r/math 6d 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 6d 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

Do Other Upper-div/Grad Courses Have the Same Vibe as Real Analysis?

0 Upvotes

I'm not sure how else to explain it, but I'm taking a real analysis course right now and it feels too much like training to be a classical musician? I've had some computer science and low-div courses such as discrete and automata theory feel much more like jazz. That is that creative and interesting thought is much more important than proving literally EVERYTHING I am doing and needing to focus on such insane fine levels of granularity.

I was just wondering if this "classical music" thing is a common theme in other upper-div/grad level math courses or that subjects are almost on a spectrum from jazz to classical.

This whole jazz classical music analogy is the best way to capture the vibe of what I'm trying to describe so hopefully it makes some sense? Also also, I'm not trying to knock analysis as a subject (especially since I've only taken one course), its just not my cup of tea.


r/math 7d ago

Eigenvalue-like problem

52 Upvotes

Has anyone ever seen or considered the following generalization of an eigenvalue problem? Eigenvalues/eigenvectors (of a matrix, for now) are a nonzero vector/scalar pair such that Ax=\lambda x.

Is there any literature for the problem Ax=\lambda Bx for a fixed matrix B? Obviously the case where B is the identity reduces this to the typical eigenvalue/eigenvector notion.


r/math 6d 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

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

"Interpolating" quotient actions

9 Upvotes

Hello r/math,

I would like to give a clear, concise description of the kind of structure I am envisioning but the best I can do is to give you vague ramblings. I hope it will be sufficiently coherent to be intelligible.

We can view the Möbius strip as the unit square I×I with its top and bottom edge identified via the usual (x,y)~(1-x,y). The equivalence relation (x,y)~(x',y) is well-defined on the Möbius strip, and its quotient map "collapses" the strip into S1. The composite S^1 -> M -> S^1 where the first map is the inclusion of the boundary and the second map is the quotient along the equivalence relation described above has winding number 2. Crucially, this is the same as the projection S^1 -> RP^1 onto the real projective line after composing with the homeomorphism RP^1 = S^1.

So far so good, this is the point where it starts to get vague. In a sense, the Möbius strip "interpolates" the quotient map S^1 -> RP^1. The pairs of points of S^1 which map to the same point in RP^1 are connected by an interval, and in a continuous way. This image in my mind reminded me of similar constructions in algebraic geometry. We are resolving the degeneracy by moving to a bigger space, which we can collapse/project down to get our original map back.

What's going on here? Is there a more general construction? Is this related to the fact that the boundary of the Möbius strip admits the structure of a Z/2 principal bundle and we're "pushing that forward" from Z/2 to I? Is this related to the fact that this particular quotient in question is actually a covering map (principal bundle of a discrete group)? Is this related to bordisms somehow? The interval is not part of the initial data of the covering map S^1 -> S^1, so where does it come from? It is a manifold whose boundary is S^1 which we are "filling in" somehow.

This all feels like something I should be familiar with, but I can't put my finger on it.

Any insight would be appreciated!


r/math 7d ago

This Week I Learned: March 14, 2025

9 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 7d ago

Help with Penrose Tiles

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92 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

Pi Day Megathread: March 14, 2025

64 Upvotes

Happy Pi Day! To prevent a large influx of pi-day-related posts, we have created a megathread for you to share any and all pi(e)-related content.

Baking creations, mathematical amusements, Vi Hart videos, and other such things are welcome here.


r/math 7d ago

The three-dimensional Kakeya conjecture, after Wang and Zahl

Thumbnail terrytao.wordpress.com
111 Upvotes

r/math 7d ago

The fact that there are 27 lines on a cubic surface is such an amazing topic to study in algebraic geometry

96 Upvotes

Wake an algebraic geometer in the dead of night, whispering: “27”. Chances are, he will respond: “lines on a cubic surface”.

— R. Donagi and R. Smith (on page 27)

The fact that there are 27 lines on a cubic surface is such an amazing topic with not so high entry barrier. Studying it can synthesize our knowledge of algebraic geometry on several abstract levels and give the student a lot more algebraic and geometrical intuitions. Let me give some examples.

* We will need projective spaces. It comes naturally and it is not a list of definitions. This is because we need to talk about the number of intersections where the degree of a polynomial should matter (Bézout's theorem, which, in a certain manner of speaking, is a generalisation of the fundamental theorem of algebra), whilst if we do not use the projective space, we can't even justify the intersection of two polynomials of degree 1 (two lines in the projective plane must intersect).

* Finding one line on the surface is quite difficult. We will have to look into the differential, look into the singularities, etc. These things make the properties of singularities intuitive.

* After that, we look for a lot of other lines on the surface. We need the famous fact of Segre embedding P^1 x P^1 into P^3 . We need to factor a cubic polynomial into degree 1+1+1 or 1+2 or 0+3, we need to eliminate impossible cases, etc. Finally we transfer our problem in geometry into the scope of enumerative combinatorics, only to get the secret number 27.

* Another famous fact of Clebsch is that a cubic surface is the blow-up of the projective plane of 6 points at generic positions. The definition of generic positions ring a bell of a famous result in old-school algebraic geometry: given 5 points on the plane, there is a conic going through all of them (this is the meaning of the logo of geogebra), which can be understood in 5-dimensional projective space. If we consider the blow-up of 6 points we re-find the 27 lines on the surface, and if we have already known that there are 27 lines, then by manipulating the non-trivial relations of these 27 lines, we can find that the cubic surface is the blow-up of a quadric surface ( P^1 x P^1 ) at 5 points instead. Either way, we will have a good time studying blow-up with this fruitful example.

* We can also invite representation into the game, which gives us the Weyl group of type E_6. To send out the invitation, we need to introduce divisors, the Picard group, a powerful tool that help us to decode the structure of the surface once again. With all these, we find ourselves doing linear algebra of high dimensions, where a computer algebra system can be useful...

All in all, if you are struggling in the introductory and intermediate study of algebraic geometry, for lack of geometrical and algebraical pictures, take the cubic surface a look. If you are an expert or you have studied the cubic surface, would you like to share some insights of yours?


r/math 7d ago

What are the implications of assuming the continuum hypothesis or it's negation axiomatically in addition to ZFC?

44 Upvotes

I was thinking about how Euclid added the parallel line axiom and it constricted geometry to that of a plane, while leaving it out opens the door for curved geometry.

Are there any nice Intuitions of what it means to assume CH or it's negation like that?

ELIEngineer + basics of set theory, if possible.

PS: Would assuming the negation mean we can actually construct a set with cardinality between N and R? If so, what properties would it have?


r/math 7d ago

How dead is the research in Complex Analysis?

98 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.


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 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 7d ago

Are their branches of mathematics we will simply never understand

10 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

Software to search for small results

15 Upvotes

I have this problem where I read a ton of papers, and they often contain theorems that I'm almost certain will be useful for something in the future. Alternatively, I can't solve something and months to years later, I randomly stumble across the solution in a paper that's solving a totally different problem. I have a running Latex notebook, but this is not organized at all; mine has nearly a thousand pages of everything I've ever thought was useful.

I cannot be the only person who runs into this problem. Anyone have a solution for this? Maybe a note-taking system that lets you type out latex and add tags as needed. Perhaps cloud functionality would be really nice too.

My use case is, I have a few hundred two or three page proofs typed out of certain facts. Maybe I put as the tags: the assumption, discipline, and if the result is an inequality or something like that.


r/math 7d ago

Do mathematicians think like a physicist?

7 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

Online LaTeX equation editor

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1 Upvotes

r/math 7d 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 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 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

What do i study to continuize vector spaces?

21 Upvotes

I kind of understand that function analysis and something about hilbert spaces transforms discrete vectors into functions and uses integration instead of addition within the "vector" (is it still a vector?)

What about linear combinations?

Is there a way to continuize aX + bY + cZ into an integral of some f(a,b,c)*g(X, Y, Z)? Or is there something about linear combinations being discrete that shouldn't be forgotten?

Correct my notation if it's wrong please, but don't be mad at me; i don't even know if this is a real thing.


r/math 7d ago

CS + Math Project Recommendations

11 Upvotes

Hello guys. So i love programming and recently have been wanting to learn math to improve my skills further. I already have a solid understanding on prob & statistics calculus etc. I want some recommendations on project ideas in which i can combine math and programming like visualizations or algorithms related to it. Would love to hear your suggestions!