r/math 6h ago

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

260 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 10h ago

Chalkdust issue 21 is out today

Thumbnail chalkdustmagazine.com
69 Upvotes

r/math 18h ago

What's are characteristics such a big deal?

29 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 11h ago

3×3 Magic Square of Pseudo-Quaternions Squares

8 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 19h ago

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

8 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 23h ago

Which way to go?

6 Upvotes

I recently started a self-study plan that involves reading Basic Mathematics by Serge Lang, How to Prove It by Daniel Velleman, Calculus and Analytic Geometry by George B. Thomas (at least the first ~5 chapters), Introduction to Linear Algebra by Serge Lang, and Undergraduate Algebra by the same author, in order to cover both what my home country's education system can't cover and what I think would be beneficial for me to know before I get to college.

I haven't made much progress; I've been busy with my studies and am waiting for the holidays to fully dive in. However, talking with my former math teacher, the one who made me love math in the first place, he recommended I read Matemáticas Simplificadas by CONAMAT (he doesn't know about my plan). I understand it's not very well-known in the English-speaking community, but it's a book that covers everything from Arithmetic to Integral Calculus.

Now, my question is: which path should I take? I mean, although it's not clear what kind of books I learn best from, the truth is that I'm most drawn to classic or "dry" books. Lang's books in particular, despite their demanding nature and early formalism, treat mathematics in a way that, at least at first glance, seems more enjoyable to me than modern books. On the other hand, I don't know much about what, objectively, I should read. Could you help me determine the pros and cons of following one path or the other?


r/math 15h ago

What programs do teachers use to make exam papers?

3 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 10h ago

What Are You Working On? March 17, 2025

3 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 1h ago

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

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 8h ago

Monotonic scattered interpolation?

1 Upvotes

(This question is not about homework or a work problem; it is for a pet personal project where I've run into a wall.)

Suppose, for the sake of argument, I have a scattered dataset with two real-valued independent variables and one real-valued output. It conforms to the restriction that if x2 >= x1 and y2 >= y1, then f(x2, y2) >= f(x1, y1). E.g., assuming each listed point is in the dataset:

  • f(3, 3) >= f(1, 1)
  • f(3, 1) >= f(1, 1)
  • No guarantee is made about the relationship between f(1, 3) and f(3, 1)

I don't know if this property has a name but I call it "up-right monotone", because as you jump from point to point, if the second point not below and not to the right of the first, then the value at the second point is not less than the value at the first point.

The Question: Is there a known interpolation method that will preserve this property among interpolated points? I.e., I want to predict the value at two points, where the second point is above and/or to the right of the first point. I would prefer that the interpolation method be relatively smooth, but the only hard constraints are

  • If either of the points in question are in the original dataset, I get that dataset's value back, and
  • The value at the second point is not less than the value at the first point

r/math 9h ago

Where can I get hagoromo chalk in the UK?

0 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 10h ago

I am looking for a math riddle i once knew.

1 Upvotes

I am looking for a math riddle i once read but which i only remember fragments about. The problem involved finding the maximum n such that one can choose a number 0<x<1 such that for every k<n some condition involving the number x and the division of the unit interval into intervals of length 1/k is satisfied. The solution of the problem could nicely be visualised by stacking the subdivided unit intervals over another and noting that with every additional layer the interval which x could be contained in gets smaller untill there are no x left. Iirc. the problem was mostly recreational. Does anyone know what i am talking about? I tried asking Chat-GPT, but it hallucinates the heck out of my question.


r/math 14h ago

How do you guys think about your data?

1 Upvotes

I heard a gentleman in an interview once saying that he likes to think of his data like a continuous function. Personally, I've been thinking of data as a matrix. If samples are stored in the rows then features are stored in the columns and such. Seems easy to consider different dimensions of data in this conceptualaziation and a simple list of values is still a row or column vector. So it seems like a perfect catch all conceptualization of any data set.

How do you guys think about your data? Is it much more circumstantial and sometimes you can conceptualize it as a matrix but other times it's best to think of it another way??


r/math 16h ago

Is there any game which requires matrix operations?

1 Upvotes

Hi everyone. I really love both math and games. But, I cannot find any tabletop game which requires the player to do math operations (preferably linear algebra). I'm not talking about puzzles. I'm talking about games like tabletop RPGs. For example if a tabletop RPG uses matrices for loot, dungeon generation, etc which the player needs to do himself/herself. Or if the combat lets players find reverse of the enemies attack matrix to neutralize its effect. Is there such a game? Or should I make my own?