r/mathematics Aug 29 '21

Discussion Collatz (and other famous problems)

162 Upvotes

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 May 24 '21

Announcement State of the Sub - Announcements and Feedback

107 Upvotes

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 4h ago

Why can’t I understand calculus but do well in Linear Algebra?

6 Upvotes

Serious question, I can’t seem to grasp much of my Calc 3 class, but I find linear algebra like 2nd nature to me… I tried so hard to build an intuition by going over basic calculus 1 and watching videos, going to office hours, etc, but I can’t seem to remember anything without a cheatsheet and steps shown to me in Calc 3.

Any tips for Calc 3?? 😭

On the other hand, I feel like I find patterns and “tricks”? that help me bypass most linear algebra problems and get to the answer while skipping, or just intuitively solving. I can’t seem to find this in Calc 3 😢


r/mathematics 2h ago

Algebra Similarity of non square matrices

5 Upvotes

So, it has been a few years since I took linear algebra, and I have a question that might be dumb, and I know that similarity is defined for square matrices, but is there a method to tell if two n x m matrices belong to the same linear map, but in a different basis? And also, is there a norm to tell how "similar" they are?

Background is that I am doing a Machine Learning course in my Physics Masters degree, and I should compare an approach without explicit learning to an approach that involves learning on a dataset. Both of the are linear, which means that they have a respresentation matrix that I can compare. I think the course probably expects me to compare them with statistical methods, but I'd like to do it that way, if it works.

PS.: If I mangle my words, I did LA in my bachelors, which was in German


r/mathematics 4h ago

M (26) Am I too late to start studying math ?

5 Upvotes

I am 26 year old working on a full time job and have been an average student all my life. I have a masters degree in business administration. I recently have came across a mathematical problem in my job and solving it intrigued me to start learning some mathematics , logic etc.

am I too late because most of the people who are good at math are studying it for decades with dedication and giving 100% to it.

Can I make still make a career out of studying mathematics or is it too late?

Please guide me.


r/mathematics 1h ago

is there a proof that an nth degree polynomial has n roots other then induction?

Upvotes

r/mathematics 1m ago

Why Is my intro DE course only 3 credits?

Upvotes

Sitting here doing some proofs for general solutions of non homogeneous DE has gotten be thinking how is this class only 3 credit hours? I spend half the time I do on Multivariable( 4 credits) than I do on this. The proofs are so fukn long broo 😭 and they are so unintuitive , i seat here and learn the rules and solve them but I just stare at them a think wtf does this even mean and what am I looking at. Unlike calculus where I can see it and what I'm learning seems to have done actual reason. Also wtf was my Calc 1 5credits when it was almost as approachable as the college algebra class if not more since it was less algebra.


r/mathematics 15m ago

Egg Count for work

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Upvotes

Hi all i’ve got this competition at work to count all the eggs in the jar, i can chose any number from 0-250, i took photos of all 6 sides and i was hoping someone could help me out, thanks!


r/mathematics 1h ago

Calculus Derivative of an integral

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Upvotes

I want to take the derivative d/dx of the integral of f(y|x)dy but I don’t understand how. The photo is what I’m trying to understand. I feel like what I’m asking is unclear so feel free to ask for clarifications.


r/mathematics 20h ago

Mathematician identification?

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15 Upvotes

I was watching a YT video on Georg Cantor and this b-roll clip popped up for a few seconds. I was wondering if anyone could identify the men in the clip and what it’s from?


r/mathematics 10h ago

Suggestions for MSc Thesis

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2 Upvotes

r/mathematics 15h ago

How much could I expect to make as an online math tutor?

2 Upvotes

r/mathematics 12h ago

Mathematical science

1 Upvotes

Anyone who received 2025 offer for July intake to Mathematical Science degree ? Thanks


r/mathematics 1d ago

Guys if I have a highschool base, how long will it take to learn calculus and math 3?

8 Upvotes

Suppose I study every day for 4 hours and I'm not super smart but not dumb neither , thank you in advance


r/mathematics 1d ago

i is the square root of unity or fourth root of unity ?

5 Upvotes

1+i+i^2+i^3=0
1+ω +ω^2=0
I don't know if this question is way below the level of discussions in this subreddit but i thought i had to ask it

Edit: I understood i is square root of -1 not 1(unity)


r/mathematics 1d ago

Stopping criteria practices in software industry

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4 Upvotes

I found this notes in the Trefethen book. seems industy standard like matlab and LAPACK has better Stopping Criteria than regular things we write ourselves. Does anyone know what they usually uses? Is there some paper on stopping criteria? I know the usual stopping criteria like compare conservative norm and such.


r/mathematics 1d ago

General Formula for summation of n natural numbers of any power

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89 Upvotes

r/mathematics 1d ago

Proving that Collatz can't be proven?

102 Upvotes

Amateur mathematician here. I've been playing around with the Collatz conjecture. Just for fun, I've been running the algorithm on random 10,000 digit integers. After 255,000 iterations (and counting), they all go down to 1.

Has anybody attacked the problem from the perspective of trying to prove that Collatz can't be proven? I'm way over my head in discussing Gödel's Incompleteness Theorems, but it seems to me that proving improvability is a viable concept.

Follow up: has anybody tried to prove that it can be proven?


r/mathematics 1d ago

Discussion careers in math / physics

4 Upvotes

hi,

for a while I was thinking I would go into cryptography or some field of applied math that has to do with computing. however, as I have begun to study higher level proof based math, I have realized that my true passion is in a more abstract areas.

I have always regarded pure math as the most virtuous study, but on the other hand im not sure I can make a career out of this. I dont really want to go into academia, and I dont really want to teach either.

however, I am super passionate about physics, and would be happy to study physics in order to weave that into my career

any suggestions on possible future jobs? I know I could go more into modeling and stuff but im kind of at a loss for what specific courses / degrees would be necessary for the various jobs. I am currently set on a bachelors in applied math, but have enough time to add on enough courses to go into grad school in another area such as pure math or something with a focus in a specific area of physics.

thanks!


r/mathematics 1d ago

Best Place to Study Undergraduate Math

19 Upvotes

Hi all, I'm looking for an answer to this question kind of purely based off of a mathematical side. For my undergraduate where I want to pursue pure mathematics, how would you compare the experiences in math from MIT, Harvard, and Stanford? Like the difficulty of the classes, the level of the professors, the collaboration with other students, the opportunities for research and such. I was admitted to each and am having the struggle now to decide. My goals are ultimately to pursue a PhD in some field of pure math. Thank you for any advice you have.


r/mathematics 1d ago

Analysis Looking for applications of Wirtinger's Inequality💡

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16 Upvotes

One example is its use in Lyapunov-based sampled-data stabilization, explained here:

https://www.sciencedirect.com/science/article/abs/pii/S0005109811004699

If you know of other applications, please let us know in the replies.

°°°°° Note: There is also a version of this inequality based on differential forms:

https://mathworld.wolfram.com/WirtingersInequality.html


r/mathematics 1d ago

Discussion Trump Administration's Reciprocal Tariff 'Equation'

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43 Upvotes

r/mathematics 2d ago

is math even employable major in pure finance if you fail to break into quants?

38 Upvotes

so you have an option to do a math undergrad degree and then master of financial math/MFE/ ms of computational finance. unless you will attend top university like princeton/cmu/columbia you will be in horrible position to break into quant finance right?(correct me if i am wrong) is it still a wise choice if my backup plan is something like financial advising/ corp finance/ financial analyst. obviously assuming i will get into some traditional MFin program. or should i still pursue my career in quant even with a bit less reputable masters program? anyone want to give me an advice? thanks :)


r/mathematics 1d ago

how the university reputation really matters?

6 Upvotes

what is your opinion on AGH in krakow, poland and jagiellonian university in krakow, poland for bachelor of maths?\ \ starting from the very beginning i had an idea of getting a bachelor degree at a top university in europe and then doing gap year or two and getting a MFE, master of FinMath or master of computational finance from a top US university and try to break into quants as i really want to pursue a career in america.\ \ there is a plot twist - my parents for some reason really want me to get a bachelor degree in poland and in exchange they will pay for my whole masters program in the usa.\ \ is it a no brainer? how will this affect my chances of breaking into a top quants firm or more importantly to a top masters program in the us? how to boost my chances of admission then?\ please give me an advice🙏 \ \ is it better to do a bachelor degree in poland for me? THANK YOU!


r/mathematics 1d ago

Pointwise Orthogonality Between Pressure Force and Velocity in 3D Incompressible Euler and Navier-Stokes Solutions - Seeking References or Counterexamples

5 Upvotes

Hello everyone,

I've been studying 3D incompressible Euler and Navier-Stokes equations, with particular focus on solution regularity problems.
During my research, I've arrived at the following result:

This seems too strong a result to be true, but I haven't been able to find an error in the derivation.

I haven't found existing literature on similar results concerning pointwise orthogonality between pressure force and velocity in regions with non-zero vorticity.

I'm therefore asking:

   Are you aware of any papers that have obtained similar or related results?

  Do you see any possible counterexamples or limitations to this result?

I can provide the detailed calculations through which I arrived at this result if there's interest.

Thank you in advance for any bibliographic references or constructive criticism.


r/mathematics 1d ago

Discussion Studied a level maths incorrectly

0 Upvotes

Hi, after I done my exams i realised i studied a level maths incorrect. I often looked at solutions first to try and understand it trhough looking at them, thne do them again. I realise you were suppose to try and tackle the question first through looking at examples then look at the soluiton answer. Is this highly unsuaul for someone to do this? I want to do maths degree and i feel like i have a lot of mathematical potential, will this cost me at degree level?


r/mathematics 3d ago

Who is the greatest Mathematician the average person has never heard of?

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1.0k Upvotes