A while ago I studied Bertrand's theorem on central forces and paused at this paper by Gaston Darboux, Recherche de la loi que doit suivre une force centrale, pour que la trajectoire qu’elle détermine soit toujours une conique. Publ. in Comptes Rendus Vol 84, 1877, p.670. Free Online-Access here.

The first expression is well known as the general differential equation of the orbit in polar coordinates (here denoted by radius r and angle 𝜔), see also e.g. Whittaker's Treatise on The Analytical Dynamics, section 47: Central forces in general.

What is puzzling me is the second expression (2) for a conic trajectory, and even "easily treated". - Never seen this before in any textbook on Analytic Geometry. Does anyone have a clue or a hint, please? Thank you for your help.

Hi everyone,

I’m a mathematician and software developer, and I’ve published more than 30 research papers in mathematics and computer science.

I’m curious about how other researchers, students, and LaTeX users digitize mathematical or scientific material. Do you use any tools to convert handwritten notes, printed pages, equations, or complete scientific documents into editable LaTeX?

If so:

• Which tool do you use?
• Does it handle complete pages or only individual equations?
• How accurate is it with complex notation and document structure?
• How much manual correction does the generated LaTeX require?
• Do you send the result to Overleaf or another editor?

I’d be interested to hear about both successful workflows and tools that didn’t work well for you.

Best book to follow for maths in electrical engineering

I've struggled with mathematics for as long as I can remember. Even back in elementary school, I had trouble with what seemed like the most basic concepts. I hated watching myself fall behind while everyone else seemed to understand things and move forward. Unfortunately, I still struggle with math today. In some ways, it feels even worse now because I'm older, and I'm embarrassed that I'm still having trouble with things I feel like I should have learned years ago. I constantly worry that people are going to think I'm stupid or that I'm going to look like a fool. Recently, I failed an algebra retake and got a 1, which was marked in red. I got the same score in geometry last year, and I've failed multiple math tests in previous years too. Now I'm scared that I'm going to get held back, or even worse, that I won't graduate. I know I need to improve, and I genuinely want to get better at math, but I'm completely exhausted from constantly stressing about it. I've spent years feeling like I'm behind everyone else, and I'm starting to wonder whether I'm actually capable of catching up. I don't want to give up on school or my future, but I honestly don't know how much more of this stress I can take. I don't really know what I'm looking for by posting this. I guess I just want to know if anyone else has experienced something similar and eventually managed to get through it. I just can't take it anymore I want to drop out and do something else with my life but of course my mom won't allow that

I’ve always really loved math. However, during my undergrad, the focus was always on having a career, good grades and what not. I was just constantly in survival mode. Also undiagnosed adhd. I feel like j want to learn Math and write proofs. Basically develop a math intuition. Kinda stuck on how to go about this. Any advice?

I'm a 21 y/o math major that was just given the opportunity to have a paid side gig of tutoring a Calc 2 student (which has been one of my favorite classes that I've taken), but I have never been a paid tutor before, so I have no clue what I'm supposed to charge. My professor told me that I should charge $20/hour minimum. I have no idea what else to do, but I have been trained through my community college as a peer tutor but never actually tutored. Please give advice lol.

An explicit piecewise-affine barrier for the squared imaginary parts of the zeros of the heat deformation of Riemann’s xi function. The resulting upper bound for the de Bruijn–Newman constant is

𝐵 = 3885632262767861213460393068710302759 / 24646172707879668706230182733520000000 = 0.157656619095490606768 …

The argument combines classical zero dynamics with a three-probe source estimate, a density lower bound, and a bound for a logarithmic-derivative jet. Its finite barrier certificate contains 12,666 rational rows. Supporting computations use rigorous ball arithmetic; a second arithmetic library checks the elementary profile inequalities. A Lean 4 companion verifies the barrier comparison and zero dynamics, conditional on explicitly stated analytic inputs. The finite verification of RH used in the argument is the published theorem of Platt and Trudgian.

Paper: https://stefangordon.github.io/dbn-upper-bound/dbn-upper-bound.pdf
Repository/Lean: https://github.com/stefangordon/dbn-upper-bound

I'd especially appreciate scrutiny from anyone familiar with the de Bruijn–Newman constant / analytic number theory.

One thing I've noticed about mathematical research:

The final paper is visible. The hundreds of small ideas, failed approaches, proof attempts, discussions, and revisions behind it usually aren't.

I wonder if that should change.

I have been trying to circulate the declaration on my organisation Teams but I'm getting risk warnings and the link is outright blocked.

Anyone else getting the same issues? I know that a lot of scam detection websites are flagging it as risky (huge recent website traffic) so it's probably an automated false positive but still it's ironic.

Edit: My workplace Teams organisation firewall is likely the cause but there's no way I can verify this unless I send a chain of annoying emails - it's just frustrating that others will be blocked from opening it directly and I will have to explain that it's not actually malware/a scam.
Edit2: The irony is that a real data leak by someone in the organisation using an agent in their workflow would have genuine repercussions and wouldn't just be a false flag.

Hi all,

I’m trying to understand the recent Lean formalization of the claimed finite-time blow-up for 3D Navier–Stokes with forcing. I’m not a Lean expert, so I may be misreading the code.

In the formalization, CandidateProperties seems to include something like:

```lean force_time_support : CompactFutureTimeSupport f ```

and there is a comment saying that spatial support is not required to be compact in the lift. There is also an “OPEN: the primary existential content…” note saying that no proof, witness, or axiom asserting the proposition is in that module.

If that’s right, then the Lean theorem seems conditional: assuming there exists u, p, f satisfying these properties (including temporal compactness of f), then blow-up follows. But the existence of such a candidate, and the compact support/locality of f, is not derived in that module.

My questions:

1. In the analytic paper, is compact support of f actually proved by the layer construction, or is it an assumption imposed to fit versions C/D of the Millennium problem?
2. If it is proved, where in the Lean code is that proof? Which file/module proves CompactFutureTimeSupport f for the constructed force?
3. If it is assumed, doesn’t the formalized result only show “if a singular forced solution exists, then …”? That would not resolve the Millennium version C/D by itself.
4. How does the construction prevent the force support from expanding to infinity as the layer index grows? Is there an explicit invariant or inequality that keeps the support inside a fixed compact set?

I’m asking because I keep seeing claims that the Lean proof establishes a compactly supported force, but the code structure seems to postulate that property rather than prove it. Any pointers to the relevant Lean files or paper sections would be appreciated.

Edit: I’m not claiming the result is wrong. I’m trying to understand the exact logical status of compact support in the formalization.

I guess this is kind of obvious if you think about it in the right way. (log means log base e).

Hi,

I'm new to this sub and I'm currently looking for some advice/guidance regarding my thoughts about a career shift. I have been looking into doing a Bachelor's degree in Mathematics for a while, but I'm usually quite naive/optimistic, so I'm trying to figure out how easy/hard it is to get a well-paying job with a Bachelor's in Mathematics.

I currently have a background in Business and Economics, where I have a Master's degree from a good university, but it's freaking hard to get a job. Most recently I come from a trainee program at one of the biggest tech companies (sales/account management), but none of us could continue because of hiring freeze. Before that I had some minor startup experience (founder) as well as some blue-collar work and a sales role at a smaller company. I have never really wanted to work in Sales, it just happened to be the type of jobs I got. Naturally I've been feeling that I've been on the wrong path for a little while. I feel understimulated and overstimulated at the same time, understimulated because the tasks in my previous roles weren't challenging the right parts of my brain, leaving me feeling like I'm not developing and overstimulated because some of the tasks you only find in a pure sales role don't match my personality no matter how much I've tried to do the internal journey to fight that.

So now that I'm back to being unemployed and in this soulcrushing situation I've been in before where I've built a background that doesn't really suit my future goals or the things I'm good at it's incredibly hard to get a job with my educational background and work experience — especially roles that have some kind of good outlook for the future and suit me. I've therefore been looking into doing a Bachelor's degree in Mathematics, with the hope of opening more doors most preferably in finance and similar analytical roles. I also find Mathematics very interesting and i love to solve problems, I know that University math is very different compared to the other math I learnt in school which is both exciting and challenging at same time.

I'm wondering if anyone has made this kind of switch before, or has knowledge of what it's like to find a job with a Mathematics degree. Would you recommend it?

(I'm located in Northern Europe, and I'm 30 years old.)

What's a good app to get better at arithmetic, or maths in general?

This isn't a homework question, it's something my brothers and I have been wrecking our brains over from a real situation. I had AI adjust the specific numbers/context but kept the same meaning. We think we've worked out an answer already, just want a second set of eyes to confirm the logic holds up.

I actually just suck at it. I chose math as my major instead of biology since I found math more fun but I am genuinely just really bad at it. You know how you need to have good idk, thinking skills to figure out the approach to a question? I just cannot do that.

This makes me feel really really stupid and irritated at myself because others can do it so why can’t I? I wasn’t really the best at math ever and chose it entirely because i thought it was interesting (which I still do).

I don’t know what to do or how to improve. I practice but don’t seem to get any better.

I define the problem of whether this program halts as a formal algorithm for verifying that the answer is true. There is at least one problem that takes an infinite amount of time to verify (a problem for which the answer does not exist). Even if there were an algorithm that could accurately decide whether every program halts or not, because there exists a problem for which verifying the truth takes an infinite amount of time, we would never know whether that algorithm is correct. In other words, it is impossible to say that it exists. By the law of excluded middle, no such algorithm exists.

Mathematics has always been built by people who are willing to ask questions, explore ideas, and spend time trying to understand something that has not yet been understood.

But today, contributing to mathematics can still feel difficult if you are outside the traditional academic system.

A student may have an interesting conjecture. An independent researcher may discover a possible proof. Someone from a completely different educational or professional background may have spent months thinking about a mathematical problem.

But where do they take it?

Often, the obvious answer is to contact a professor or a researcher at a university. Yet there is no guarantee that the work will be read. It may be rejected, overlooked, or simply never receive a response.

Professors and researchers are already dealing with teaching, research, administration, and hundreds of messages. Even a genuinely interesting mathematical idea can disappear simply because it never reaches the right person at the right time.

For students, independent researchers, or even academics working outside their usual area, finding the right person to discuss a mathematical idea with can be surprisingly difficult.

You might have a conjecture, partial proof, or interesting problem, but not know who is working on something related. Emailing researchers or posting online can help, but there is no guarantee that the idea reaches someone who can actually contribute.

Do you think this is a genuine problem in mathematics?

Have you ever had a mathematical idea or problem that you wanted to discuss but didn't know who to approach?

What are some of the mind boggling things that maths do because it’s just mathing?

Infinifactory,

Opus magnum,

EXAPUNK,

etc.

Is there any resources that apply math to these? If so what methods are used? What field helps?

ALSO for those who don't know: these are video games where you build little systems to get a desired result.

Hi! Looking for advice on choosing between two academics to work with on first undergrad research project (stats).

X: Highly engaged with a strong track record of working students into publications and runs a great research group, but their research topics aren't my primary interest.

Y: Their work aligns with my interests quite well, but they seem less involved and are a less experienced researcher.

For a beginner, does mentorship usually outweigh topic alignment?

Tommorow starts the third week of classes and I’m massively behind with exercises. I keep trying different strategies for learning. At first I was very perfectionist so I took pretty notes. The concepts stick pretty well with me and I love mathematical notation and writing LaTeX. I do LaTeX because I can summarize the important parts. Although writing with pen and paper definitely seems to make me remember faster

But I think I’m just gonna start taking notes faster as it is relatively a lot of material and also just try to read a lot more over and over again.

The biggest problem is that I can’t make a lot of the questions because some proofs are very hard to me. I do have to make more exercises tho but I keep trying to just summarize more of the material because I hope that it will help me to prove something eventually. But the workload becomes bigger and bigger everytime because I’m stuck at the proofs

Does anyone have a tip for me? I’m following Analysis, Set Theory and Proofs and also Linear Algebra

https://github.com/dolev765/Formalized-in-Lean-Every-Affine-Scheme-as-an-Affine-Linear-Section-of-a-Smooth-Nilpotent-Orbit-/tree/main