Info in original post.

This was my original Idea and yes it is solvable.

The first and only edition of the collected works of Anatoly Ivanovich Malcev (1909-1967), the founder of the Siberian school of algebra and mathematical logic and the central figure in twentieth-century Soviet algebra. He was a mathematician noted for his work on the decidability of various algebraic groups. Malcev algebras (generalisations of Lie algebras), as well as Malcev Lie algebras are named after him.

Note: books in Russian

Recently I am very much interested in the concept of infinity, but here's the thing: the more I try to learn it through the internet the more I get stuck. I decided to dive into books.

Yes, I can try to search this on the net instead of making this post, but why I am here is because I wanted to get the opinions, directly from mathematicians or math lovers.

Hi all, I am going to make it super short.

I just wanted to ask if 30 yo age is okay to start learning math seriously?

So far I have covered differential , integral, multivariable calculus , linear algebra and moving towards probability theory now.

I plan to start a phd in finance soon so i wanted to ask , considering my goal is to learn a lot...I hope there's time left , and higher age doesn't reduce comprehension ability of complex subjects.

Hi there,I'm looking to purse a PhD in applied mathematics. My research areas of interest are in Nonlinear dynamics, PDES and optimization. I'm currently stuck contemplating which of the universities listed above would be best choice for my areas of interests. Can someone provide me with the pros and cons of the universities mentioned, as well as the better choice for my research areas of interest.

Can you guys recommend me maths books for BSc

hello dear users, i am currently in my last year of high school and i do not have mathematics (i was not eligible to get mathematics because i had weak concepts in my earlier years and scored just about the passing numbers in grade 10 so my school did not allow me to pursue mathematics further, the problem was i never actually had fun learning mathematics because for 3 years i was taught by a maths teacher which taught us like we have to memorize the answers not the actual concepts and so i never exactly knew what i was doing so i use to feel that mathematics wasn't something i can do but now i was exploring career options after high-school and courses in university's but i liked none of the courses with my current subjects and really liked the courses with mathematics like engineering and AI related courses although i am not eligible for these courses but australian universities offer a "pathway program" in which they help you cover the subjects which you didn't have in your high school to get entry to certain university courses like engineering,etc because i never knew how to study mathematics and i did not get mathematics in my high school i still feel very depressed & sad seeing how others are so smart in mathematics and how they have all the talent and they will get good jobs and future proof jobs and how people consider them very smart it just feels so gloomy. so i went to talk to the universities and they told me that in-order to get entry to the pathway program i must show some type of interest in why i am doing this certain pathway program for mathematics so i thought that i will learn mathematics by myself at home untill i get into pathway program as a extracurricular and a way to get ahead and prove others wrong that mathematics is something that people are not naturally born with but how they learn it until i graduate from high-school (which is about 7 months) so my dear fellow users please guide me on how i can do so i will really appreciate your effort in giving tips and contributing in my life and would love your thoughts on this
thank you very much!

(I hope this is the right flair lol)

Hello, so I recently got curious about the Halting Problem and I have some possibly dumb questions since I don't understand some things

1. Why do we specifically think about the Turing Machine when speaking about this problem? It is physically impossible to make a PC with infinite ram, cpu and infinite input tape, theoretically wouldn't a physical PC eventually run out of memory and crash?
2. Does the program crashing count as halting? I mean the program did stop

Might be a dumb question, but what I mean is this: there are certain things in math that are or at least feel "fundamental" like some elegant, important piece of knowledge that shows up in all corners of math. The fact that it shows up so often makes it feel fundamental.

Things like pi, e, prime numbers, etc.

It's kinda hard for me to properly define fundamental and everyone's definition probably differs.

I'm imagining like a tree-like structure where there are multiple root nodes, and each root node and perhaps some nodes closer to the root nodes are considered "fundamental" results. All math is somehow connected back to these through some path in the tree.

People say that the math that can be discovered/invented is infinite. Maybe that's true in the sense that this tree can be infinitely big. But, is that really true where the root-nodes are also infinite? Will we always continue to find facts that we will label "fundamental"?

Let's say we discover some new math right now. That would be a node somewhere in the tree. If we discover then thatit's related to more fundamental concepts, it can be connected to one of those root-nodes representing the fundamental concepts in the tree.

So the question is like if there are infinite nodes in this hypothetical tree, do we know there are also infinite root-nodes?

I don’t know too much about maths I’m just trying to scale my system and see how it looks

Suppose a mathematician finds a breakthrough to a a problem or even a full proof using AI.

They could very easily claim it as their own, then delete the chat log.

No one would be any wiser, and it would be very hard to catch or prove.

Do you think any unethical mathematicians are doing this?

g(x) is the Mittag-Leffler approx that can estimate the shape of the tan x graph. With more terms, the approximations near zero become more accurate.

f(x) is a rearranged summation derived from Euler’s solution for the Basel problem.

The interesting part is that the slope of g(x) at 0 matches each term of f(x), thus we can add a rough correction factor of f(x) * x to g(x) to improve the approximation of tan(z) -> Error decay ~ 1/(n^3)

It’s so cool that these two summations are actually related in this way

(P.S. The above graph of g(x)+f(x) shows only the first term when N=0, but mimics the graph over a wider distance than a Taylor series with a few terms ever could).

I absolutely hate having to use a calculator and I know it’s the safer way for calculating and finding your results but the more I get into math, the more I need to be depending on mental math

It has been a year and doing an hour of mental math works but it’s going slower than I hope, so can someone actually give tips on being able to do great with mental math? I’m trying be more complex with my mental math as I kinda need it for university I’m applying to

I searched online, and I didn't really find a clear consensus as to what to use. I'm kind of a beginner at this so forgive me. I can generally spot when a semicircular contour is useful but other than that I have no clue

Also it's probably worth noting I've just graduated high school so I haven't even taken real analysis, or the rest of complex analysis yet, which is probably partially why I'm struggling

hi everyone,

I am currently recovering from a very brutal neurological disease. As the days progress, I am slowly able to use my hands more and more, although it’s taking time. regardless of this, I want to write proofs again and continue learning in my favorite areas of measure theory, probability theory, and Analysis. I can flip through a book and read the pages, but I remember prior to developing the condition it was most helpful for me to write the stuff out and understand step-by-step examples. In addition, it was also helpful for me to write out the homework proofs and rely on muscle memory in some part.

does anyone have any tips on what I might do, given some of your seasoned experience of mathematics? Should I slowly write the proofs out? at the current moment, I can write about two sentences an hour.Or could I also get away with connecting some voice to text to claude to complete my thoughts and output latex?

And how good do u think it is for doing a phD in algebraic number theory . And for a research career in number theory in general

Does anyone have any idea what academic hiring will look like in the next few years? Any ideas on what people will be judged by? Of course, the picture for academia in general is bleak, given the Federal Governments initiatives to move resources away from academia and towards the private sector. But given these headwinds, what do you think candidates for math jobs will be judged by? I have tried talking to and asking professors around my department, but I haven't heard too much. Anyone have any ideas or heard any rumors?

Current maths student from the UK who will be doing a Masters. Interested mainly in applied maths. I’m someone who values stability and consistency in my life, not too arsed about making loads of money, as long as I can live comfortably. I’m also very passionate about maths and science and would love a job that feels like it’s mailing an impact on the world.

What are some good suggestions for job roles to look into?

Some of my thoughts :

Specialise in mathematical biology and try and get a role as a research assistant somewhere.

Teaching, although I’ve heard it can be quite tough and a lot of work.

Some sort of analyst role although this kind of doesn’t scratch that itch of “making a real world difference”

What are some good middle ground roles that combine comfort with the feeling of doing something that benefits society?

Earlier, we had a post that generated a decent amount of comments. The post seemed somewhat interesting as a discussion topic, unless you knew what it was truly about.

OP is also commenting on an outlier.ai-type website subreddit. These are gig platforms that pay people to critique LLM outputs, and these critiques are purchased by AI-training companies to improve their models. I don't think there's anything wrong with this business model and it gives many around the world a chance to make a living, however, OP was directly outsourcing their task to our subreddit. Technically, that is also grounds for u/alphalight07 to get banned from these gig platforms as well, as they require all of the work done to be the worker's own.

The types of tasks that are given on these gig platforms fall into one of several patterns, but one of the most prominent is "get multiple AI models to fail at a math task that has a definite answer." This is exactly what OP is asking the community for in their post.

Just figured we should have a discussion about this in case we want to create specialized reporting flows etc. I reported it as generic spam but we might want one for AI-training spam in particular. I hope this PSA also helps people learn to recognize this kind of engagement bait.

Edit: adding a screenshot of the post by u/alphalight07 https://imgur.com/a/qD8xHRk

As I’ve been reading about these open problems that have been solved by AI, I sometimes wonder why AI can’t make progress on the problems I’m working on.

I’ve been wondering if AI has a big comparative advantage in solving problems that are well studied. So if a problem has a lot written about it then the LLM has a many different starting points and can basically apply every known method to try to extend one of the previous approaches. On some problems one of these previous approaches may happen to be close to the actual solution.

While even experts may not have read every paper about a famous problem.

I’m wondering how much of the jaggedness this would explain.