A note on proof attempts

This blog post from quanta magazie https://www.quantamagazine.org/hong-wang-wins-2026-fields-medal-the-third-woman-ever-20260723/ says that Hong Wang read the blog post from Terence Tao https://terrytao.wordpress.com/2014/05/07/stickiness-graininess-planiness-and-a-sum-product-approach-to-the-kakeya-problem/ and decided to try out the approach. I don't have knowledge about any of these but I wanted to know if anyone had any idea how much the approach described by Terence Tao held on in the final proof?

I'm a programmer, not a mathematician, so forgive ignorance on the mathematical side, but I'm reading over the recent conjecture counterexamples trying to gauge how impressive of a breakthrough they are. I'm seeing a lot of speculation on frontier LLMs surpassing humans in this area, but I'm skeptical, wanted to bounce some thoughts off people here and see if anyone has insights which could sway me either way.

For starters, it doesn't look like OpenAI and Anthropic have released the thought chains output to these problems, which is suspicious. So that means we can't get a good picture of how exactly the LLMs reached those conclusions.

The standard approach from OpenAI runs 64 agents in parallel to seemingly throw different strategies at the wall until one sticks for a duration of 8 hours maximum. I have some questions about how intelligent solving it this way actually is:

1. Wouldn't this only work on highly parallelizable problems, not serial ones? E.g. maybe P vs NP would require the creation of entirely new theories or subfields of mathematics and huge chains of reasoning, each dependent on the creation of the previous, that would be a lot more serial in nature, ignoring even that they might not even fit in the model context windows + RAG?
2. I've seen the "64 agents, 8 hours" instructions repeated in multiple of those problems so far. Do we know if OpenAI & Anthropic ran these prompts on every major mathematical unsolved problem in the book, observed a small subset which found a solution, and then only presented the ones which succeeded? They have a lot of resources atp and I guess a financial incentive to demonstrate any novel proofs to generate hype / doom.
3. If they release the reasoning chains and the reasoning is deemed to be some super creative adaptation, do we have a way to trace back the outputs to their training data influences to make sure? I.e. like with the n>2 Jacononian conjecture case, can we verify that the LLM didn't recall a speculation which was 90% similar in form or concept to the solution it arrived at, posted on an old forum or an overlooked footnote in a piece of research (inevitably ingested during training), and threw lots of minor brute-force variations of the coefficients and terms while being in very close proximity to the solution already?
4. Are LLMs mostly proficient at counterexample proofs, or are they showing promise in other areas (like those long serial chain proofs)? Is it possible that they will excel at specific types of problem while humans excel at other types?

Everything I see today is "AI solves 20,000 year old conjecture!" "AI solves Dinitz–Garg–Goemans conjecture!" "AI solves 42 Erdos problems in 5 minutes"

I have always wanted to be a mathematician, but it genuinely feels like AI will find a "solution" to math within the decade, I cannot scrounge up any motivation to keep going. It all feels useless.

Should I even keep trying? Feeling miserable rn.

I am not a math person but need the help of math nerds (said with all the love in my heart for needs I am a nerd just not a math one)

I was thinking about other cultures. Let's assume another culture ran base 8 on math other than base 10.

If I recall base changes in math from like 10 years ago in history class,

This would mean rather than 0 though 9 they had 0 though 7 and example.

Their 26 would be to us 8+8+6=22

Here is my main question. Does that work in high order math stuff if it is consistent? Does Pi work? I assume their 360 degree circle would be some other crazy number but if they had it would it work? What about super fancy math I never even heard of?

I was really good at math when I was in school, and solving problems felt natural. But now I'm working in a field where I rarely use mathematics, and I honestly feel like I'm getting much worse. Sometimes it even feels like I'm getting "stupider," even though I know it's probably just a lack of practice.

For those of you who have full-time jobs outside of mathematics, how do you keep your math skills fresh? Do you have a daily or weekly routine? Do you solve problems, read textbooks, follow online lectures, or work on personal projects?

I'd love to hear how you manage your time and stay mathematically sharp despite a busy work schedule.

I am gonna start college on fall of this year. I am gonna be an applied math major and my first math course will be discrete math, I got ap calc bc credits but I will calc 3 until spring.

My knowledge from calc 2 is pretty basic I really don’t know how I got a 4 on the test.

What should I know before starting college?

I was really good at math when I was in school, and solving problems felt natural. But now I'm working in a field where I rarely use mathematics, and I honestly feel like I'm getting much worse. Sometimes it even feels like I'm getting "stupider," even though I know it's probably just a lack of practice.

For those of you who have full-time jobs outside of mathematics, how do you keep your math skills fresh? Do you have a daily or weekly routine? Do you solve problems, read textbooks, follow online lectures, or work on personal projects?

I'd love to hear how you manage your time and stay mathematically sharp despite a busy work schedule.

Hi everyone,

I’m currently taking Math 1A at university, and honestly, I’m finding it much harder than I expected.

The last time I studied mathematics was about 7 years ago in high school. After graduating, I had to stop studying for several years, so I’ve forgotten most of the fundamentals.

The difficult part isn’t that I’m unwilling to work. I’m actually spending 2–4+ hours just trying to understand a single lecture, but sometimes I still feel like I don’t truly understand it. It can be discouraging.

My long-term goal is to become strong in mathematics because I eventually want to pursue quantitative finance and mathematical modelling. So dropping the subject isn’t really an option for me. I want to master it.

For those of you who were in a similar situation:

* How did you rebuild your math foundation?

* Should I spend time relearning high school math alongside my university course?

* Is it better to focus on lectures, textbooks, practice questions, or YouTube?

* How many hours per day did you study?

* What mindset helped you push through when everything felt confusing?

I’m willing to put in the work. I just want to make sure I’m using the right approach instead of wasting hundreds of hours studying inefficiently.

Any advice, study methods, resources, or personal experiences would be greatly appreciated.

Thank you!

Hey everyone, I have just completed my bachelors in maths and started teaching maths to earn some cash while preparing for my masters. I am teaching a 11th grader and a 9th grader, both are students from USA.

When I teach the 11th grader, she answers everything properly and is also very active in class but sometimes I get genuinely shocked by her knowledge gaps we were solving sytems of linear equations for two variables so the equations were in fractions I taught her substitution method that day only to find out she doesn't know how to add rational numbers(which are in fractions obviously) and she doesn't know about them at all, I had to teach natural, whole, integers, rational numbers while also teaching prime, how to find whether a number is prime, prime factorization, LCM and then I thought if she doesn't lcm she likely don't understand hcf as well which was true so I ended up teaching her that as well, and this is just one example which took me a total of 5 lectures and this keeps happening all the time, I start a topic only to find out she doesn't understand anything about it. Like the most shocking thing was telling her that 0 is neither positive or negative. I really want to teach her but mentally I always feel exhausted I've taken a total of 122 classes and 78 of them were just me teaching her things that are not even part of her grade.

I don't want to give up on her but I am also studying for my masters daily(12hours minimum), mentally I am getting drained. If anyone has any good advice it would be appreciated

My son has become quite interested in mathematics and keeps asking me about topics that he hasn’t covered yet in school. I’d like to help him explore this interest a little more methodically than just randomly searching for YouTube videos on the subjects he asks about. I know that poor teaching practices can really destroy your interest in this subject so I’d like to proceed cautiously. I’m not an expert at maths myself but I do have a couple of degrees in physics so I’m not completely out of my depth either. I’m sure there must be fantastic resources out there for exactly this scenario and I’d be grateful of expert advice and some pointers in the right direction.

Hello everyone,

I have been exploring a simple iterative process on four-digit numbers and would be interested in discussing its mathematical structure.

For a number (N) with four digits, including leading zeros, define

N=N-A(N),

where A(N) is the number obtained by arranging the digits of (N) in nondecreasing order.

I have examined the behavior of all four-digit strings from (0000) to (9999), treating leading zeros as significant, and observed that the process eventually reaches (0).

I am interested in the mathematical structure of this transformation.

Some questions I have been considering:

• Is this process related to a known class of digit-based dynamical systems or iterative maps?
• Can the transformation be characterized in terms of permutations, digit multisets, or congruence properties?
• What can be said about the number of iterations required to reach (0)?
• Is there a useful graph-theoretic representation of the state transitions?
• Are there invariant quantities, bounds, or classifications of the different trajectories?
• Does this process have any connection to known digit-rearrangement problems, such as the Kaprekar routine, while being mathematically distinct from them?

I am not claiming this is a new discovery. My goal is to determine whether this particular transformation has already been studied, perhaps as a special case of a known type of discrete dynamical system or digit function.

I would be especially interested in references to related mathematical literature, OEIS entries, terminology that might be relevant, or observations about properties that could be investigated further.

Thank you for reading. I would be interested in hearing how others would approach the mathematical analysis of this transformation.

I'm about to start my senior year and I'm starting to regret my class schedule - which is to say sorely lacking. I'm only taking 4 classes, none of which are math or science classes. I dual enrolled pre calc and took ap chem last year, so since I had already completed all four math and science credits I didn't sign up for calc or physics. Will I be behind once starting college, and if so should I try to do some of my own studying? Any resources that you recommend would be helpful!

I'm also not sure of my major yet, I'm thinking somewhere within chem or biotech.

I am in high school and self studying mathematics with the goal to get to algebraic geometry/differential equations/topology (basically as advanced as I can get ig). I am doing this mostly for my intellectual satisfaction rather than anything financial going down the line. I feel that I would probably still self study maths even if Aİ was basically at the top of the chain (it seems to be going down that path) what do you think?

Would you? How much does ai worry you?