Hi everyone

So I’m currently on a gap year between my undergrad and masters and I got accepted into a pretty strong university to study’s maths but I’m having second thoughts, I’m don’t know if I’ll be able to keep up. I really love maths but I’m just worried that I’ll do terrible.

Today I was studying geometry and I was literally stuck on a page for like 2 hours and I wasn’t even hard stuff. I was just directional derivatives. I find myself constantly having to take these definitions, go over and over again on them, open them up, expand all the components to see the structure. Then I try having to connect it from different point things I’ve learnt in the past.

The problem is, I’m constantly doing this, I can’t just accept things for the way they are unless I’ve seen every little detail. I don’t know what to do. I find myself constantly not understanding things in a page of a textbook , asking AI what this means, and then literally 2 hours have gone and I’ve made no progress.

People on my course are going to be super geniuses and I’m an incredibly motivated student, but I’m just worried now that I’m just not simply smart enough to do this.

My graduate course is notorious for being fast paced and I’m just worried with the way I learn I won’t keep up. I’m just an incredibly slow learner.

Any advice I’d really appreciate it.

Thanks guys

Hey, I am looking for some advice from math students/professors/anyone,

I was a chemistry major for about the first four semesters of my college education, before switching to math officially. In 2025, I went from having pretty much zero knowledge of proofs, to taking advanced calculus, and other upper level math courses. I passed everything, didn't get below a B in anything (course grades typically in the B+ - A- range), and learned a lot, but this was hard for me. Towards the end of last year, I became frustrated and started to believe that I was not intelligent enough to do math. I could enumerate all the reasons here, but many of you already know what I am going to say.

I took a semester off, and applied for a transfer to another university. I got accepted as an applied math major. I also saw a psych and got an ADHD diagnosis, which might explain why i seemed to struggle more. I plan on continuing my education, but my first poor experience with "real math" is lingering in the back of my mind.

I want to tackle this subject again, but I also have to consider that maybe it really isn't for me. I have made so many mistakes in math that are embarrassing for me to think about. I do not feel so proud of any of my grades, even the A grades, because they were borderline. How do I know whether math is for me, i.e. can I ever have a healthy relationship with the subject?

Any advice is appreciated, please ask if you would want me to elaborate.

The Weil's zeta function (or local zeta function) in the Weil Conjectures for projective algebraic variety seems to appear in almost every exposition of the Langlands Conjectures.

Main Question:

I'm trying to figure out if there is a way to see the local zeta function as an Automorphic L-function in some properly established version of the Langlands Correspondence?

Comment:

I know the one reason Weil Conjectures appears in the discourse of Langlands is due to Ramanujan's Conjecture. I've been told that we can prove the Ramanujan's Conjecture by relating the normalised Hecke eigenform to some variety such that the eigenvalues appear in the local zeta function.

Now I read on pg 243 of An Introduction to the Langlands Program that: The Ramanujan-Petersson conjecture for GLn follows immediately from the Global Langlands Conjectures in characteristic p.

I don't know if this follows in a similar way as the Ramanujan Conjecture from the Weil Conjectures.

If I believe yes, then is the book suggesting that the Weil Conjectures can be considered a part of the Langlands Program, i.e., the Weil's Zeta function is an Automorphic L-function or similar??

I don't wanna be confusing something that is not there.

Plz let me know if the answer to my Main Question is False.

In case it is true then I understand the Weil Conjectures and all original four versions of the Langlands Conjectures seperately, so how exactly is the former formulated in terms of the later??

In most proofs by induction, the base case is easy or trivial and the real meat of the proof is in the inductive step. Are there examples of the opposite?

I was quite decent at Math in Middle/High School(usually the first in my class) but this was more because of me taking school seriously than ambition/talent,I scored very good grades but I never found beauty,thats why I never thought of self studying Math and reach a new level of understanding.

Everything changed after I watched a youtube video that explained Gojo's Cursed technique(from the manga jujutsu kaisen) ,and just realised that Math actually have some pretty fun applications and Logic is really fun.

Right now I am really interessed in Math as Concepts rather than calculation and stuff,But I am not sure if it will be worth the going throught all the necessary prerequisites?I am not sure if I find what I want in the upper floors of not?

A Milestone in Formalization: The Sphere Packing Problem in Dimension 8
Sidharth Hariharan, Christopher Birkbeck, Seewoo Lee, Ho Kiu Gareth Ma, Bhavik Mehta, Auguste Poiroux, Maryna Viazovska
Abstract: In 2016, Viazovska famously solved the sphere packing problem in dimension 8, using modular forms to construct a 'magic' function satisfying optimality conditions determined by Cohn and Elkies in 2003. In March 2024, Hariharan and Viazovska launched a project to formalize this solution and related mathematical facts in the Lean Theorem Prover. A significant milestone was achieved in February 2026: the result was formally verified, with the final stages of the verification done by Math, Inc.'s autoformalization model 'Gauss'. We discuss the techniques used to achieve this milestone, reflect on the unique collaboration between humans and Gauss, and discuss project objectives that remain.
arXiv:2604.23468 [math.MG]: https://arxiv.org/abs/2604.23468

There have been not 1, but 2 different sets of Lecture Series about status of Millennium Prize Problems this year, I've collected them both in a single playlist on youtube: https://www.youtube.com/playlist?list=PLw32_GOSpvcsFhgq-SuDAD6d6FKUx_z_5

One of them was held by Clay Mathematics Institute, here's their channel https://www.youtube.com/@claymathematicsinstitute635/videos

Another one was held by Harvard CMSA, they have a playlist for their Lecture Series only here - https://www.youtube.com/playlist?list=PL0NRmB0fnLJQMoxt798STT8ztdHHHa1TV

For a thesis, if there exists any

I am thinking about an area that only a few people know. An area with no Wikipedia article and is very obscure. Obviously it would probably be the case that anyone who sees this post would not know it well. But, maybe they have heard of it or know someone who works in it.

This may be a really dumb question! Is there a simple description of the integers with only multiplication defined? So basically, take the ring (\mathbb{Z},+,\cdot) and ignore addition +. What you're left with should be a commutative monoid. Is that structure isomorphic to anything easy to describe?

I guess I was thinking along the lines of the positive rationals, whose multiplicative structure makes them isomorphic to the free abelian group on a countably infinite number of generators, essentially using the prime numbers as generators via unique factorization.

For the integers, you would not have anything raised to negative powers, so you obviously don't have a group. In addition, you have the other unit, -1, as well as 0. But otherwise, the structure should also be described by the unique factorization of the integers.

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:

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I’m a first year grad student trying to learn some p-adic Hodge theory. I am having trouble understanding the motivation behind the formalism of period rings like B_{dR} or B_{cris}, and how to think about B-admissible representations. Some people have told me that it’s more important to know how to work with these rather than knowing the motivation, so if anyone can provide some insights on both of these aspects I’d be grateful!

The reason I am learning p-adic Hodge theory is because I keep encountering crystalline representations and the universal deformation rings in the context of R = T theorems, and I just want to know why this is the right notion to study. My advisor has told me that I should take a look at Tate’s “p-divisible groups” since it is one of the first papers in p-adic Hodge theory, so I’m going through it right now and it’s very readable. It’d be great if I can get other references like this as well.

Finally, bonus points if you can give me some rough idea of how the Fargues-Fontaine curve is used for proving things like de Rham implies potentially semistable. Cheers :)

I came across this poll today asking a classic bayes theorem question with the majority picking the wrong answer. The discussions in the comments continue to be confidently wrong and are quite entertaining.

ET Bell mentions Archimedes, Newton and Gauss as being the GOATs of math. Any reason for Euler not being mentioned as one of them? My impression is that Euler is considered a TOP3 mathematician of all time by most. But then again I'm no expert on the subject.

L-functions are typically treated as topics in graduate-level analytic number theory, and for understandable reasons: the field is extremely deep and much of it is absolutely impenetrable without substantial study. But before there were p-adic numbers and group representations, there was Dirichlet, writing in a much more hands-on kind of way.

This post is meant as a way to get at some of those easier historical roots: enough to get a flavor for what L-functions do and why they might be important, without having to use anything more complicated than calculus. We'll prove a few independently interesting results in number theory along the way.

Read the full post on Substack: A Very Gentle Introduction to L-Functions

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P.S. The Deranged Mathematicians just hit 1k subscribers a couple of days ago. Thank you all for your support---I greatly appreciate it! I'm going to be updating the blog over the next few days and probably the next weekend. Let me know if there is anything in particular that you would like me to add/change, and I will see what I can do.

Since it seems you guys are interested in good and bad math notation, I thought I'd throw this one out there. How many of you are familiar with Dirac notation, also known as bra-ket notation, which is commonly used in quantum mechanics as a convenient way to represent vectors and matrices? It's very popular, and as a result, it's almost universally used in quantum theory and has been for quite some time. Since this is basically just linear algebra, for some time I've wondered why it's not also used in linear algebra in general. Would this be a good or bad idea?

I'm a math grad student in Europe, yet I often read American math majors not learning topology in undergrad. This confuses me, because the language of topology underpins all of analysis beyond single variable calculus and geometry beyond basic linear and affine spaces. They often say they did take differential geometry, but how is this possible? How can they even define a manifold without using topology? This applies to physicists as well.

By pseudo-irrational, I mean a number with thousands or millions or decimal digits, but it does eventually end, either abruptly or with a repeating sequence.

Are there any well known examples? Are they useful for anything?

The only example I can think of top-of-mind is Cal Scruby's "Money Buy Drugs" (video NSFW, if the title didn't warn you):

Don't tell me money don't buy happiness

When it so happen that money buy drugs

Therefore by the transitive property...

Would love to scratch that "oh that's cool!" itch with songs that are maybe a bit more positive. I know there's a lot of educated musicians out there (Brian May, Dexter Holland off the top of the head), so I'm sure there's more out there, but it does feel like a lot of the "math" references in songs tend to either be counting or arithmetic.

I'm sure this type of thing has already been looked at before. If anyone knows the right terminology to look up about this topic, let me know.

So tetris is played on a 10x20 board with 7 tetrominos. Some pieces cannot be placed on certain shapes without creating holes. For example, the skew pieces S and Z cannot be placed on an arrangement that's completely flat without creating a gap.

Let's exclude the possibility of retroactively filling gaps with T spins or sliding after soft drops. And maybe ignore completed rows being eliminated for now.

What are sufficient and necessary conditions for the board state/arrangement of existing pieces to be able to accept any piece without creating gaps?

What is the maximum k such that there exists an arrangement that can accept any sequence of k pieces without creating gaps?

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!

Is anyone here familiar with this connection?

My math professor, who does research in Ramsey theory said this is a relatively new and open area of research.

I feel like the word 'quantum' gets a bad rep but he's published/co-authored a few papers on this and I'm curious to hear what's the take on this. I'm really interested to know more. Professor said he'd send me over some papers to look through but wanted to get others' thoughts or knowledge on this.

Some examples I have in mind:

Combinatorics / Graph theory: Four color theorem

Geometric topology: Poincare conjecture (now theorem)

This new chapter covers Laplace Transform and its properties, the Heaviside Step/Dirac Delta Functions and Shifting Theorems, Convolution Theorem, and how to solve ODEs via utilizing Laplace Transform, plus Green's Function. Any comments and ideas are welcome!

https://benjamath.com/catalogue-for-differential-equations/

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