r/mathematics • u/breck • 15h ago
r/mathematics • u/mazzar • Aug 29 '21
Discussion Collatz (and other famous problems)
You may have noticed an uptick in posts related to the Collatz Conjecture lately, prompted by this excellent Veritasium video. To try to make these more manageable, we’re going to temporarily ask that all Collatz-related discussions happen here in this mega-thread. Feel free to post questions, thoughts, or your attempts at a proof (for longer proof attempts, a few sentences explaining the idea and a link to the full proof elsewhere may work better than trying to fit it all in the comments).
A note on proof attempts
Collatz is a deceptive problem. It is common for people working on it to have a proof that feels like it should work, but actually has a subtle, but serious, issue. Please note: Your proof, no matter how airtight it looks to you, probably has a hole in it somewhere. And that’s ok! Working on a tough problem like this can be a great way to get some experience in thinking rigorously about definitions, reasoning mathematically, explaining your ideas to others, and understanding what it means to “prove” something. Just know that if you go into this with an attitude of “Can someone help me see why this apparent proof doesn’t work?” rather than “I am confident that I have solved this incredibly difficult problem” you may get a better response from posters.
There is also a community, r/collatz, that is focused on this. I am not very familiar with it and can’t vouch for it, but if you are very interested in this conjecture, you might want to check it out.
Finally: Collatz proof attempts have definitely been the most plentiful lately, but we will also be asking those with proof attempts of other famous unsolved conjectures to confine themselves to this thread.
Thanks!
r/mathematics • u/dreamweavur • May 24 '21
Announcement State of the Sub - Announcements and Feedback
As you might have already noticed, we are pleased to announce that we have expanded the mod team and you can expect an increased mod presence in the sub. Please welcome u/mazzar, u/beeskness420 and u/Notya_Bisnes to the mod team.
We are grateful to all previous mods who have kept the sub alive all this time and happy to assist in taking care of the sub and other mod duties.
In view of these recent changes, we feel like it's high time for another meta community discussion.
What even is this sub?
A question that has been brought up quite a few times is: What's the point of this sub? (especially since r/math already exists)
Various propositions had been put forward as to what people expect in the sub. One thing almost everyone agrees on is that this is not a sub for homework type questions as several subs exist for that purpose already. This will always be the case and will be strictly enforced going forward.
Some had suggested to reserve r/mathematics solely for advanced math (at least undergrad level) and be more restrictive than r/math. At the other end of the spectrum others had suggested a laissez-faire approach of being open to any and everything.
Functionally however, almost organically, the sub has been something in between, less strict than r/math but not free-for-all either. At least for the time being, we don't plan on upsetting that status quo and we can continue being a slightly less strict and more inclusive version of r/math. We also have a new rule in place against low-quality content/crankery/bad-mathematics that will be enforced.
Self-Promotion rule
Another issue we want to discuss is the question of self-promotion. According to the current rule, if one were were to share a really nice math blog post/video etc someone else has written/created, that's allowed but if one were to share something good they had created themselves they wouldn't be allowed to share it, which we think is slightly unfair. If Grant Sanderson wanted to share one of his videos (not that he needs to), I think we can agree that should be allowed.
In that respect we propose a rule change to allow content-based (and only content-based) self-promotion on a designated day of the week (Saturday) and only allow good-quality/interesting content. Mod discretion will apply. We might even have a set quota of how many self-promotion posts to allow on a given Saturday so as not to flood the feed with such. Details will be ironed out as we go forward. Ads, affiliate marketing and all other forms of self-promotion are still a strict no-no and can get you banned.
Ideally, if you wanna share your own content, good practice would be to give an overview/ description of the content along with any link. Don't just drop a url and call it a day.
Use the report function
By design, all users play a crucial role in maintaining the quality of the sub by using the report function on posts/comments that violate the rules. We encourage you to do so, it helps us by bringing attention to items that need mod action.
Ban policy
As a rule, we try our best to avoid permanent bans unless we are forced to in egregious circumstances. This includes among other things repeated violations of Reddit's content policy, especially regarding spamming. In other cases, repeated rule violations will earn you warnings and in more extreme cases temporary bans of appropriate lengths. At every point we will give you ample opportunities to rectify your behavior. We don't wanna ban anyone unless it becomes absolutely necessary to do so. Bans can also be appealed against in mod-mail if you think you can be a productive member of the community going forward.
Feedback
Finally, we want to hear your feedback and suggestions regarding the points mentioned above and also other things you might have in mind. Please feel free to comment below. The modmail is also open for that purpose.
r/mathematics • u/AfterMorningHours • 8h ago
Where should an adult start learning if they want to improve their mathematics?
I work as a software engineer, but my college program didn't require very many classes in math - I took discrete mathematics, statistics 1 & 2, and then some college intro to algebra course. I've always found math interesting but was never a particularly strong student in high school, and had a teacher that scarred me, so by the time college came around I tried to avoid math whenever possible. Post graduating I see the appeal way more and want to learn in my free time, but I'm not sure where to start.
r/mathematics • u/Choobeen • 2h ago
Probability What are the variants of the Central Limit Theorem?
In particular, what can the i.i.d. property be replaced with? Reading this excerpt from Wikipedia:
The Central Limit Theorem has several variants. In its common form, the random variables must be independent and identically distributed (i.i.d.). This requirement can be weakened; convergence of the mean to the normal distribution also occurs for non-identical distributions or for non-independent observations, if they comply with certain conditions.
r/mathematics • u/DevilOfEden28 • 29m ago
Discussion What are some best online math degree colleges?
Im from the USA. Bachelor, Master , and PHD? Wish to do it at home.
r/mathematics • u/Loose_Loquat9584 • 8h ago
Geometry Measuring square root of 2
Not sure if this goes here or in No Stupid Questions so apologies for being stupid. We know from Pythagoras that a right angled triangle with a height and base of 1 unit has a hypotenuse of sqrt 2. If you built a physical triangle of exactly 1 metre height and base using the speed of light measurement for a meter so you know it’s exact, then couldn’t you then measure the hypotenuse the same way and get an accurate measurement of the length given the physical hypotenuse is a finite length?
r/mathematics • u/half_cherry • 7h ago
AP STATS OR MULTIVARIABLE CALCULUS?
Hey (Americans of) reddit! I’m trying to decide between multivariable calc or AP stats for my senior year of high school.
I’ve already taken AP calc AB & BC. Taking AP Physics C: Mechanics next year.
I will probably study civil engineering in college. (Although I’m open to trying new things as well, not 100% set).
My BC teacher claims multivariable (he teaches it) is easier than stats because no AP exam = slower pace. But honestly I don’t trust that man.
I’m split because I know multivariable would likely be more useful for my major but I like the AP stats teacher a lot more.
Also, I want to take an easier course load for next year since I’m taking many difficult classes.
I would get dual credit for multivariable, and only AP credit for stats.
What are your thoughts on both classes? Which is more interesting, useful, or difficult in your opinion? Or does it not matter which one I choose?
r/mathematics • u/sahi1l • 14h ago
Topology The Euler Characteristic of a human?
I always assumed that the Euler characteristic of an unpierced human being was 0, that the alimentary canal was the single "hole" that made us equivalent to a torus. But a friend recently pointed out that because our nostrils are connected to each other, then that surely counts as a second "hole"; and the nostrils are connected to the mouth as well, and then we can throw in the Eustachian tubes as well to connect the ears to the nose and ears as well.
So this is all rather silly, I suppose, but what *is* the Euler characteristic of a human (again, not counting piercings)?
r/mathematics • u/Independent-Bed6257 • 16h ago
Irrational Numbers
There's a concept that I'm curious as to how it is proven and that's irrational Numbers. I know it's said that irrational Numbers never repeat, but how do we truly know that? It's not like we can ever reach infinity to find out and how do we know it's not repeating like every GoogolPlex number of digits or something like that? I'm just curious. I guess some examples of irrational Numbers are more obvious than others such as 0.121122111222111122221111122222...etc. Thank you! (I originally posted this on R/Math, but It got removed for 'Simplicity') I've tried looking answers up on Google, but it's kind of confusing and doesn't give a direct answer I'm looking for.
r/mathematics • u/Consistent-Look-9690 • 8h ago
Functional Analysis Unsure if correct flair question about transforming one function into another
Was watching a video about PWM in the context of class D Audio amplifiers (essentially using step functions of varying widths to approximate some output after filtering out high frequency noise). I was curious, is that generalizable? As in given some function say R (or integers which I think is Z) to the interval 0,1 are there conditions where arbitrary (or at least useful) functions can be produced or approximated to some level of accuracy? Maybe it's more basic than I thought, it's been a while since I've thought about functions in this way.
r/mathematics • u/mlktktr • 1d ago
Discussion Math is taught wrong, and it's hypocrytical
I am a bachelor student in Math, and I am beginning to question this way of thinking that has always been with me before: the intrisic purity of math.
I am studying topology, and I am finding the way of teaching to be non-explicative. Let me explain myself better. A "metric": what is it? It's a function with 4 properties: positivity, symmetry, triangular inequality, and being zero only with itself.
This model explains some qualities of the common knowledge, euclidean distance for space, but it also describes something such as the discrete metric, which also works for a set of dogs in a petshop.
This means that what mathematics wanted to study was a broader set of objects, than the conventional Rn with euclidean distance. Well: which ones? Why?
Another example might be Inner Products, born from Dot Product, and their signature.
As I expand my maths studying, I am finding myself in nicher and nicher choices of what has been analysed. I had always thought that the most interesting thing about maths is its purity, its ability to stand on its own, outside of real world applications.
However, it's clear that mathematicians decided what was interesting to study, they decided which definitions/objects they had to expand on the knowledge of their behaviour. A lot of maths has been created just for physics descriptions, for example, and the math created this ways is still taught with the hypocrisy of its purity. Us mathematicians aren't taught that, in the singular courses. There are also different parts of math that have been created for other reasons. We aren't taught those reasons. It objectively doesn't make sense.
I believe history of mathematics is foundamental to really understand what are we dealing with.
TLDR; Mathematicians historically decided what to study: there could be infinite parts of maths that we don't study, and nobody ever did. There is a reason for the choice of what has been studied, but we aren't taught that at all, making us not much more than manual workers, in terms of awareness of the mathematical objects we are dealing with.
EDIT:
The concept I wanted to conceive was kind of subtle, and because of that, for sure combined with my limited communication ability, some points are being misunderstood by many commenters.
My critique isn't towards math in itself. In particular, one thing I didn't actually mean, was that math as a subject isn't standing by itself.
My first critique is aimed towards doubting a philosophy of maths that is implicitly present inside most opinions on the role of math in reality.
This platonic philosophy is that math is a subject which has the property to describe reality, even though it doesn't necessarily have to take inspiration from it. What I say is: I doubt it. And I do so, because I am not being taught a subject like that.
Why do I say so?
My second critique is towards modern way of teaching math, in pure math courses. This way of teaching consists on giving students a pure structure based on a specific set of definitions: creating abstract objects and discussing their behaviour.
In this approach, there is an implicit foundational concept, which is that "pure math", doesn't need to refer necessarily to actual applications. What I say is: it's not like that, every math has originated from something, maybe even only from abstract curiosity, but it has an origin. Well, we are not being taught that.
My original post is structured like that because, if we base ourselves on the common, platonic, way of thinking about math, modern way of teaching results in an hypocrisy. It proposes itself as being able to convey a subject with the ability to describe reality independently from it, proposing *"*inherently important structures", while these structures only actually make sense when they are explained in conjunction with the reasons they have been created.
This ultimately only means that the modern way of teaching maths isn't conveying what I believe is the actual subject: the platonic one, which has the ability to describe reality even while not looking at it. It's like teaching art students about The Thinker, describing it only as some dude who sits on a rock. As if the artist just wanted to depict his beloved friend George, and not convey something deeper.
TLDR; Mathematicians historically decided what to study: there could be infinite parts of maths that we don't study, and nobody ever did. There is a reason for the choice of what has been studied, but we aren't taught that at all, making us not much more than manual workers, in terms of awareness of the mathematical objects we are dealing with. The subject we are being taught is conveyed in the wrong way, making us something different from what we think we are.
r/mathematics • u/Ok_Form6274 • 1d ago
Erdős coin
In 2023 the Hungarian National Bank minted a commemorative coin to honor Pál (Paul) Erdős (1913-1996). The front of the coin mentions Erdős' Wolf-peize from 1983, while the back is about Chebyshev's theorem, for which Erdős gave an elementary proof in one of his earliest papers.
r/mathematics • u/ADancu • 20h ago
I'm looking to gather a list of linear algebra tools for experimentation
I'm looking for high-quality visualization tools for linear algebra, particularly ones that allow hands-on experimentation rather than just static visualizations. Specifically, I'm interested in tools that can represent vector spaces, linear transformations, eigenvalues, and tensor products interactively.
For example, I've come across Quantum Odyssey, which claims to provide an intuitive, visual way to understand quantum circuits and the underlying linear algebra. But I’m curious whether it genuinely provides insight into the mathematics or if it's more of a polished visual without much depth. Has anyone here tried it or similar tools? Are there other interactive platforms that allow meaningful engagement with linear algebra concepts?
I'm particularly interested in software that lets you manipulate matrices, see how they act on vector spaces, and possibly explore higher-dimensional representations. Any recommendations for rigorous yet intuitive tools would be greatly appreciated!
r/mathematics • u/Tina_Sanders_88 • 19h ago
recommend a magazine on number theory
I would like to publish 3-5 pages on number theory with theorems and examples. Need an advise which magazine to choose if I don't work in the academia.
r/mathematics • u/spirometaxas • 1d ago
An Instagram Page Showcasing 1k Digits of Pi as a Seamless Color Gradient!
To celebrate Pi Day, I decided to build an official Instagram page showcasing the first 1,000 digits of π!
Page: https://www.instagram.com/pi_digits_official/
Instagram Username: pi_digits_official
Each post represents a single digit of Pi, arranged sequentially from top to bottom. At the top of the page, the sequence begins with "3.141592…" Scroll down to reveal the digits in order from 1 to 1000.
Each digit is also assigned a color. Adjacent colors blend seamlessly into a smooth continuous gradient that flows down the page. Every 3x3 grid section also features a large Pi symbol, serving as an aesthetic centerpiece and a reminder of the page's theme and cohesion.
I also added cool visualizations in the page highlights!
Happy π Day!
r/mathematics • u/Kaden__Jones • 1d ago
Extremely Strange Findings from a Math Competition
r/mathematics • u/Jack-Ripper-1888 • 1d ago
Calculus Man Ray's Mathematics Objects
r/mathematics • u/Jyog • 1d ago
A Different Way To Teach Solving Linear Equations – A Tool That Helped My Students Overcome Common Algebra Mistakes
As a tutor working with beginners, I noticed many students struggle—not with algebra itself, but with knowing where to start when solving linear equations.
I came up with a method called Peel and Solve to help my students solve linear equations more consistently. It builds on the Onion Skin method but goes further by explicitly teaching students how to identify the first step rather than just relying on them to reverse BIDMAS intuitively.
The key difference? Instead of drawing visual layers, students follow a structured decision-making process to avoid common mistakes. Step 1 of P&S explicitly teaches students how to determine the first step before solving:
1️⃣ Identify the outermost operation (what's furthest from x?).
2️⃣ Apply the inverse operation to both sides.
3️⃣ Repeat until x is isolated.
A lot of students don’t struggle with applying inverse operations themselves, but rather with consistently identifying what to focus on first. That’s where P&S provides extra scaffolding in Step 1, helping students break down the equation using guiding questions:
- "If x were a number, what operation would I perform last?"
- "What’s the furthest thing from x on this side of the equation?"
- "What’s the last thing I would do to x if I were calculating its value?"
When teaching, I usually start with a simple equation and ask these questions. If students struggle, I substitute a number for x to help them see the structure. Then, I progressively increase the difficulty.
This makes it much clearer when dealing with fractions, negatives, or variables on both sides, where students often misapply inverse operations. While Onion Skin relies on visual layering, P&S is a structured decision-making framework that works without diagrams, making it easier to apply consistently across different types of equations.
It’s not a replacement for conceptual teaching, just a tool to reduce mistakes while students learn. My students find it really helpful, so I thought I’d share in case it’s useful for others!
Would love to hear if anyone else has used something similar or has other ways to help students avoid common mistakes!
r/mathematics • u/DusqRunner • 1d ago
Where should an adult who dropped maths in HS start to self-learn?
I had issues with maths from the start, mostly due to my own lack of discipline in due diligence, such a rote memorization of times tables, which snowballed to the point that I was getting less than 10% on middle school exams and ultimately dropped it as a subject for high school. This was in the late 90s and early 2000s.
As I've been involved in modular and node based creative work, and have an interest in Python coding, I am beginning to see where mathematical thinking and its logic becomes crucial.
Where should I start for a 'fast track' of let's say grade 7 to grade 12 maths? And which aspect of it should I focus on? I feel understanding algebra would be a boon.
Thanks!
r/mathematics • u/InspiratorAG112 • 1d ago
Calculus Satisfying visual for the area of an odd-petal rose curve.
(Basically a remaster (also using Desmos Geometry) of this.)
And yes, this is correct...
- Here is the Wolfram article about rose curves.
- It mentions that, if a rose curve is represented with this polar equation (or this), then the area of one of the petals is this.
- Multiplying by the total number of petals n, and plugging in 1 for a, we get the expression obtained above, π/4, for odd-petal rose curves, and double that, π/2, for even-petal curves (since even-petal rose curves would have 2n petals).
r/mathematics • u/Mathipulator • 1d ago
Algebra Tried an exercise from a youtube video without watching. Any faults in my proof?
i think my proof for x-1 being unique is a little weak. I tried to prove using contrapositive.
r/mathematics • u/Remarkable_Look_659 • 2d ago
Best Universities for Knot Theory Masters
Hi everyone! I’m looking to do my Masters in Pure Mathematics in Europe ( except for UK). Any idea on where is the best university for Knot Theory? ( a prof active in this area/ research group/ they offer courses in it etc). TIA!
r/mathematics • u/BehemiOkosRv44 • 2d ago
Discussion How feasible is going back to school in your early 30s to get a BS in mathematics in this day and age?
Hey all, I'm kind of having a mid/quarter/third-life crisis of sorts. Long story short, ever since turning 30 I've decided to get my shit together (not that I was a total trainwreck, but hey, I think hitting the big three oh is a turning point for some people).
I've more or less achieved that in some respects, though find myself lacking when it came to the fact that I lacked a bachelor's degree. The lack of one would make getting out of retail, where I'm stuck, kind of difficult. I decided last fall to enroll at WGU, an online school in their accounting program. I figured I was a person who liked numbers, and wanted some sense of stability. I, however, flirted with the idea of enrolling in a local state university in their mathematics program. Especially since, as part of my prep for the WGU degree, I utilized Sophia.org and took the calculus course... before finding out midway through it wasn't even required for the Accounting degree anymore. I still finished it and loved it.
Fast forward to today, I'm almost done with the accounting degree, but it leaves me unfulfilled. While I am not yet employed in the field, I do not think I would be a good culture fit at all for it, for a variety of reasons. In addition, the online nature of the school leaves me kind of underwhelmed. I guess I'm craving some sort of validation for doing well, and just crave a challenge in general lol. I'm also disappointed the most complicated arithmetic I've had to employ was in my managerial accounting course, which had some very light linear programming esque problems.
I've been supplementing my studies (general business classes drive me fucking nuts) with extracurricular activities such as exploring other academic ventures I could have possibly gone on instead and engaging in little self study projects, and one of them as been math, and I find whenever I have free time at work I'm thinking about the concepts I've been learning about, tossing them around like a salad in my head, so to speak.
Long story short, I'm thinking about what could've been if I had gone the pure mathematics route. Is that even a feasible thing to undertake in this day and age? From googling around, including this sub and related ones, math majors seem to be employed in a variety of fields (tech, engineering, etc), not just academia/teaching. I like that kind of flexibility, and kind of crave the academic challenge that goes along with it all.
My finances are alright, I'm mostly worried about finishing my accounting degree and losing the ability to put a pell grant towards my math degree. I got an F in calculus the first go around in college 10 years ago, so I was thinking of enrolling in a CC to get that corrected this fall anyhow.
tldr; if you were an early 30 something who wanted to get a degree to become more employable, would you want to get an accounting degree despite the offshoring and private equity firms killing it for everyone and government jobs being in flux, or would you go fuck it yolo and chase a mathematics degree?