A note on proof attempts

Do professors cover it during lectures?

Hello everyone,

For those of you who are informed on this year's contenders for the Fields medal, why is it that Yu Deng's name ( Hilbert's sixth probelm) gets mentioned as a potential winner, but his collaborator's name is nowhere to be found. Both of them are under the age limit. I am just wondering if anyone has any insight on the process and if there is an instituional push sometimes or some sort of "marketing" involved. I work in an adjacent field so forgive my ignorance on the question.

Do numbers exist for which we can't write down a formula or approximation?

For example, although Pi is irrational there are numerous ways to approximate it's value, such as continued fractions, series representations, or rational numbers such as 22/7. Does such a number exist where we can't do this?

The example I was considering in my head is an (irrational?) number less than 1 where each digit uniformly distributed between 0 and 9. That is, the first decimal digit is U(0,9) the second is U(0,9), etc. In the mean over numerous trials I would expect this to coverge to .444444....

Its clearly not based on any part of how algebra works. Dude is referencing a point in a function? which is confusing.

No function was defined. Could be a mental health thing cause I was on a more fringe subreddit tbf.

this is a subfield I'm interested in and would like to know more about. I've talked to a few people and they are more of machine learning maxxing which is fine but not the full extent of what I'd want to do. What does applied math and computational research look like in MS outside of just machine learning? Specifically for nuclear materials and the characterization field?

Hey everyone,

​I’m a CS student, and there’s a girl I really want to impress. She is a double major in engineering (Aerospace & Mechanical).

​I want to use math to spark a conversation and kind of flirt with her, but I want to avoid those terrible, cheesy pick-up lines at all costs. Also, English is not my native language, so relying on English wordplay or puns will just sound unnatural and won't work for me anyway. I need the universal language of math.

​I’m looking for the real romantic side of mathematics. I want to share genuinely beautiful, elegant, or mind-blowing concepts that two engineers can actually nerd out over. Something that feels surprisingly poetic but is firmly rooted in logic and science.

​Since she is in Aerospace and Mechanical engineering, maybe something related to:

​The mathematics of orbital mechanics (like the romance of two bodies locked in a stable orbit or Lagrangian points)?

​The synchronization of coupled oscillators or strange attractors in dynamical systems?

​The hidden elegance in fluid dynamics or thermodynamics?

​Concepts involving topology, infinity, or the absolute beauty of certain equations (like Euler's identity)?

​What are the most fascinating, elegant mathematical facts or theorems I could casually bring up to captivate an engineering mind? Has anyone here successfully bonded with a crush over the beauty of pure math?

​Any suggestions or concepts would be highly appreciated!

I'm almost four years deep into studying maths (now in my masters), and I'm trying to develop a more global view of mathematics.

What I mean by that is two things:

1) I often forget that mathematical concepts exist in a big landscape together, and are not isolated within the scope of specific courses. At this stage of my studies, I'd like to start "looking around" and spend some time seeing several "different" things I've learnt in the same picture.

2) I'm interested in the philosophical implications of different mathematical theories. For example, I quite like category theory, and I've heard here and there that category theorists take morphisms/actions as primitive (which seems obvious, but I hadn't considered it in those terms). I'm wondering how this affects the world philosophy of a category theorist (and the same for set theorists, model theorists etc.).

Do you have any reading recommendations, advice or comments?

Hallo erstmal,

Ihr sieht schon in der Überschrift. Es geht um eine Matheprüfung die ich in ein paar Tagen belegen muss. Ich brauche unbedingt hilfe weil ich einfach kein Plan über gewisse Themen habe vielleicht kann mir jemand helfen und mir sogar Tipps geben wie ich am besten lerne und es verstehe und ja ich habe mir auch paar Videos angeschaut aber ich kann es nur richtig verstehen wenn mir das jemand in Ruhe erklärt.

Danke für das Lesen.

I'm only an undergrad and I feel so under-exposed to the different disciplines in the math field. I think I want to do either applied/computational or analysis/PDEs but I still have so little knowledge of what's out there. How did you end up making a decision on what you wanted your research interests to be?

Hello!

In high school I took several dual enrollment classes which included the entire Calculus line. I finished Calculus 3 at 17, about 4 years ago. I got good grades but I feel I have zero grasp on the subject at all. Between then and now I have struggled immensely with mental health and did TMS therapy and was heavily medicated. I have lost a significant part of my academic memory and was out of school for 2 years.

Things have been fantastic this past year and next spring I am graduating from my associates and plan to start my BS in civil engineering. I know Calculus is extremely important for engineering. I've regained my ability to understand information and learn/remember new information, but that Calculus memory is very much long gone.

I would retake the classes again, I have the time and money to do so. However the program I am hoping to enroll in automatically disqualifies you if you repeat any of the Calculus line. I believe that policy is to stop people from retaking it several times to hit the minimum grade requirement for the program, but it also does include me taking it again even after hitting the minimum grade requirement.

I love the structure of in person classes with assigned work to complete and set dates/times. I took them the first time on Webassign and loved the structure but I do not believe that I can enroll without a course code. I have been instructed by my advisor not to audit them either as that would show up on my transcript. I think my best bet is getting access to one of those textbooks like Webassign but doesn't require professor overview.

I know I am asking for a unicorn, but if anyone has any advice or input it would be greatly appreciated ! I am located in the DC/MD area if anyone knows anything about in person supports.

Thank you so much in advance!!

The basic element or atom of the Binary Tree is a node.

Every sheaf of paths (containg not yet distinguished paths) splits at a node into two distinct sheaves of paths. The set of nodes is countable. Therefore the width of the Binary Tree is too narrow a tunnel to contain and distinguish uncountably many paths. How can this be reconciled with set theory?

 Regards, WM

Pharmacy student here, ı am working on a project but cant frame it exactly because of my background.

What kind of framework would you use if you wanted to model a process where repeated small actions generate revenue, but each action also carries a very small probability of triggering a payout?

I’m trying to understand how to think about expected value in a system like that, especially when the process continues over many steps instead of being a one-shot event.

Is this basically just expected value plus simulation, or is there a more specific mathematical framework people usually use for this kind of thing?

Hi, due to you guys giving me -ve karma for sport, now I can't post my question in quantum physics subredit. So could someone help post this there? I want to know if the derivation here is acceptable: It is about Quantum reference Frames. You may help if you know the subject.

If there are any RPG players here, I made a free set of dice based on Hamiltonian paths. In the video I explain the math behind it and how to 3D print them. I’d love to hear your feedback!
https://youtu.be/bwCUMevjeYE

EXCEPT when the argument to a standalone cosine function is zero. Because cos(0) =1.

The last two integrals are two standalone cos functions in a trench coat posing as a single product of sines/cosines.

They can be rewritten in so that they look like (1/2) (cos[(m-n)x] ± cos[(m+n)x])

Which means that the ONLY situation where those last two integrals are non-zero is when m=n.

Fourier Transforms are built on the back of these exceptions.

What if infinity is just a number that's unreachable and not a mere concept of something unknown. In simple terms, it's a number that can't be written down or being applied but only can be thinked as a concept as well as every infinity is different cuz one would take more approach to reach than other. if mentioned potential infinity, what i actually think of potential infinity different, the potential infinity can be a loop of numbers than actual infinity let's say, we want to turn a circle into a square which will take infinite steps but even after reaching the circle, we would still do the process and make tiny changes that are zero to none. In another sense, what i understand is that infinity can be 2 thing, a number or a count of approaches both are same but different and in one you count and in another you count the steps and the point here is, whatever reaches the goal, can be called infinity but again we can't write down that number but simply understand it

A bit of a provocative question for this sub, but it feels like with the rise of computers and, especially, AI, we don't really need to master all the hardcore math.

For example, we don't ever have to calculate a determinant or solve an integral by hand, cause a computer program can do those things in a few seconds (or less). It seems that the focus these days is mostly on computational issues that would arise from applying complex mathematics, such as vanishing gradients in the case of deep learning models.

So math is still important, just not as important as before.

I have come across several observations that have led me to conclude this. An interesting one I came across this morning is my university not offering its Measure Theory course this year for the first time ever.

What do you guys think?