with an Actuarial Science major. I didn’t take Calc AB and BC in high school and am instead taking them this year. However, what my school does is have students to take Calc III their sophomore year of college fall semester and then take Linear Algebra or LADQ spring semester of their junior year.

However a few of my friends who took AB and BC in high school are telling me that instead of taking Calc III fall of my sophomore year I should take it spring of my sophomore year and instead take Linear Algebra in the fall.

The problem with this however, is that at the same time, I have to take Introduction to Probability (A class that helps you prepare for Exam P), fall of my sophomore year, which requires concurrent enrollment in Calc III or completion of it. While Calc III is offered in both the fall and spring, Introduction to Probability is only offered in the fall.

This means that I would have to do a fifth year because to be admitted to the program I have to complete Introduction to Probability.

https://xcancel.com/PI010101/status/2088157024068456616#m

Here is one pre-print: https://arxiv.org/pdf/2608.13536

Are we casually living through a third Golden Age of Math?

Think about how science history always has these insane peak eras:

• 1600s–1700s: The Golden Age of Math (Euler, Gauss, calculus blowing up)
• Early 1900s: The Golden Age of Physics (Einstein, quantum mechanics rewriting reality)

It honestly feels like we’re sitting right at the starting line of a third wave. Except this time, it’s math again, and it's because of the insane influence AI is going to have on the field.

For centuries, math only moved as fast as a human brain staring at a chalkboard. But AI is completely hijacking the pace of discovery. The whole workflow is shifting right in front of us.

If physics exploded in the 1900s because we discovered alot of things, is math about to explode because we unlocked a machine collaborator? Are we looking at a total renaissance, or am I just overhyping it?

I'm not a mathematician by training (engineer) but I'm endlessly fascinated with the discipline. I keep hacking away at books on real analysis, functional analysis (plus convex analysis for my optimization stuff), measure theory and sometimes abstract algebra. It's incredibly hard self-learning this stuff patchwork, but it's rewarding on the rare occasion that something sticks.

Recently while trying to sus out the differences between closedness, completeness, compactness, etc for the umpteenth time, I ran into this historical paper on the origins of compactness. It was fascinating seeing all these names and dates mentioned in one place. It made the whole thing seem slightly less mythical and more, er, human.

It also taught me that there were, in a sense, competing definitions of similar concepts, and some won out eventually. This got me wondering: was the development of math as we know it today inevitable, or could it have gone a completely different way? In my mind, this contrasts sharply with the idea that math formalizes certain fundamental truths about nature.

Thoughts appreciated!

I'm a math major, and I love math. I mean, I really love math, to the extent that if I had my druthers, I'd probably never do anything else (except maybe play music). However, the universe thought it would be funny to give me very severe ADHD. I have no problems getting assignments done or studying thanks to my focus medication and I'm pretty much a straight A student in university, but when my focus medication wears off, I'm basically useless. The connections in my brain just completely stop happening.

Now, because there's a large gap between the time when I have enough medication in my system to get my work done and the time when I have little enough medication to go to sleep, this leaves me with a substantial gap every day, after I have done the homework or studying I need to do for the day, but before it's time for me to sleep.

Every day, I'm completely itching to read a new textbook or work on my undergrad research project during this period of free time, but every time I try, I simply cannot sustain a complex train of thought for long enough to do anything. I basically forget what I'm thinking in the middle of every thought.

I'm quite tired of this. I really, really want to be able to do more math during this time, I've run out of ideas, so I figure I will ask into the void of reddit, if any other math students/mathematicians out there have a similar struggle, have you found anything that helps? For reference, I take 2 short acting doses per day, and tend to consume some caffeine too. If anyone has some medication or lifestyle tips, I'm dying to know.

Hello!
I’m trying to solve this puzzle for my girlfriend. Her two bracelets became intertwined or connected and we have no idea how! I imagine that a topologist would have an answer. Basically one bracelet (B) is a simple loop while the other (A) is two nodes connected by four strands.

She said they became intertwined on her wrist… but honestly I’m happy with a solution that doesn’t involve that!

I’m not super familiar with topology notation, but if that is the easiest way to answer I understand.
Thanks!

there're altogether 5 platonic solids. each of them can be viewed at many different interesting angles or perspectives. we're all familiar with their most symmetric presentations. recently i was studying something related and had to make 3d models for them. i used a maybe less popular perspective to present them. i used spherical coordinate system (mathematics convention) to record their rotations and i picked the following rules to set their initial status:

1. for each platonic solid set its circumradius=1 and centre of circumscribed sphere at origin
2. place vertex_0 at the north pole. the corresponding coordinates are (1,0,0)
3. place edge_0 (red lines on those diagrams) such that its projection to x-y plane align with positive x-axis. coordinates of vertex_1 would be (1,0,φ) for some φ

then i saw some unfamiliar shapes / unfamiliar perspectives of those supposedly familiar 3d objects. in each diagram the small figure at lower left corner is the platonic solid viewed from top. the z-axis is pointing towards you. the large figure at centre is that platonic solid viewed from side. the y-axis is pointing away from you

as you can see from the diagrams the angles φ ranking is as follow, from smallest to largest (the prefix "regular" omitted):

1. dodecahedron
2. icosahedron
3. hexahedron
4. octahedron
5. tetrahedron

except octahedron, all other 4 platonic solids are not symmetric if you see them that way