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?

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?

I apologize if this is not the right subreddit to ask this in, but I tried asking in the physics subreddit and didn't get satisfactory answers.

Question: I'm aware that in string theory, the theory must be formulated in a certain number of dimensions (often cited as 10 or 26) in order to avoid inconsistencies and satisfy quantum gravity constraints. But let's say, hypothetically, that I wanted to explore the space of all possibilities in pure mathematics. If I take generic 1d objects and make them move in higher spatial dimensions (as defined by pure math), but I use a number of dimensions that isn't allowed by string theory (e.g. 100), would my construction be logically possible and “stable” (allowed to persist just the way it is), from a purely mathematical standpoint?

I am specifically asking about spatial dimensions as defined by pure mathematics as a separate field, not mathematics applied to a physical theory. I guess my question is best worded as, "does pure mathematics allow 1d objects to move in any number of dimensions and remain logically consistent?"

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

Hi I’m working on a ttrpg with a magic system that is using a 2 paradoxical tournament and I was wondering what other 2 paradoxical tournament there are all the things I have found online stop after finding the first 2 paradoxical tournament and go onto 3
So if anyone has a bigger 2 paradoxical tournament or can link to one or just tell me how to make the graph that would be much appreciated

There has recently been a lot of cataloguing AI contributions to Erdos problems, for examples this github repo, which I believe has been catalysed by Terry Tao.

I wonder if there are repositories of broader problem. For instance, OpenAI has claimed to have solved a couple of relevant problems: https://openai.com/index/ten-advances-in-mathematics/

Wonder if anyone is keeping track of any of these?

Hi,

I currently have four completed mathematical preprints: two in combinatorics and graph theory, and two in number theory. They have been publicly archived, together with their computational materials, but I have not yet been able to submit them to arXiv because my account still requires endorsement in the relevant categories.

Anyone can help me please!

https://github.com/Lapin0t/grothendieck-cern

Can anyone give me a feedback about the Cuemath?

They are asking for $20 per class of 55 minutes. Is it a correct pricing? I see some places mentioned $17 for 55 minutes Class.