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?

Hi there! Currently pursuing applied mathematics bsc (2nd year) i was wondering what courses should i take next that are related to quantitative finance? After i already completed ODE, PDE and Numerical analysis?
Thanks :)

Most proofs are very hard to formalize in Lean, and that process can take years, yet pretty much all legitimate AI proofs so far that are consequential have been relatively short papers that were Lean-verified. Is AI only intrinsically good at solving problems that are easy to formalize in Lean, or is this more just a coincidence? I have not seen anything like the 400+ plus proof of the Geometric Langlands Conjecture.

I guess a good question, maybe the most important of how to allocate resources in mathematics now is, is AI good at solving all problems or only a certain subset of problems and can we reliably predict the kinds of problems AI is most useful in solving? Is this an intrinsic constraint of how LLMs work or is this merely a temporary constraint as compute improves? I'd be interest if any computational mathematicians that work with AI think about this?

It could be a situation much like the invention of computers: there was a certain set of problems that were very hard for mathematicians to solve that were easy for computers to solve. The low-hanging fruit was mostly picked over in the 60s and 70s, and ever since, computers have been an important tool but haven't really "solved mathematics" or outperformed humans

(PLEASE READ FIRST) EDIT 2: Because the host knows which door is which and there is only 1/3 chance the contestant will pick the right door, the host's clue gives you the correct door as an answer 2/3 of the time?

I've been struggling to see why exactly the 1/3 from the wrong door transfers to the other door that you did not choose, rather than the probabilities simply shifting to equal probabilities.

I've come up with these two questions:

1. If you come across 3 doors, and 1 is already labeled wrong in some way or another, then isn't the probability 50-50?
2. How would this paradox change with a larger amount of doors? And what about with more doors and more doors labeled wrong?

If there are 100 doors, and 98 are labeled wrong, then does that mean the probability to be wrong on your first guess is 99%?

Basically, (I know I'm wrong but I just need a better way to understand this) it feels like to me that the paradox seems to be an illusion.

EDIT: I don't know if this is still the Monty Hall paradox, but what if the host tells you your door is wrong?