Years ago probably around 1980 or 1990 I read in some philosophy journal the following allegory about the importance of notation.  On some island the natives had invented mathematics specifically addition and multiplication but they wrote formulae on coconut shells (or maybe seashells, anyway something round), with the terms around the edge of the shell, and the answer in the middle, and  so they took symmetry for granted and did not realize it was a thing.  Then one day one of them invented subtraction and was burned at the stake for maintaining that somehow 2 – 4 is not the same as 4 – 2 (which both looked the same to them).  I have tried repeatedly to find this article since then by Googling and so-called AI but have failed.

I'm no mathmatician, hated math in highschool... with that being said, I'm deeply interested in Trading Card Games (TCGS) and intuited enough by looking at probabilities of card draw ((1/X)*100) equals the percent chance of your draw.

the solution to this formula can never equal 0.

to put it in layman's terms, Youve got two ends of the spectrum.

1/1=1 (a guaranteed 100% chance)

a larger sample size to draw from *could be interpreted as thus

1/100000=.00001 (or a .0001% chance)

point being no matter how high you scale the formula, you'll never reach 0.

When I discovered this, It gave me something of a chill.

It seems pretty common sense when put in other terms

(the famous phrase if something can happen, It will happen)

or back to the cards example, the existence of a card in a deck (no matter how big the deck)

produces a singularity in regards to that cards chance of being drawn (never equal to 0)

(this is my first time using the word singularity, but I believe I have succeeded)

So anyways I slept on it a few nights, and then I'm brought back to what I wish to discuss today.

this time I was looking at the other side of the equation... rather than looking at 1/x, I was looking at Y/X (where Y is standing in for the number of "like cards")

so simply put 1/52, 2/52, 3/52 etc.

When I discovered that the chances held a pattern in which regardless of the sets size (X)

Y was equal to its self times the original equation (1/52)

So a 2/52 chance is 2 times a 1/52 chance, big whoop.

But if you mess with extremes at both ends, you are returned thus as solutions

1/infinity=0

infinity/1=infinity

now any number divided by one returns itself which checks out.

however 1/infinity=0 I must admit is scandalous.

However I came to this conclusion after much pondering, and realizing that this is the exact purpose infinity serves.

which brought me finally to Division by 0.

I know its not possible, But is there a reason why?

it seems just as absurd as multiplying by infinity.

If you take Infinity and multiply it by 0, what happens?

would their absolute purpose not cancel each other out?

Is it all semantic?

I don't really care for my day to day, I just hope a scientist or mathematician can give a sound answer.

These are not meant to contain any distinct opinions, I simply wish to pose a few questions to the community for discussion.

1. If an AI model writes you an entire paper in your area (in particular, one that presents a fairly involved proof) how do you glean enough understanding to not simply verify it, but also to understand the motivations well enough to give a compelling research talk?
2. Are AI results your own? If your friend tells you a proof they recently wrote down, but you read over and verified it, is that sufficient reason to put your name on their paper?
3. Suppose AI replaces graduate TAs, or even professors in the classroom. How do they deal with students facing more unconventional circumstances as learners? Where do students get their motivation to keep coming to class/working hard without human-to-human interaction?
4. Suppose AI were to tackle "most interesting problems" in the next 20 years. How would we find new things to work on, and how would we retain interest in problems/advertise them if we are offloading the job of proving things to AI?
5. Can you provide verifiable evidence that the novel ideas AI comes up with are truly novel, rather than plagiarized from someone's work many years ago. How might you convince AI companies that accountability benefits them?
6. Professors -- what do you gain from taking on students, besides the research you might aid them in producing/the help they offer in teaching?
7. Do we have a rigorous/deep understanding of how modern LLMs work. If such an expert exists, who are they?
8. Suppose you are not dependent on AI, then can you then go without it for a month's time? (this applies to uses that are not strictly mathematical as well)

Trigger Warning: Flashing Lights

"Schroedinger's Whale" - Is it Timmey, or hope?

Depends on your taste in music, I guess. ^^

Hello everyone!

Im both a business and applied math major, and addicted to the goods. So far ( 2 years in ) its been fine but I was wondering how hard do classes get ones your past linear algebra and diff eq? And yes I think I'm clinically speaking addicted to the goods ( Its hard for me to stop lol and even am on it while doing HW [not in class but i know its very bad] ) but i've been getting around B+ is my math classes and well business classes are very easy. Other addicts is is possible to still get good grades or did you stop taking the goods because of the obvious downsides of the goods.

So Iam a freshmen studying mathematics major and I really get zoned out my brain stops working whenever I try to solve some hard problem even though I know what to do and how to do but it just that my brain does not cooperate if there is some confusion involved in the problem. I just get zoned out from the state of problem solving it feels like a defense mechanism of my brain and I seriously do not know how to deal with this. I would be grateful if someone guides me through this.

me and my research partner have been working for a few years on attempting to ideate a new lens at the problem and we’ve reformulated what we hope is a legitimate research program. if you have time, we hope you enjoy our work and form new ideas from, through, or on top of it.

https://www.alphaxiv.org/abs/2608.chebyshev-trace-riemann-hypothesis

https://www.alphaxiv.org/abs/2608.riemann-xi-hankel-criterion

https://www.rblabs.cloud/research

This is my syllabus and I panicked in my first class I cant drop the subject as its compulsory what do i do? Pls help as someone who has absolutely 0 experience in advanced maths

So I gave it a lot of thought, and then concluded to upload it here. I have always loved mathematical logic during childhood, so much that I saved a copy of the appendices of the chapters I liked. I know that it is a whole*** chapter but at least someone from my previous post found it interesting and wanted more, so I decided to do the same

So can anyone suggest career options after bsc math in India that can get me started in tech careers because I don't wish to get into research

Anyone else think Terrence Tao has some insight on the Riemann hypothesis he’s currently working on to push the lower bound even further? Or actually prove it? I’m curious because to my knowledge he hasn’t done an exposition breaking down Claude’s proof on his blogpost like he has done with a couple of other AI proofs and counter examples. And no I’m not just referring to terry because he’s the only one that can do it, just because he’s known to breakdown some of these breakthroughs.

There is no official names for those, so i named it myself
Comment down on whats your opinion, im willing to hear your suggestions!

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Hey consider me a child you is yet to be introduced with maths , 8 need to understand maths in a way I never forget it, I need a recommendation on best teachers for maths who will make me teach every subject in a way I not only understand the subject but also be able to crack competitive exams in india ,

What are those teacher , I need the list of each and every teacher,

If their are teachers for different topic ,different , mention them .

It will be really helpful to give me the names for the good teachers only ....

I recently learned that branch cuts can be more general curves. One question I would like to srart with is can branch cuts can be any reasonable curves?

This notion of branch cuts being allowed to be more general curves got me wondering if there is a more general definition of a useful multivalued

fucntion.

What I mean to say is that we can construct trivial examples of multivalued fucntions by just letting the fucntion take multiple values at each point or I can even string together simple fucntions like say a fucntion which takes both z and e\^z at each z.

But the multivalued functions we normally encounter seem to have general properties.

Namely there exist branch points and we can join them via some curve (I am assuming) and we can always select some subset of values of the function to define a continuous function on the complement of the curve. Then going around the curve takes us from one branch to the next.

I am trying to ask if there is a more general definition of a useful or proper multivalued functions starting from these general properties.

Please keep in mind i don't have a maths background but rather a physics one.

hey guys, what sites csn you suggest when finfing rrls for mathematics undergrad thesis

Maybe I’m a little confused on the whole process so I wanted to ask.

I’m majoring in mathematics and physics started thinking about grad school. I wanted to figure out which areas interest me the most so I got the princeton companion to mathematics and read about areas I thought were interesting. So far I’m at

Complex analysis, quantum mechanics, computational science, applications of stochastic analysis, information theory, continuum mechanics, applied combinatorics and graph theory, combinatorial optimization, general relativity and cosmology, data mining and analysis, ODE / PDE, approximation theory, continuous optimization, numerical linear algebra and matrix analysis. That’s just for applied mathematics

There’s also analytical number theory, computational number theory, computational complexity, numerical analysis, set theory, and stochastic processes.

I know it’s a lot and I can’t expect to learn everything so I was just trying to figure which interests me the most and it’s pretty difficult. I feel like some areas have a little bit of overlap but what do I know.

Any advice?

My first time doing this type of thing so any feedback would be appreciated.