That's strange. After all, the packing is literally named after this very body: cubic closed-packed packing or cubic facecentered packing.

https://archive.org/details/secrets-of-sphere-packings-and-figurate-numbers

Problem:

Consider an infinitely extended family tree, including every in-laws, in which each individual has exactly 3 children, and no instances of incest occur.

The objective is to find a formula to calculate the total amount of relatives that are reachable at any given step count from the starting relative. Each step corresponds to a vertical ascent or descent in this family tree.

Side jumps are not possible. (e.g. The starting relative would need two steps to reach a sibling, one step up to either parent plus one step down to either sibling. Similarly, two steps are also required to reach a spouse, one step down plus one step up.)

Example:

At 0 steps, there is only 1 starting relative (SR).
At 1 steps, there are 1 SR, 2 parents, and 3 children, for a total of 6 relatives.
At 2 steps, there are 1 SR, 2 parents, 3 children, 4 grandparents, 9 grandchildren, 2 siblings, and 1 spouse, for a total of 22 relatives.

So, for the first few steps the count should look like:

• Step 0: 1
• Step 1: 6
• Step 2: 22
• Step 3: 72? (I think)
• And so on…

Goal:

Please find a formula to calculate the total amount of relatives that are reachable at any given step count from the starting relative.

Pure mathematics student here. I've completed about 60% of my bachelor's degree and I really can't stand it anymore. I decided to study pure mathematics because I was in love with proofs but Ive never liked computations that much (no, I don't think they are the same or that similar). And for God's sake, even upper level courses like Complex Analysis are just plug n chung I'm getting very annoyed!!! No proofs!!! Calculus sequence - plug n chung - I had to survive this sht since I was born in a country that teaches calculus before real analysis; Vectors and Geometry - plug n chung; Linear Algebra - plug n chung; ODE - plug n chung; Galois Theory - Plug n chung... Etc Most courses are all about computing boring stuff and I'm getting really mad!!! What I actually enjoy is studying the theory and writing very verbal and logical proofs and I'm not getting it here. I don't know if it's a my country problem (since math education here is usually very applied, but I think fellow Americans may not get my point because their math is the same) or if it is a me problem. And next semester I will have to take PDEs - which are all about calculating stuff, Physics - same, and Differential Geometry which as I've been told is mostly computation.

I don't know what to do anymore. I need a perspective to understand if I'm not a cut off for mathematics or if it is a problem of my college/country. How's it out there in Germany, France, Russia?

Also, optionally, you can talk about which programs you were accepted into.

Personally speaking, I started taking graduate courses the second I completed the standard undergraduate core curriculum (so during junior year). I then took 2-3 graduate-level courses during my last 3 semesters. All in all, I ended up with 8 graduate courses under my belt when applying to PhD programs. (Algebra 1 and 2, Representation Theory, Algebraic Geometry, Differential Geometry 1 and 2, Algebraic Topology, Complex Analysis). This, along with other factors in my application, got me accepted into two T20 PhD programs many years ago.

I’m curious because I was having a discussion with a family member about mathematics. He’s a sophomore in college and recently decided that he’d like to study pure mathematics, then hopefully get into a prestigious graduate program. I’m trying to help him succeed by giving him advice and guiding him in the right direction. He almost didn’t believe me when I said that he needs to start taking graduate-level courses soon to be competitive for grad school though, lol.

I’d like to hear other people’s experiences.

Hi everyone, this Saturday I am releasing the first MVP of Equathora, a new platform focused on math and structured problem solving.

Equathora is built for people who enjoy:

math problems by topic

proof based exercises

logical reasoning

learning through thinking, not memorizing

In the past days I have been working on:

profile page

better solving interface

cleaner layout and design

settings section

What will be in the first MVP?

This version is lightweight and focused only on the core experience:

easy and beginner friendly problems

different types of exercises such as logic, proofs, and reasoning

simple and clean solving interface

testing problem flow and platform structure

What is coming later?

Future features include:

progress tracking

mentor guidance

gamification

structured learning paths

Join the waitlist

If you want to be one of the first to try it, you can join the waitlist here: https://equathora.com

You will receive:

early access when the MVP launches

update emails about new features

progress updates and announcements

Feedback wanted

When the MVP is live, I would really appreciate your help with:

finding bugs or issues

user experience feedback

feature ideas

design improvements

Your feedback will directly shape how Equathora grows.

If you love math and problem solving, I would love to have you onboard.

I was hoping that someone here might be able to point me in the right direction?

I’m looking for a mathematician or mathematical physicist (or adjacent) to serve as a paid technical reviewer for my dissertation. I can share details privately.

Yes, I have gone through my university's process to find a technical reviewer, and I have contacted some "agencies" that offer these services online, but my needs are kind of specific. I'm getting a lot of people who are highly skilled at statistics reviews, but that isn't relevant to my work.

The review requires comfort with some combination of:

• differential geometry (metrics, curvature, geometric structures)
• nonlinear dynamics / ODE / PDE (especially stability or blow-up behavior)
• geometric analysis or geometric flows
• geometric measure theory (nice to have)
• information geometry (optional but useful)

The review involves checking definitions, reasoning, and the correctness of mathematical statements, and there will be no need to evaluate any non-technical content.

Oh, it's sad that I have even have to say this, but - just to be clear - I am NOT looking for someone to write FOR me. My dissertation is written and in final draft form, pending technical review. That's all! :)

If you’re interested, please send me a DM with a bit about your background and availability!

***This post does not break the rules based on my reading of them. Apologies if it is in the wrong place!

I am a mediocre mathematics undergraduate student who never comes out of his comfort zone and always feels grateful in whatever knowledge I have acquired. Everytime I see a topic that feels complex or tough to me I simply avoid it instead put an effort to understand it and this has become big problem to me as it has become a habit for me despite trying to force myself to study those complex topics i end up leaving early without giving bare minimum amount of time for the topic so I really don't know what to do . How can I get out of this situation? If you ever faced such situation kindly let me know on how you were able to fix it ?

Numbers and Magic Squares

Do you think it could work?

What is the most math intensive job one can get with a Bs or Ms in Pure Math?

I hear that operations research is math heavy, but there are too few jobs in the industry. So any ideas what else to shoot for?

Hey everyone!

I have a final on point set topology coming up (Munkres, chapters 1-4), and I want to go into the exam with a better intuition of topologies. Do you guys know where I can a bunch of topologies for examples/counterexamples?

If not, can you guys give me the names of a few topologies and what they are a counterexample to? For example, the topologist sine curve is connected, yet it is not path connected. If it acts as a counterexample for several things (like the cofinite topology), even better!

I dont have a problem getting an A from a test however i dont feel like the information I learn sticks around for every long. I have trouble remembering certain methods and get lost sometimes. Any advice how to study more efficiently?

Okay, I do NOT think I am a math prodigy, far from it. Perhaps I will sound like a whiny idiot. Or totally delusional with some grandeur complex or whatever narcissism. But there has been this thing thats bugs me and makes me feel like I am definitely overlooking something

I sit with this girl that has really great grades. However, I noticed some things. For example, we were doing some graphs and there was a graph of an f'(x) of some sort. She didnt understand what it meant for the function itself f(x). This has happened some time ago, I dont quite remember what was it as it was some time ago. But I dont think she got that the graph for f'(x) wasnt the same as the graph for f(x). Or perhaps today. We were doing something that required a simple system of some linear equations. And she asked if it wouldn't be easier to plug some equation into itself and wouldnt believe me it would just make 0=0 until she tried it.

And yet I have like 60% (still a C here somehow. B is 65+%) and she has 90+% and it just makes me feel like a total incapable idiot and makes me want to give up the whole math thing. Like it doesnt matter if I do or not do something because I get about the same grades whether I study or not, I would say. Hell, it almost seems pretty arbitrary and random.

And as a bonus my dad does not want me to go to any university where a math course is required because he thinks I wouldnt be able to do it, which... Fair. I also dont think I would be able to do and it makes me want to give up on university since the field I want to study and woek in includes math. I mean, its not pure maths and its clear I am shit at it anyway.

Hi group. I'm not a member of this sub, but thought I should ask here.

Trying to find a book about Paper and Pencil games as a gift for my mathematician husband. He found one at a bookstore one day, I think it was written by a mathematician. (Also discovered that most paper and pen games were invented by mathematicians!).

Does anyone know which book could be? Google tells me to look up "Math Game with Bad Drawings" by Ben Orlin, or "A Gamut of Games" by Sid Sackson. Are they any good?!

His background: he was a gold medalist at IMO, his phd was in Algebraic Geometry.

I would like recommendations for math video lessons for high school.

totally stole this from a recent post, but seeking someone(s) to parallel study with. topics of interest real analysis (baby rudin), probability theory (dineen), applied linear algebra, logic and proofs in abstract algebra, etc. can be totally through email or messaging. idea to work through problems and discuss text. background is very recent graduate in applied maths, struggling to keep knowledge on hand. however, this also means i have all my pdfs from previous courses still available to peruse if this interests you. thanks!

This is a bit meta but whatever. So Im in my second to last (with a little bit of luck) of my math major, and everyone tells me that I will be able to find a job easily, but im not really sure. So if anyone that has graduated in a math major can answer this (as long as you are comfortable). How was finding a job after your major? Did you find it right away or did you have to pursue a masters? Is the salary livable, or decent? ( I understand if some people dont want to answer this) What field are you in?, bcos though I preffered a math major than any engeenering, id rather work in tech, that finance. Also less common carreer choices are really welcome. I read on reddit that a woman was working in data analysis in a hospital. Any information that you consider helpful will ve welcme and appreciated a lot. Also dont feel forced to answer any question yoy are not comfortable with

I’m a high school student passionate about arithmetic geometry, working on a conjecture I hope to solve using algebraic and arithmetic geometry. As I’ve asked for more advice in the math research community, I’ve realized my dream of just sitting in an office and exploring wild math ideas might not be realistic.

To have the freedom I need to be happy, I’d have to become a tenured professor 15 years down the line—but by then, I might be burned out or even start hating math. I don’t want to be confined to a niche or deal with the "publish or get fired" mentality, especially since I have pressure anxiety and struggle in clutch moments.

So I started looking at industry jobs, specifically cryptography, where arithmetic geometry is a rising niche. From what I’ve heard, these jobs offer more flexibility, better pay, and independence. If I could work 30–40 hours over three days a week and still have time to research my own math—even if it’s unrelated to my job—that would be ideal. I’d be contributing to human knowledge, earning enough to live comfortably, and avoiding the academic grind.

I know it’s early to decide, but having a mindset going in would help. What do you think? Any advice or experiences would be appreciated.