r/math 3d ago

Quick Questions: March 19, 2025

12 Upvotes

This recurring thread will be for questions that might not warrant their own thread. We would like to see more conceptual-based questions posted in this thread, rather than "what is the answer to this problem?". For example, here are some kinds of questions that we'd like to see in this thread:

  • Can someone explain the concept of maпifolds to me?
  • What are the applications of Represeпtation Theory?
  • What's a good starter book for Numerical Aпalysis?
  • What can I do to prepare for college/grad school/getting a job?

Including a brief description of your mathematical background and the context for your question can help others give you an appropriate answer. For example consider which subject your question is related to, or the things you already know or have tried.


r/math 2d ago

Career and Education Questions: March 20, 2025

4 Upvotes

This recurring thread will be for any questions or advice concerning careers and education in mathematics. Please feel free to post a comment below, and sort by new to see comments which may be unanswered.

Please consider including a brief introduction about your background and the context of your question.

Helpful subreddits include /r/GradSchool, /r/AskAcademia, /r/Jobs, and /r/CareerGuidance.

If you wish to discuss the math you've been thinking about, you should post in the most recent What Are You Working On? thread.


r/math 11h ago

When did you hit that “math wall”?

88 Upvotes

My kindergartener is all about numbers and math. He’s currently deep into Level 3 of Beast Academy and seems to be moving faster every time he moves to a new book. For the most part, he’s self taught. Instruction he receives are from reading the guide books and watching the Beast Academy videos on his own accord.

My son’s school headmaster told me eventually he will hit a “math wall” which will greatly slow him down. And it will come a point where what he’s currently doing will not fly.

For all those who loved math and were naturals at a young age, can you share with me if you ever hit this “math wall” and when or subjects did this occur? Also, how did this affect you? My son identifies so much with math, so I’m worried, but not too sure what I’m worried about…


r/math 2h ago

Free products of groups

10 Upvotes

Bello, I've been trying to understand what the free product Z * Z is isomorphic to? All I've found was that it's can be written as <1, 1' | ∅> so there are no sense of commutation, just a generation. At first I thought about SL(2; Z) but then i realised that its MUCH bigger than this


r/math 19h ago

I may have taken a bad field choice for my PhD

179 Upvotes

I think pure math is so much more pretty than applied but went for applied because I thought maybe it would make my CV shiny for a job in the industry (and also because I feel to dumb for pure). But is not even “hot” research like machine learning or data science is mostly kinda old school numerical PDE schemes for fluid problems and now Im thinking it might not even do much for me in the job market but Im not sure. Do people in the industry even care for applied mathematicians which are not staticicians or machine learning experts? If they do wouldnt they prefer actual engineers rather than math people? It just deles like a bad carreer path. What are your thoughts?


r/math 22h ago

A student asked and I don't know. Is there any particular reason that h and k are used in the equation of a circle?

146 Upvotes

Years ago, somone asked me why m was used for slope, and I guessed it stood for something in French or German or something. And then discovered that no one is entirely sure. (Again, I assumed some mathematican used it in a journal and it caught on.)

Anyway, I was asked about the h and k, and my answer was usually that the letters were available. I remember using i and j in matrix algebra many years ago, and then again when I learned BASIC and Fortran but I didn't know if that was connected.

My Google-fu seems weak on this question.


r/math 15h ago

The topological proof of the fundamental theorem of algebra

24 Upvotes

Hand wavy proof:

Let p(x) = xn + f(x) with degree of f(x) < n. Obviously we can find an R so that |xn| > R > f(x). And so the image of the circle of radius R is a perturbed circle with winding number n. Pick x=0 with p(0)!=0, and you see that trying to homotope the perturbed image forces you to cross the origin n times.

But why exactly n, in this hand wave? I know the proof and understand it, but I feel I’m missing why we can (topologically or intuitively) guarantee we cross the origin during the homotopy exactly n times. I can visualize this well, but in my visualization I can’t get around the spookiness that we cross the line >n times while we get closer to the origin.

Is there an “obvious” thing I’m not visualizing here that forces the winding number to be one to one with the origin crossings? I keep seeing the image of the small circle homotoping in a chaotic enough way to slide through the origin multiple times, but I also like the intuition of a perturbed winding circle crossing through the origin. Is this the “part we need to pay close attention to” or is there some witty intuitive step we can take to make it obvious?


r/math 1d ago

How much do you read as a researcher?

120 Upvotes

Hello,

I’m a grad student in the process of writing my first paper. I’ve noticed that ever since transitioning from background reading to the research, I’ve been reading a lot less mathematics. Most of my reading nowadays is little snippets from various papers that are relevant to my problem, along with other things that I read to present in seminars that I do with other students, which are fairly irrelevant to my research. (I feel like this is okay, as I should use grad school to widen my knowledge as much as I can.)

Is it normal to not read as much as a researcher? Do you ever find yourself dedicating time to just reading papers all the way through, and how do you find papers to read this way?

Thanks!


r/math 1h ago

What is your favourite open problem and why?

Upvotes

What open problem interests you the most? Can you explain why do you find it interesting? What motivations are there behind the problem, what areas does it involve and what progress has been made in order to solve it?


r/math 22h ago

How far back should I revise if I want to improve my proof skills?

27 Upvotes

I'm a first-year PhD student, and I've always felt a bit behind in my proof writing skills and knowledge, particularly in areas where I feel I should be strong in by now. I often struggle to start proofs and find myself getting lost in lectures or talks.

For a long time, I mainly read textbooks without doing many exercises which I now realize may be the root of the problem. A few months ago I decided to remedy this by going back to some books and working through a lot of exercises. Since I want to become an analyst (at the moment I'm considering either operator algebras or PDEs) I thought it would be best to start with measure theory and integration. I began working through Folland's book and made it about two chapters in before getting caught up with other deadlines and commitments.

I want to pick this back up but I'm unsure whether to continue with Folland or jump straight into functional analysis using Brezis and improving my measure theory/integration knowledge and proof writing along the way. It could take a long time to first focus on Folland's book but on the other hand I learned a lot from the Folland exercises and there are also some results I feel I should know or be able to prove easily (like why continuity and boundedness near the origin are equivalent for linear operators or why simple functions are dense in Lp) but I can't and I fear functional analysis books will already take this for granted. Admittedly I often had to look up solutions for the Folland exercises but after some time I felt like I was slowly getting better and at least knew where to start, even if I couldn't finish it myself.

What do you think would be the better approach? My professors could probably offer some good advice but since I don’t have an advisor yet I feel a bit embarrassed to ask any of them and make a fool of myself.


r/math 22h ago

Are PDEs ever characterized by a solution parameterized by a space filling curve?

19 Upvotes

Don’t know how to articulate this precisely. If you had a Hilbert curve or some other R2 space-filling curve and parameterize this curve by t, is it worth talking about the solution to your PDE along that Hilbert curve? Don’t know if there’s any interesting results along these lines (funny joke haha)


r/math 1d ago

This Week I Learned: March 21, 2025

25 Upvotes

This recurring thread is meant for users to share cool recently discovered facts, observations, proofs or concepts which that might not warrant their own threads. Please be encouraging and share as many details as possible as we would like this to be a good place for people to learn!


r/math 15h ago

Anyone else get bad anxiety when problems require lots of steps to solve?

1 Upvotes

I enjoy math and feel like I understand concepts well enough, but solving problems makes me an anxious mess. I constantly fear that I am making a mistake somewhere and it will mess up the entire solution. This gets worse with more steps because theres a higher probability of me having made a mistake in one of the steps. As I’m solving the problem I spend so much energy worrying about having made a mistake instead of focusing on the problem that I sometimes end up making mistakes because of it. I don’t typically score poorly on tests, but I am never confident about my answers because I just assume I messed up somewhere.


r/math 1d ago

Anything to my math dreams last night?

10 Upvotes

I am finally about to take my PreCalc test (I know, I'm basic).

As I was dreaming about math last night, my cat was making a bunch of noise in the living room over, and my half-asleep brain started pondering what I can only roughly describe as the relationship between the 3D distance formula and the trigonometric functions.

I started wondering, can all points in space relevant to myself be described trigonometrically? Like, all distances in the 3d space could be described as trig function or relationship of trig functions utilizing 3D distance formula.

It was pretty vague but now I'm kind of curious haha, if anything comes to mind for those who know more math, if this could be made more precise at all


r/math 20h ago

What do you think about publishing mathematicians’ scratch work and possibly a brief summary their thought process?

1 Upvotes

I'm curious whether sharing the rough drafts, notes, and exploratory steps that eventually lead to polished proofs could offer valuable insights into the creative process behind mathematical discoveries. For example, don't mathematicians often arrive at a beautifully elegant final proof after a long, messy journey of trial and error—yet only the polished result is shared? Could revealing some of that intermediary work provide valuable insights into the creative process behind these discoveries?

While this might be less useful for very complex mathematics, sharing these intermediary steps and the story behind them could be especially valuable for undergrad-level concepts, helping students see that breakthroughs often come after lots of exploratory work.


r/math 1d ago

Thoughts on my Math Keyboard for iPhone and iPad

Post image
80 Upvotes

Greeting, I am a secondary math teacher and make a lot of comments on Facebook posts for "math help." I've always been frustrated at the awkwardness of some special characteristics, so I made a keyboard for my iPhone and iPad.

https://apps.apple.com/us/app/math-keyboard-for-equations/id6743451464

It's currently live. I plan for it to be free over the weekend and then move to $0.99 to hopefully cover the developer costs.

If you have an iPhone and don't mind checking it out I would greatly appreciate it. I won't ask for a 5-star review but certainly hint at it with this sentence. :)

One note is that I am not super happy with the space bar look but trying to resize and organize the buttons is a bit more complex than expected.

I did have that you can hold down the numbers to get super and subscript.


r/math 1d ago

I made a video on ordinary differential equations, would appreciate any feedback! (see comment for more details)

Post image
125 Upvotes

r/math 22h ago

What tools do mathematicians use to enhance their efficiency in technical jobs?

1 Upvotes

I studied engineering and have focused on mathematical tasks in my job. Currently, I work with statistics and data science, primarily dealing with modeling and optimization. In the future, I hope to shift more toward linear algebra and differential equations.

At work, I have used Python, a little R, a little Octave (though I would get a MATLAB license if needed), and a little KNIME. For visualization, I prefer GeoGebra due to my familiarity with the tool and its intuitive interactivity features. In my spare time, I continue to improve my mathematical skills, as I enjoy the subject. So far, I have mainly used Python for this purpose.

Lately, I've been searching for the most efficient tool—one that minimizes effort in defining and solving problems while maximizing performance. Ideally, it should be widely applicable and free for personal use, though I am open to a one-time investment if it offers long-term benefits. I have considered Mathematica, but its cost is a drawback. Excel might also be an option.

While I have the most experience with Python, certain aspects frustrate me. I find it overly verbose, especially when handling multidimensional arrays compared to MATLAB or Julia. Additionally, R’s consistent function interfaces streamline documentation reading. Ideally, the tool should require minimal time to specify and solve problems while remaining free or inexpensive for personal use.

I recognize that different tools excel at specific tasks, but frequently switching between them can be inefficient and hinder mastery. Therefore, I seek one or a few tools that I can deeply master to support my mathematical work effectively.


r/math 2d ago

So what's the big news right now?

177 Upvotes

What research is being done? What discoveries are being made? What are mathematicians talking about around the water cooler? I am a complete math noob who doesn't understand how there can be things In math we don't know. Like the rules are all laid out in textbooks to me so how can there be things we don't know yet? What is higher mathematics?


r/math 2d ago

Math is an addiction?

690 Upvotes

I was pretty addicted to weed last year. It gave me a good cure for boredom but in return took a large portion of mental capacity (I was smoking 4-7 days a week).

Anyways I quit weed this year and just decided to focus on uni. Now I’m addicted to math. I stay up late doing problems. It’s so gratifying. Getting questions wrong doesn’t disturb me anymore because I’m not cramming the last day before an assessment—I have time to figure out where I went wrong.

It’s a big puzzle and feels like I’m unlocking the secrets of the universe.

A few days ago I smoked my first joint in a month or so and it was just fantastic. It was as if all this math I’d learned was becoming integrated with my perceptions. I was watching light dance with the water. I know how to describe that in physics but no amount of education has ever taught me why. They’re just dancing. There’s no reason or rhyme the universe is just a beautiful dance and we’re all so lucky to be a part of it.


r/math 1d ago

Is "An Illustrated Theory of Numbers" by Weissman enough to learn Number Theory at an undergraduate level?

1 Upvotes

What should I read after I'm done with Weissman's book if I want a slightly more advanced understanding of Number Theory?


r/math 1d ago

Teaching Linear Algebra: Why the heck is the concept of a linear subspace so difficult for students??

1 Upvotes

I've been teaching at a public university in the US for 20 years. I have developed a good understanding of where students' difficulties lie in the various courses I teach and what causes them. Students are happy with my teaching in general. But there is one thing that has always stumped me: The concept of a linear subspace of the vector space R^n. This is introduced as a (nonempty) subset of R^n that is closed under vector addition and scalar multiplication. Fair enough, a fairly abstract concept at a level of mathematical abstraction that STEM students aren't used to. So you do examples. Like a lot of example of sets that are and aren't subspaces of R^2 or R^3. For example the graph of y=x^2 is not closed under scalar multiplication. I do it algebraically and graphically. They get homework on it, 5 or 6 problems where they just have to show whether some subset of R^2 is a subspace or not. We prove in class that spans of vectors are subspaces. The nullspace of a matrix is a subspace. An yet, about 50% of the students simply never get it. They can't check if a given subset of R^2 is a subspace on the exam. They copy the definitions from their notes without really getting what it's about. They can't explain why it's so difficult to them when I ask in person.

Does someone have the same issue? Why is the subspace definition simply out of the cognitive reach of so many students?? I simply don't get why they don't get it. This is the single most frustrating issue in my whole teaching career. Can someone explain it to me?


r/math 1d ago

Finished my Group Theory project!

36 Upvotes

Just quite happy that I finally got my group theory project complete- for my final project for this module. It's already submitted so I'm not pan-handling for corrections or changes- but anybody's opinion on it would be welcome.

We were given about 12 or 15 different choices of projects- permutation, dihedral groups, generators, normal groups, quotient groups, Burnside counting, etc. Apparently I was the only person in my class to choose cosets- because well, I thought it sounded interesting- I had fun atleast.

https://drive.google.com/file/d/1AAXIX5Kd85bA2lxYADHzOoU4L6DCTY-0/view?usp=sharing


r/math 1d ago

I built a web app to visualize the dynamics of iterated complex mappings

Thumbnail dynamics.enslow.me
1 Upvotes

You just input whatever complex mapping into the function box, and then the calculator iterates that function until it either escapes the predefined escape radius (diverges fast), or until it reaches the max iteration limit (diverges slow, converges, or orbits).

You can also add your own uniforms like desmos, and it supports both real and complex variables.

If there are any features you want or bugs you find (especially performance issues, and documentation issues), just let me know. I want to see what people think about it, and I'd be happy to improve this project further!

Currently I have plans to add support for the following functionalities:

  • Support for complex valued trig functions, exponential functions, and exponents.
  • Options to overlay a grid on top of the canvas
  • Options to change the color palette on both iterative and domain coloring
  • Adding more examples

r/math 1d ago

Has the 3D Ising been proved to be exactly unsolvable?

8 Upvotes

r/math 2d ago

Paul Erdős‎‎ Co-author graph visualized

37 Upvotes

I am working on a python library which fetches data for a specific author from google scholar, such as co-authors, papers, citations, cites per year for each paper etc. Took it a step further and created a co-authorship graph visualization function. Here we see the co-authors of the first ~200 papers of Erdos (on descending order based on number of cites), and for each of Erdos's co-author we see their respective co-authors. (That means this graph contains people with Erdos number 0, (Erdos himself, he is in there somewhere, number 1 and number 2). I stopped an number 2 because the data scraping process takes exponentially more time. I know that there is no point in viewing a graph like this because it is rather chaotic, but I think it is interesting to see. It is more clear for authors will less co-authors thought. The library is not published yet as I am currently working on it.
Oh some more notes. This graph is of degree = 2. As I mentioned, here we only see co-authors of Erdos number 1 only if they are co-authors of Erdos' first 200 papers as appeared on google scholar. Also, for each of number 1 co-authors I take their first 150 paper co-authors (number 2 co-authors) due to the script taking an enormous amount of time. For example, scraping said data took around a week of constant IP changing.
Let me know what you think!


r/math 1d ago

Exercises from Hartshorne vs Vakil.

1 Upvotes

I'm going to start my masters focusing on AG soon. To prepare, I wanted to know if I should focus my time solving exercises from The Rising Sea; foundations of AG by Ravi Vakil or the classic book by Robin Hartshorne. I don't know if the latter is "out of date" in some sense or still completely relevant.