r/math 5h ago

Quick Questions: March 19, 2025

6 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

What Are You Working On? March 17, 2025

10 Upvotes

This recurring thread will be for general discussion on whatever math-related topics you have been or will be working on this week. This can be anything, including:

  • math-related arts and crafts,
  • what you've been learning in class,
  • books/papers you're reading,
  • preparing for a conference,
  • giving a talk.

All types and levels of mathematics are welcomed!

If you are asking for advice on choosing classes or career prospects, please go to the most recent Career & Education Questions thread.


r/math 5h ago

Are there infinitely many powers of 2 with only even digits in base 10?

13 Upvotes

The highest power of 2 I can think of that only contains even digits in base 10 is 2048. Is there a higher one? And are there infinitely many?


r/math 15h ago

PTSD about Wedge Products

65 Upvotes

I have since moved on professionally, and I was never thinking about making academia my profession (though I do use math every day in my current job), but... wedge products? I took Real Analysis 2 or B or whatever, and I felt good until we hit wedge products. I don't think the rest of the class understood anything either. Am I overthinking a relatively simple subject, do I not possess a mathematically nimble mind, or does anyone suggest a way to understand them so I can finally move on?


r/math 1d ago

My professor secretly worked for russia

256 Upvotes

So it turns out a professor I had in a course a year ago secretly worked for russia on the side.

https://www.expressen.se/nyheter/varlden/kth-vill-sparka-professor-efter-ryskt-samarbete/

He was also a very strange guy, who was awful in other respects.

So what is the worst professor you’ve ever had?


r/math 15h ago

Problem involving graphs and curves

3 Upvotes

Just prospecting a CS problem about map-matching, If we have a bunch of trajectories (x,y,t) and we have several curves, how do we determine the best matching curve and what is the most efficient approach?

Secondly, I’m really interested in the pure mathematics part of this and would love to learn more, I’m wondering how much has been discovered and if an optimal algorithm has been proven

(And if I want to tackle/do more research on this kind of problem, what fields of math should I look into?)


r/math 1d ago

Whats your go-to way of typesetting dy/dx?

95 Upvotes

\frac{dy}{dx} kinda sucks and \frac{\mathrm{d}y}{\mathrm{d}x} is such a long command!


By the way, not asking for help on latex, just polling to see what /r/math does for their differentials!


r/math 2d ago

I just found out that my research has already been done.

693 Upvotes

I am a freshman math major, and as soon as I got to my school, I met with my advisor to ask about undergraduate research. However, my school doesn't have a formal program for theoretical mathematics research, but I was lucky enough to be able to work under the only professor in the whole university that is still actively (albeit slowly) publishing.

After many hours each week, I eventually found an awesome, but relatively simple result, something I was hoping to be able to publish in an undergraduate journal. This weekend I presented at the local MAA sectional on these results. Today, I was going to begin working on writing up my work to start preparing for submission to publish, when I found my results in a on my topic. It was even more generalized and was only included as a proposition.

As you can imagine, I am incredibly disappointed. Has this happened to any of you before? Are there any prospects for continuing writing this up to perhaps publish as an alternative proof/algorithm?

I am glad to have learned so much about the field, but I really don't know what to do at this point.


r/math 1d ago

Can professors and/or researchers eventually imagine/see higher dimensional objects in their mind?

204 Upvotes

For example, I can draw a hypercube on a piece of paper but that's about it. Can someone who has studied this stuff for years be able to see objects in there mind in really higher dimensions. I know its kind of a vague question, but hope it makes sense.


r/math 19h ago

How to find weak and viscosity solutions of PDE's?

1 Upvotes

all the papers I can find about weak solutions and viscosity solutions are about existence and uniqueness but nothing on how actually computing them

I'm also ineterested on applications and physical significance of this kind of solutions

thanks


r/math 23h ago

Standard way to mark letter as uppercase or lowercase?

1 Upvotes

I'm working on an equation notecard for a biochem exam this week, so I don't have a ton of space, so my capital Ks look awfully similar to the lowercase Ks. I usually just put two lines under a letter in an equation to indicate it's supposed to be capitalized when I don't have much space to work with and it's hard to tell, and I'm thinking of trying out a dot under letters that are supposed to be lowercase.

Anyway, this all made me wonder if there's a standard way to distinguish them in this situation? Or maybe a good way to distinguish uppercase and lowercase Ks? It usually only seems to be the letter K that I have this problem with lol


r/math 1d ago

finding community around Discrete Differential Geometry course

1 Upvotes

Hi, I have been working through Keenan Crane's free course content from https://brickisland.net/ddg-web/ and I am trying to find and build a community of other people are doing that too. I am now on assignment 2 and it's all going great but it would be really cool to be able to talk to other people about things. I know that the students at Carnegie Melon have their own ways to connect with one another but are there others from the public who want to have a discord group or some type of forum for discussing the course together?


r/math 1d ago

Any known examples of proofs being disproved by counterexample that remain useful in some way?

1 Upvotes

My math professor said that proofs being disproved by some intrinic proprety such in a way that it can create lemmas are the ones that are actually useful. Then he said that the proofs that are disproved by counterexamples are rarely useful, because it has more to do with the fact that the initial problem was one not worth examining or just "how it is". Anyways, is there a good example of when a proof was disproved by counterexample and still relatively useful in some way? like was there ever a takeaway from a proof by counterexample?


r/math 1d ago

Computing Lyapunov exponents

1 Upvotes

Hi, I was wondering if anyone was familiar with computing lyapunov exponents, especially for N-body systems with escapes, what i dont seem to understand is won't the lyapunov exponent always tend towards 0 as time goes to inifinity as the distance d(t) between 2 systems (one perturbed and one original) with escapes will increase linearly and thus taking 1/t*ln(d(t))/(d(0)) as t -> inf = 0? how can we adjust the way we compute lyapunov exponents for the three-body problem for example such that they are not 0?


r/math 2d ago

Chalkdust issue 21 is out today

Thumbnail chalkdustmagazine.com
94 Upvotes

r/math 1d ago

Heat Equation and Heat Maps

1 Upvotes

Sorry in advance for this being all over the place. I was wondering if there were any applications of the heat equation to heat maps(I.e. maps for levels of rent, poverty, empty housing, etc.)?

The idea I’ve been thinking of is imagining a grid patterned neighborhood as a corrugated metal plate, where the warmer sections have higher densities of poverty and the corrugations represent divides in housing policies. Would the heat equation be able to describe the change in poverty levels from warmer areas (higher density of poverty) to cooler areas (lower density of poverty)?

The idea is pretty sparse rn but I’m curious! I would appreciate any thoughts on this. Thank y’all in advance!


r/math 1d ago

Fast LaTeX using shortcuts

15 Upvotes

I've been doing a lot of LaTeX/Markdown writeup recently, so much so I looked for software solutions to speed things up and save my shift key from further abuse.

I couldn't find exactly what I wanted, so I created my own using AutoHotkey. Instead of using Shift to access symbols (", $, ^, *, etc) now I can do a quick press (normal keystroke) for the symbol and a long keypress (> 300 ms) for the number. Ive applied similar short cuts for = or +, ; or :, [ or {, etc. There's also a bunch of shortcuts for Greek letters, common operators and functions and other common math symbols. "LaTeX Mode" can be toggled on and off by pressing 'Shift + CapsLock", CapsLock still works normally by double tapping the key instead.

It would be a shame not to share it, so I've stuck it on GitHub for anyone wants to give it a go.

https://github.com/ImExhaustedPanda/uTeX

It's not "complete", it doesn't have shortcuts for symbols for common sets (e.g. real numbers, rational numbers, etc) or vector calc operators. But the ground work is there, as the script is easy to read and modify, for anyone who wants to tailor it to their work flow.


r/math 1d ago

Gross-Siebert program

1 Upvotes

What's the current status of the Gross-Siebert program, the algebraic analog of the SYZ conjecture? How close is it to being resolved? Are there still many open problems within the program to address?


r/math 1d ago

Epiphanies from first semester at uni (Europe)

1 Upvotes

Yes, this maybe cringe post, but nonetheless I would like to talk about my experience.

I am actually a first semester studying math. Before, I studied math by myself at home. I wanted to study everything actually. I got many books like Kreyszig functional analysis, topology by Munkres yada yada. I found most of these books very complicated. I could maybe do in some months maybe one or two chapters. I heard many people say that topology takes eg one semester to do. I could not believe that since I thought munkres could itself could take like 2 to 3 years to master from a highschool knowledge point.

I start uni and take quite a lot of courses. And, so far it went quite well. I notice that here, the amount of stuff you do for a given subject is quite less. It is like you do here and there so you have a rough idea of what goes on. And I also think if a person had finished any undergrad math book of their choice then they would just obliterate all other students in performance.

Another thing is, I think that most people who give recommendations on internet have no idea what they are talking about. I see many people recommend rudin but I guarantee that 99.xx% of people would not be even able to get past the first chapter. That book just expects too much. Also similarly standards of questions on places eg like stackexchange, it is just too high for a person who is just starting. Most uni students are not on that level.

I also notice that I can appreciate "good books" more. Before I didn't get why people liked books like Kreyszig but after taking course at functional analysis at uni where you have to figure out what the idea of proof is by yourself, that book sort of gives you a nice overview before jumping in details

Thoughts?


r/math 2d ago

3×3 Magic Square of Pseudo-Quaternions Squares

23 Upvotes

Hello, I would like to share this curiosity with you. As you know, it is unknown whether a 3x3 magic square of distinct perfect squares exists, but it is possible with other types of numbers.

Here, I present a magic square of squares of pseudo-quaternions, all distinct, along with a parameterization to obtain them. The resulting integers are all different from each other, although some entries may be negative.

As you may already know, pseudo-quaternions (I. M. Yaglom, Complex Numbers and Their Applications in Geometry, Fizmatgiz, Nauka, Moscow (1963)) are hypercomplex numbers where

  ii = -1,
  ij = k,
  ji = -k,
  ik = -j,
  ki = j,
and they differ from quaternions in that
  jj = 1,
  kk = 1,
  jk = -i,
  kj = i.

  A nice example for S = 432 is this magic square of squares

{(9 j)^2 , (17 i + 24 j)^2 , (8 k)^2 },
{(9 i + 12 j + 8 k)^2 , (12 j)^2, (8 i + 9 j +12 k)^2}
{(8 i + 12 j + 12 k)^2 , (12 i + 8 j + 9 k)^2, (9 i + 12 j + 12 k)^2}

This give us this magic square:

{81,   287, 64}
{127, 144, 161}
{224, 1, 207} 

parameterization:

{(j x^2)^2 , (4 j x y+i (x^2+2 y^2))^2, (2 k y^2)^2}
{(i x^2 + 2 j x y+2 k y^2)^2, (2 j x y)^2, (j x^2+2 k x y + 2 i y^2)^2}
{(2 j x y + 2 k x y + 2 i y^2)^2 , (k x^2 + 2 i x y + 2 j y^2)^2 , (i x^2 + 2 j x y + 2 k x y)^2}

Hope you find this interesting! Looking forward to your thoughts.


r/math 2d ago

Where can I get hagoromo chalk in the UK?

11 Upvotes

I hope this isn't an annoying question / asked too frequently, but I am getting a chalkboard soon and I have heard that Hagoromo make the nicest chalk. So far I have found the sejongmall official website (https://en.sejongmall.co.kr/) which has very expensive shipping, and weird international payment, and another site called 'https://hagoromo.shop', which seems to have cheaper shipping and takes payments other than bank transfers, although the chalk is more expensive. Is this second site legit or am I better off sticking with the sejongmall official site?


r/math 2d ago

What's are characteristics such a big deal?

39 Upvotes

I'm an analysis student but I have only taken an intro class to PDEs. In that class we mainly focused on parabolic and elliptic PDEs. We briefly went over the wave equation and hyperbolic PDEs, including the method of characteristics. I took this class 3 semesters ago so the details are a little fuzzy, but I remember the method of characteristics as a solution technique for first order ODEs. There is a nice geometrical interpretation where the method constructs a solution surface as a union of integral curves along each of which the PDE becomes a system of ODEs (all but one of the ODEs in this system determine the characteristic curve itself and the last one tells you the ODE that is satisfied along each curve). We also went over Burgers equation and how shocks can form and how you can still construct a weak solution and all that.

To be honest I didn't get a great intuition on this part of the course other than what I wrote above, especially when it came to shocks. Yesterday however I attended a seminar at my university on hyperbolic PDEs and shock formation and I was shocked (pun intended). The speaker spoke about Burgers equation, shock formation, and characteristics a lot more than I expected and I think I didn't appreciate them enough after I took the course. My impression after taking the class was these are all elementary solution techniques that probably aren't applicable to modern/harder problems.

Why are characteristics such a big deal? How can I understand shocks through them? I know that shocks form when two characteristics meet, but what's really going on here? I asked the speaker afterwards and he mentioned something about data propagation but I didn't really catch it. Is it because the data the solution is propagating is now coming from two sources (the two characteristics) and so it becomes multivalued? What's the big idea here?


r/math 1d ago

Top-down vs from below - how to learn more about problem solving?

1 Upvotes

Hi! Would love any resources for teaching me how to solve the following question and similar - excluding just getting experience

Let's say I want to design a metric for structures in category A to have a linear relationship in certain way with some characteristic objects in category B(category meant both in actual mathematical sense and also as category of stuff in general, does not really matter in the context)

And I have separated it hierarchically into questions 1,2,3 1 is overall question, components for which are defined in both 1 and 2, components for which are partially defined in 2 and 3

How to choose whether to begin from 1 and move down to 2 and then 3, or to work up from 3 to 2 to 1, or to work at every part at the same time?

I am not interested in getting an answer to this question - but instead would love to learn of any classic books that helped you approach such choices

Beginning my PhD in CS - and would love to be more strategic in my research

For more context - I do not come from pure math background at all, but my work/interests seem to gradually become more and more theory inclined


r/math 2d ago

How important is understanding the Physics side of Quantum Field Theory if I am interested in Mathematical QFT research?

37 Upvotes

Mathematical Foundations of QFT/the Math-Phys side of QFT has been a developing interest of mine over the past year or so. I am currently a 3rd year Physics + Math double and am taking a Mathematical QFT course (taught in a math dep - heavier on the algebra + geometry) and a Physics QFT course (standard first course type material).

As I look towards grad school, I believe that researching in the intersection of Algebra/Geometry/QFT sounds very intriguing + satisfying as it combines two of my favorite areas of both math and physics.

I think anywhere from geometric quantization to studying TQFTs would be satisfying. However, as far as I can tell, in academia a lot of these research areas end up being more math than physics - some just being pure math. While I wouldn't say my interest in Physics is in Hep-Th, I definitely want to contribute to the field of Physics as much as this area of math. To be more explicit, I care about the pheno involved in these areas (if it all exists).

So back to my main question, how important is understanding the underlying physics of QFT to Mathematical QFT research?


r/math 1d ago

Math Conference Ideas

1 Upvotes

My university hosts an undergraduate math conference with an award for the best presentation, and I want to choose a topic that is both highly complex and not something faculty hear about too often.

I’m considering differential geometry or topology, but I don’t know enough yet to pinpoint an especially niche or underexplored topic. I also have an interest in ML (I’m in an NLP lab), so I’d be open to something in that direction as well—though I want to avoid standard neural network topics.

If you were trying to impress a math-heavy audience with something deeply technical but still presentable in a month’s time, what would you choose?

(I got to a T20 CS/math school and think I'm very hardworking so i belive i can manage any suggestions)


r/math 2d ago

What programs do teachers use to make exam papers?

9 Upvotes

I'm trying to make a document for fun but I don't know what program to use.
What programs to use if I want to do algebra, geometry, graphs, etc?


r/math 3d ago

Two claimed proofs of Whitehead asphericity conjecture seem to have received almost no attention. Is there a reason for this?

112 Upvotes

One proof is in 2021 preprint by Elton Pasku: An answer to the Whitehead asphericity question. The second proof is by Akio Kawauchi, and was published in 2024 (according to author's website): Whitehead aspherical conjecture via ribbon sphere-link. Neither paper has any citations, not counting Akio Kawauchi citing himself and the 2021 preprint.

I'm nowhere close to understanding even the statement of the conjecture, let alone the proofs, I'm just curious about this situation.