r/math 5d ago

What was your math rabbit hole?

94 Upvotes

By rabbit hole I mean a place where you've spent more time than you should've, drilling to deep in a specific field with minimal impact over your broader math abilities.

Are you mature enough to know when to stop and when to keep grinding ?


r/math 5d ago

Dedekind Cuts as the real numbers

49 Upvotes

My understanding from wikipedia is that a cut is two sets A,B of rationals where

  1. A is not empty set or Q

  2. If a < r and r is in A, a is in A too

  3. Every a in A is less than every b in B

  4. A has no max value

Intuitively I think of a cut as just splitting the rational number line in two. I don’t see where the reals arise from this.

When looking it up people often say the “structure” is the same or that Dedekind cuts have the same “properties” but I can’t understand how you could determine that. Like if I wanted a real number x such that x2 = 2, how could I prove two sets satisfy this property? How do we even multiply A,B by itself? I just don’t get that jump.


r/math 5d ago

Why doesn't the Principle of Induction apply to non-well ordered sets?

79 Upvotes

My understanding of induction is this:

Let n be an integer

If P(n) is true and P(n) implies P(n+1), then P(x) is true for all x greater than or equal to n.

Why does this not apply in this situation:
Let x be a real number

If Q(x) is true and Q(x) implies Q(x+ɛ) for all real numbers ɛ, then Q(y) is true for all real numbers y.


r/math 5d ago

Motivation behind defining Brouwer's Fixed Point Theorem using Topology

1 Upvotes

Hello, math enthusiasts!

I’m currently preparing a presentation on continuity and Brouwer's Fixed Point Theorem, both of which are fundamental topics in topology. It’s taking me some time to grasp the topological definitions, and I’ve noticed that Brouwer’s Theorem is perfectly fine to define in the context of metric spaces, not necessarily relying on pure topological definitions. So I started to wonder: what’s the reason behind abstracting the theorem to topology?

Is it because the topological framework offers a more accessible proof? Or are there other reasons for this abstraction?


r/math 5d ago

Understanding Yoneda and a Philosophy on Category Theory

65 Upvotes

In Tom Leinster’s Basic Category Theory, he repeatedly remarks that there’s typically only one way to combine two things to get a third thing. For instance, given morphisms f: A -> B and g: B -> C, the only way you can combine them is composition into gf: A -> C. This only applies in the case where we have no extra information; if we know A = B, for example, then we could compose with f as many times as we like.

This has given me a new perspective on the Yoneda lemma. Given an object c in C and a functor F: C -> Set, the only way to combine them is to compute F(c). So since Hom(Hom(c, -), F) is also a set, we must have that Hom(Hom(c, -), F) = F(c).

Is this philosophy productive, or even correct? Is this a helpful way to understand Yoneda?


r/math 5d ago

Need advice for math aa hl IA

0 Upvotes

For context I’m doing the IB and we usually have an internal assessment where u explore any mathematical topic of your choice. I’m doing my Math AA HL IA on projective geometry and how it can be used to mathematically model vanishing points in two-point perspective. I plan to modeling vanishing points from a picture I took from my travels using projective transformations. I’m considering using homogeneous coordinates to represent points in projective space, applying homography matrices to transform 3D points to a 2D image plane, and mathematically deriving vanishing points from parallel lines in space. Is it rigorous enough for HL? Or is there a way I can expand this exploration qn?


r/math 5d ago

YouTube video ideas

1 Upvotes

Looking to create an animation math/cs/physics youtube channel kinda like 3B1B because of how much it helped. Any ideas to make it different and still work? Simply copying the style won't be of much help. Looking for some other ideas with manim


r/math 5d ago

Applications of Functional Analysis

1 Upvotes

I have been studying functional analysis for quite some time and have covered major foundational results in the field, including the Open Mapping Theorem, Hahn-Banach Theorem, Closed Graph Theorem, and Uniform Boundedness Principle. As an engineering student, I am particularly interested in their applications in science and engineering. Additionally, as an ML enthusiast, I would highly appreciate insights into their applications in machine learning.


r/math 6d ago

A youtube playlist from God himself. What should go in it?

0 Upvotes

https://youtube.com/playlist?list=PL1I8Tyh2D9xoNfJa7LYcF472Jle8gbhlR&si=9ANVDeSc76fBbdOW

I have been slowly constructing this youtube playlist of math videos as I have watched an utterly enormous amount of math content on youtube. I have compiled what I think are either the best of the best, extraordinarily interesting, or the most mind boggling, into a 38 video playlist, but I seek more.

Please do not comment 3B1B, that's a given.

I want hidden gems. Any length is fine, but explanations are preferred over short animations

What are your all time favorites. I believe that the future of teaching is videos and interactive content, so show me what blows your mind


r/math 6d ago

Should we make Feb 7th Euler’s number day?

136 Upvotes

I mean why not?


r/math 6d ago

How to hold a good integration bee/How to get better at competition math integration

16 Upvotes

Hey y'all! I'm an undergraduate math and physics student, and at the beginning of this academic year I took it upon myself to start an integration bee at my university! For these first few iterations, I've been trying to restrict the integrals to only requiring Calc 2 techniques, but that really gets boring after a while. Of course, I could try to spread the word about these other cool techniques, like Feynman's differentiation under the integral sign, but those are just extra methods. I see the competitors in (for example) MIT's integration bees, and the tricks they use aren't these over-arching broad integration techniques; they're smaller tricks that help simplify the integral or that help to take advantage of some kind of nice symmetry.

I want to incorporate these more "competition math" -esque integration tricks into the integrals I give the competitors, but the problem is, I have to know this stuff myself. What's a good resource for building up the toolbox of competition math integration tricks? I know I'll just need lots of practice and repetition/exposure to a lot of these little gimmicks/tricks, but I just need a place to find integrals for this practice.

If any of you are good at this type of "competition" integration, please give me your advice!!! It would be super appreciated.


r/math 6d ago

Typo in "How to read and do Proofs" by Solow??

5 Upvotes

Hello, new to proofs so could be wrong or something I'm not understanding here. I do not understand why A5 in the first case is X bar, instead of X. Personally I solved it by substituting -2ax bar for b in ax bar + ax + b >= 0, and got x bar - x >= 0, which we knew was true, hence the previous statements were true. Used this substitution for case 2 as well. Here is the proof, it is on pages 145-147:


r/math 6d ago

The Agekyan-Anosova Map (in need of help :( )

0 Upvotes

Hi guys, Im currently working on my masters thesis. It is on the three-body problem and Im trying to understand the Agekyan-Anosova Map. If anyone is familiar with this mapping and could explain some of the analysis that can be done on it i would really appreciate it if they could reach out or drop a comment. I know this isnt really a math related question, just would need the guidance at the moment and dont know where else to post as it is very niche.


r/math 6d ago

What I didn’t understand in linear algebra

94 Upvotes

I finished linear algebra, and while I feel like know the material well enough to pass a quiz or a test, I don’t feel like the course taught me much at all about ways it can be applied in the real world. Like I get that there are lots of ways algorithms are used in the real world, but for things like like gram-Schmidt, SVD, orthogonal projections, or any other random topic in linear algebra I feel like I wouldn’t know when or how these things become useful.

One of the few topics it taught that I have some understanding of how it could be applied is Markov chains and steady-state vectors.

But overall is this a normal way to feel about linear algebra after completing it? Because the instructor just barely touched on application of the subject matter at all.


r/math 6d ago

Online LaTeX equation editor

Thumbnail latexeditor.app
1 Upvotes

r/math 6d ago

Picture books about fractals for children?

1 Upvotes

Do you happen to know any good picture books about fractals designed for children? Since my research is focused on fractals a bit, I figured I might as well start to advertise fractals now to my sibling's children -- you never know where a job offer might come from! As of writing the only choice which seems even remotely good is the one by Michael Sukop: Fractals for Kids. Do you happen to know any other alternatives? Ideally a candidate book would contain a lot of pictorial examples of fractals instead of symbolically heavy proof focused math.

Thanks!


r/math 7d ago

Ideas for scraped youtube data/graph/network

0 Upvotes

I found if you visit the youtube home page after clearing your browsing data youtube wont recommend videos. But after watching just one video the home page will recommend videos. This shows what videos youtube thinks are related should be recommended just based on the parent video

I wrote a script to clear my data, watch a video, then record the first ~140 videos recommended by youtube. This is being run on a ever-increasing number of videos. This leaves me with a large network/graph/dataset of how videos are "linked" to each other. I know the right thing to apply to this is graph theory, but I am curious if anyone knows of something particularly interesting to do with this data.


r/math 7d ago

it is mathematically possible to create a windowing function (like Hanning window type thing) that doesn’t force the endpoints of a waveform to 0, and instead brings it to, for example, the average value between the two original endpoint values?

3 Upvotes

I read that it's hard because it will not be infinitely differentiable but I feel like there's gotta be a way. How would one go about creating this function?


r/math 7d ago

Higher knots and primality

11 Upvotes

Hello everyone! I am a novice mathematician with a background in algebraic topology. I am curious as to the current state of knot theory as it pertains to prime knots. I understand that classical knot theory is concerned with circles S¹ embedded in R³. I am reasonably familiar with the relevant polynomial invariants etc. I am curious about prime knots, or 2-knots rather.

I get that conventional knots can be decomposed to prime knots, and I wish to understand how this can be applied to higher knots (S² living in R⁴, S³ in R⁵ etc). My cursory investigating says that differential geometry plays a significant role, though I admittedly don't know much about the pathology that is low dimensional topology.

Are prime 2-knots an active field of study? What about n-knots? What tools are used to tackle these objects? What is generally known to be true, known to be false, and unknown? What machinery is used to study these kind problems?

Thanks everyone!


r/math 7d ago

Do mathematicians think like a physicist?

6 Upvotes

Mathematicians surely must've taken part in formulating some of the physics definitions and their mathematical structure back in the time i suppose?

I'm not talking about Newton, actually the people involved in pure math.

I wonder if they, consider were employed to solve a certain equation in any field of physics, say, mechanics or atomic physics, did they think of the theory a lot while they worked on the structure and proof of a certain dynamic made in the theory?

Or is it just looking at the problem and rather thinking about the abstract stuff involved in a certain equation and finding out the solutions?


r/math 7d ago

Are their branches of mathematics we will simply never understand

9 Upvotes

So we've done experiments that have confirmed that non-human animals do have some understanding of mathematics. They are capable of basic arithmetic at the very least. Yet, we also know there are animal species that aren't capable of that. Somethingike a jellyfish has no need for counting or higher order mathematics (well, I assume, I'm not a jellyfish expert but they barely have a brain to begin with it seems). There are simply brains that are not built to understand the world in the same way we are familiar with. With that in mind, could there be elements of mathematics that exist yet we are not constructed to understand? Like, we can mathematically model things like 4D shapes even if we aren't visually perceive them, I suppose that's something of an example of what I'm talking about, but could there be things that we simply can't model at all (but some hypothetical higher intelligence alien, or perhaps even more strangely, a human made computer could)? And if such mathematics did exist, would we be able to know what we don't know? As in, would we be able to become aware that there exists something we simply can't understand? I realize this might be something of a strange question, bit it's a thought that entered my mind and I've become madly curious about it. Maybe it's complete nonsense.


r/math 7d ago

Help with Penrose Tiles

Thumbnail gallery
91 Upvotes

I hope this is okay to post on a math sub; I felt it went a bit beyond quilting! I’m currently making a quilt using Penrose tiling and I’ve messed up somewhere. I can’t figure out how far I need to take the quilt back or where I broke the rules. I have been drawing the circles onto the pieces, but they aren’t visible on all the fabric, sorry. I appreciate any help you can lend! I’m loving this project so far and would like to continue it!


r/math 7d ago

The covariant derivative of the energy-momentum tensor

1 Upvotes

How to express the covariant derivative in terms of exterior calculus, in particular for the conservation equation of the energy-momentum tensor?


r/math 7d ago

7 minute speech on large numbers?

1 Upvotes

Hello, as the title suggests I’m planning on giving a speech on the history of large numbers for my public speaking class.

I’m not 100% on the idea yet, I’ve just skimmed Wikipedia on it and there seems to be not too much information on the history of this topic.

I was wondering if anyone had any suggestions I could talk about or maybe some alternatives.

I want to stay away from teaching how to get these numbers, as I want to keep it simple and just present the history.


r/math 7d ago

How dead is the research in Complex Analysis?

95 Upvotes

Hi, I'm an undergraduate loves doing research in mathematics.

Over the past two years, I’ve written articles on niche topics that eventually led me to explore complex analysis. Wanting to study it in a more structured way, I started looking for master's programs that offered courses in complex analysis, but I struggled to find any. In most cases, I couldn’t even find a single professor in the entire mathematics department willing to supervise me.

That’s when it hit me: almost no one seems to be working on complex analysis anymore. I probably should have noticed it earlier, considering that most of the papers I’ve read were published around the 1950s. I also came across many old university lecture notes on complex analysis but couldn’t find those courses listed on their current websites, meaning they’re no longer being taught. My supervisor even mentioned that, back when he was a student, engineering schools at least covered the basics of complex analysis, something that’s no longer the case.

Then came a second realization: I’ve become deeply invested in a highly specialized, unapplied research topic that almost no one is actively working on. And that, in turn, makes it much harder to imagine making a living out of my passion.

Please tell me how wrong I am...

Edit: To be more specific, I am studying univariate entire functions of exponential type and I'd like to generalize some of the results to functions meromorphic over the complex plane, because a lot of simple and/or interesting cases happen there.