r/mathematics

So i was thinking that, in an examination, we often assume that getting rank 1 is the hardest.

But, many times the person who got rank 1 is not only relatively the best, but also closer to best on an absolute level. So if someone strives towards being the absolute best then they can achieve rank 1.

But now lets say a person wants a specific rank, lets say 22nd, and he wants to be as close as possible(say margin of +-2). Now he needs to be relatively worser than 21 candidates and relatively better than the rest. This is different from targetting being absolute best as in case of rank 1. So it appears, targetting and getting this rank is harder than rank 1.

I want to understand, how can i mathematically approach this? Take and suggest any assumptions or parameters. Also, if we do quantify it can we get a threshold and thus the rank which is hardest to obtain which may fall below 1?

This problem isnt for undermining the importance of rank 1, because most people target rank 1 as they sit in an exam rather than having a specific numeral target other than 1.

I know that a "quadrant" is any section or area that is divided into four equal parts, which usually creates 4 squares inside of one big square. But what if those same 4 squares were rearranged and strung out linearly—as horizontally? What would that type of layout be called?

I'm thinking of the Audi logo and the Olympic rings as if they were only 4 of them, now imagine if the rings were squares instead of circles. So in this case, the squares don't necessarily need to be directly side by side horizontally. They could be interlocked and overlap. What is the word for that?

This is a quite long read, but I hope you will take your time and share your critique and wisdom. I also know it's quite a common topic these days and might be annoying by now, but still. I want discussion, your actual thoughts. If this interests you at all...

I am currently a first-year pure mathematics student. How did you change your approach to doing math when AI came, now that it can "understand" the vast majority of problems? No matter what math problem I throw at it, it solves it. I know this is because it's in its training data; we can assume it has no creative, original insights, and we can argue and debate about how these things operate. But the fact is: it solves the problem, it outputs the proof, it gives the answer. And it's just a matter of time before hallucinations are reduced to zero.

I understand that I am naive and may have a limited understanding of the world and of "real world" problems, not just textbook ones or olympiad ones. And I honestly started to hate it when people say that math is a human endeavor and that it's just so fun solving and exploring problems together. Like, yeah, it's fun, but that immediately reduces the significance of math to something like chess. What I mean by that is this: before AI, when you solved some kind of problem, it felt magical, meaningful, something that would let you solve harder problems and contribute to the world. Thinking about the problem, that was the fun part. But most importantly, not only that: it signified some kind of intellectual superiority, bonded tightly to one's identity; for some, the whole world could be looked at through a mathematical prism. Then, when you didn't understand what to do, maybe you asked your peers, or professors, or experts, and you always knew there would be someone smarter than you. And that's okay, totally okay: you would learn from them, you would get inspired, and you wouldn't really care whether you'd manage to get a Fields Medal or whatever. But you knew you would be needed. Just a small fraction of the population is actually good at math, and an even tinier fraction actually puts in the work to become even greater. Now it just feels... meh, to be honest.

Then some will say: if calculators were invented, why do we still teach basic arithmetic? Well, I agree with that. It is, of course, to develop thinking skills, basic skills, something all of us globally should know. But when it comes to dedicating your prime years to learning advanced mathematics... well, you know what I mean.

Still, the reason I chose a pure math degree is that I am good at math (well, based on what grades and standardized test results tell me) and, most importantly, I do like math and actually view it as the universal language and something beyond... I believe no one has yet invented a better way to train the mind than mathematics, and I have yet to meet anyone complaining of having too much general aptitude. Learning mathematics helps develop the ability to think logically, analytically, and critically, to structure and organize, to process information, and it also trains the problem-solving skills that help us explore and understand the world. "Mathematics should be learned if only because it sets the mind in order," as the Russian polymath Mikhail Lomonosov said.

I mean, it's quite paradoxical at this point. I remember when I was in middle school, I really liked word problems. I would solve dozens of them, searching for ever harder and harder problems; that's how I really ingrained my first glimpses of learning in my mind, of how applicable math can be. When solving problems, I would do most algebraic manipulations with a CAS calculator, because I already knew how to do those, and I often thought: what if there were a system that could actually understand word problems? And here, bang! We have LLMs that can now solve the vast majority of them. I would have loved to have that at that age. How much more I could have learned and accelerated! But now I find it very hard to find the same motivation. Maybe because it's the real world now: how will I make money?!!!!!! Maybe I just should have gone into medicine, the field least affected by AI in the long term. But I don't like medicine. Never did.

So yeah, math is sublime, powerful, a universal language, and applicable. In the same way, AI is just math and nothing else: a huge, complex mathematical structure, a function. And then: we are all going to die, aren't we? So the last day on Earth won't really matter that much. Then I think: why learn anything at all? If AI can do anything, why should we learn? Why should we exist at all, maybe just end our existence? What's the point of it all? So, of course: we learn, we get better at what we do, and we simply know that we can't avoid taking risks, and so on.

So, my question after this monologue. I am not asking you whether it's worth learning mathematics; I do have a plan: pure math as the equivalent of a hardcore brain gym, then maybe a master's in machine learning/AI, and then work on AI, improving it. But the thing is, I often find it hard to believe what I want to believe. Do I believe it, or what? Also, I will most certainly not take the fully academic path, like a math PhD; I am more interested in application, and the only reason I am taking a pure math degree is that it is purely abstraction-loaded, believing it will train me, and I enjoy it. But how do I keep learning? How do I stop just thinking and thinking and posting questions on forums, and actually just do things? Maybe I am going insane, or maybe I am just so f**king stupid.

So please, share your wisdom.

I'm his older brother, currently in college majoring in chem engineering. My younger brother is 15 and spends most of his free time doing mathematics. He also keeps a diary where he writes down his mathematical ideas, observations, achievements, and anything interesting he comes across.

This is some of the things he has independently worked on:

Rediscovered the basic trigonometric ratios before learning them in school.

Explored prime-generating polynomials. Explored ideas related to the nth prime.( He was 13 yr old innocent guy then )

Arrived at symmetric variation of the Goldbach conjecture.

-Investigated prime around expressions of the form 2^n + 6 ( if n is even then primes are -3 and + 1 from it and if odd then -1 , +3 from it , works for n as 1,2,3,4,5,6,16,18 etc.

Developed an infinite-triangle method for approximating polygon and segment areas.

Created generators for Pythagorean triples.

Arrived at the positive-index binomial theorem formula by observing patterns in expansions and translating those observations into a general formula.

Etc etc much more a lot of work and ideas he has he is kinda obsessed

I'm not claiming that any of these are new discoveries or that he has solved any famous open problems. I know it's possible that many of these ideas already exist and that he may have rediscovered known mathematics independently.

I'm just curious how unusual this kind of mathematical journey is for someone his age, and what you think would be the best direction for him going forward.

I have trouble solving for the square root of large numbers. Is there a way in finding out the square roots?

Hello everyone,
I am 29M. I am currently enrolled in a Masters program for computer science. It’s time for my thesis and I wanted to do something related to categorical quantum mechanics and something related to lean theorem prover. I was happy at first to see that I get to work on something so cool.
But right now it feels like it’s overwhelming to learn everything there is. Learning category theory, topology, interactive theorem proving and on and on. Some days it’s exciting as I am able to connect some wonderful dots and it’s good but some other days it’s just hell breaking loose and I even cannot pick up my pen.
Worst of all my advisor has a minimal knowledge as I was the one to choose the topic and it feels lonely there is no one to share what I have learnt and what holes I have in that learning and where to go from there.
I simply don’t know if it’s just a phase or I am in a roadblock or I just chose something completely out of my hands.
Can you please tell me what I should do?
(Currently I am trying to look some relationships between graphs and quantum contextuality like can there be local global section failure in things like traffic . It’s just a hunch but I don’t know )

I’ve seen other posts about this and the replies are usually just clearing up confusion rather than answering my question. Yes, the fourth dimension works in math and engines, but just because it works doesn’t mean it exists. In the universe, does a fourth spacial dimension ACTUALLY exist? If it didn’t why does it make sense with all our math, why is there no problems?

Hi everyone, I am a 16 year old kid I am prepping for JEE one of the toughest examinations of the world which provides admission in engineering colleges in India. I am an 11th grader and currently enrolled in a coaching institute (institutions specially designed for preparation of such exams) I struggle to understand the concepts that are taught to us because my teacher focuses upon rote learning of formulas and expressions. He explains concepts very superficially and gets agitated if you ask hi doubts. The thing is that I enjoy math but the focus from learning concepts to just trying to clear an exam has ruined the essence of the subject for me. therefore, I have come here to ask all of you for help and how to study balancing both the exam and the subject and developing the correct methodology to study.
I will be thankful for all yours guidance and suggestions.

I always enjoyed maths at school mostly for solving problems and it give me a big sense of enjoyment when I do, I want to get back into it, I understand most the basics but idk where to practice them, do I come up with questions my self or is there a place on the internet. I want to use maths for enjoyment and time spent with my brain so to speak and be able to solve questions without paper. But also to understand the universe more and the nature around me. I’m not an academic, I left school at 16 a few years ago, to simplify my question I just want to know how you guys practice and create/find puzzles to solve

why do zeta zeros behave statistically almost exactly like the eigenvalues of large random Hermitian matrices? seems like we are verging on something huge connecting primes with quantum theory but don't know what instrument to use to crack it open. anyone have any fun context or pet hypotheses?

I need a list of the best and most widely loved math textbooks as well as a good list of beautifully-designed math textbook covers.

What do y'all think fit this description?

We can visualize a sphere in 3D, but if t is time, does this equation describe an object that exists only for a finite duration? Or is it simply a static 4-dimensional sphere whose 3D "snapshots" change over time? Does this mean we'd see a sphere that grows and then shrinks over time? Or is that interpretation mathematically misleading?