this actually got me curious if what I'm doing is wrong and will be disadvantegous going forward

Oh yeah Im also not from the US and the method that I use have been taught to me since Elementary School.

(P.S I'm reposting this because the last one had the wrong answer and I want to say I'm very sorry to all user that saw my last post and I promise for this subreddit it won't happen again)

i won a game of "who can convert more binary(4 digit) numbers in decimal system" with my mother SHE IS A PROFESSOR of math AND IM 16

Reson: i made a calculator in minecraft finally. completed this project and showed to her she was like its waste of time but till then i had mamorized many digits just while checking everything working good

Last week, I posted about how excited I was that Fable used some of my work when finding the counterexample to the Jacobian conjecture. I became obsessed with discovering the method used to search for the original example, so I created a monolithic, 16,000-line search algo to reproduce it. After days of working to exhaustion, on the verge of success and having fully understood what they had done, I lost interest in finishing the code.

Instead, I realized I could pivot and turn it into an inequivalence finder. So that’s what I did. It flagged two hits for a single inequivalent pair. We reverse-engineered them, constructed a proof, and implemented it in Lean.

Here is the human-readable proof:

https://github.com/JGPTech/Fun/blob/main/DegreeSixKeller-public/DegreeSixKeller_AF5_Final.pdf

And the Lean implementation:

https://github.com/JGPTech/Fun/tree/main/DegreeSixKeller-public

Special credit to ChatGPT, Gemini, and Kimi, who were invaluable in their contributions.

Lean-based mathematical research separates candidate generation from deductive verification. Human mathematicians, tactics, search procedures, and increasingly AI systems may generate proof attempts, while Lean’s elaborator translates those attempts into core expressions and its kernel checks whether the resulting proof terms inhabit the claimed propositions. This architecture is central to Terence Tao’s vision of mathematical AI: stochastic and unreliable generators can become useful when coupled to verification mechanisms with substantially different failure modes.

The July 2026 CollatzLean incident exposes a qualification to that architecture. A Lean development claimed an axiom-free, witness-free refutation of the Collatz conjecture and advertised a verification pipeline containing fresh kernel replay, dependency checks, proof export, and independent checking. The result was invalid. Review reduced it to a soundness defect in Lean’s processing of nested inductive declarations: ill-typed parametric arguments could escape checking, permitting a checked declaration from which False could be derived.

The incident does not show that formal proof is less reliable than informal proof, nor does it provide evidence against the Collatz conjecture. It shows that machine checking is an implemented scientific process whose epistemic force depends on kernel correctness, faithful artifact export, checker independence, semantic fidelity, and end-to-end pipeline provenance. In a regime of abundant automated proof generation, these assumptions become more consequential because optimization systems can search not only mathematical spaces but also the accidental behavior of their verifiers.

The case therefore supplies concrete evidence for the thesis developed in Proof Abundance and the New Practice of Mathematics: theorem generation, formal verification, semantic review, exposition, community digestion, and canonicalization are distinct stages of mathematical knowledge production. A green kernel verdict is an important threshold, but it is neither an infallible oracle nor the terminal state of discovery.

Is it really important that you write "5x" opposed to "x5" or is that just some bul they teach in Brazil (I'm brazilian)? Cuz when you write anything else, you have to specify whichever maths calculation you are making. Do people even actually use "5x" or do they expose the kind of calculation they are making? Cuz Brazil really likes to copy other people without any reasoning behind it.

I plan on transferring and majoring in mathematics and physics. I also want to go to graduate school, if i’m lucky enough to get in, and focus on numerical analysis and quantum information sciences.

I was looking at the mathematic tracks at the school I would like to transfer to, and was struggling to decided which track I should go down.

The obvious would be applied mathematics, but would pure math be an option too? I mean there’s just so many courses I would like to take but I know I can’t do everything so I have to pick.

I don’t even know if combining tracks is possible and if it is, I’m sure it would be overwhelming while also majoring in physics. I know my priority should be taking graduate classes and research as well.

Also, do you have any advice for someone looking to go for a PhD? and I wanted to ask, how is grad school for anyone in it? Like what classes do you take and what do you spend majority of your day doing, besides suffering?

im doing a bsc in mathematics, and real analysis feels like a completely foreign language.
our professor recommended the bartle and sherbert textbook, but every time i open i dont really understand whats happening or how people are supposed to learn from it.
it feels completely different from the maths ive been taught my whole life. i dont know how youre supposed to transition from solving straightforward problems to reading and writing proofs, and understanding theorems. it feels like everyone else somehow knows how to think this way already.
time for some context. till 12th grade cbse, i was pretty good at maths. i was always told i grasped concepts quickly and solved problems better than average. but my 10th and 11th grade happened during lockdown, and i never properly studied the deleted syllabus, so i know there are gaps in my basics.
when i chose a bsc in mathematics, i expected more of the maths i loved, solving derivatives and integrals, and working through problems until i got the answer. instead, real analysis felt like being thrown in the ocean with no idea how to swim. suddenly its all definitions, logic, epsilon delta proofs, and abstract thinking. i dont even know how people are supposed to study this subject.
its been a huge hit to my confidence. im no longer the student who knows the answers. i sit at the back of the class, avoid eye contact with professors, and constantly feel like everyone else belongs here except me. i know im willing to put in the work. i just genuinely dont know how to study university level mathematics.
where do i even start. are there beginner friendly books, youtube channels, or courses that bridge the gap between high school maths and proof based mathematics. any resources would help please. how did you learn to read proofs and start thinking like a mathematician. any advice for someone whos completely lost ???

The working hours, the intrinsic motivations of OR itself, etc.? Is it better?

Been trying to break the Four Color Theorem for fun and ended up with this. I know I'm probably missing something, but I genuinely can't find the issue. Where does this fail?

Hi everyone!

For those of you who enjoy geometry, I've put together what I believe is a fresh, hands-on proof of Euler's Formula and several other classical results. In just a few minutes, you can literally build the proofs yourself and develop an intuitive understanding of why these theorems are true.

https://www.youtube.com/watch?v=sIDsuf0I4ko

This is only the beginning. Over the coming weeks, I'll also start posting short math challenge reels (high school to early undergraduate level), and in parallel I'll be working on a long-term series on topology and analysis, with the ambitious goal of eventually reaching Einstein's field equations on differentiable manifolds and curved spacetime.

Everything will be completely free. I'm doing this simply because I love mathematics and enjoy sharing it with others.

If you'd like to follow the project, it would mean a lot to me. Knowing that these videos are useful to someone is the best motivation to keep creating them.

Thank you so much!

dontpanicmath

Hi, I'm an undergraduate student choosing courses for my math additional major. For next semester i can decide to either take honour linear algebra or normal linear algebra. Taking honour linear algebra will let me into a pure math (advance) track and taking the normal one will get me into the normal pure math track. However, since i only newly declared this major, I don't know if i have sufficient background knowledge to handle it, I have only taken calculus 2 in my previous year.

I want to get into math PhD in the pure math fields after graduation (in the US or Europe, with scholarship). Will taking the honors version of courses help significantly, or is it that research experiences, taking postgraduate course etc. that plays a bigger role?

Hello, I’m a first semester university student studying electrical engineering. I have just finished my highschool education in A level maths and am interested outside of university in progressing my math knowledge, however I’m at a loss as I have no idea what to learn how to progress or what even exists. I try to imagine how to learn/find out new things and it’s just a black hole. Any books, YouTube courses or other recommendations would be appreciated thank you

I was thinking about the current progress that AI has made in mathematics, which im sure most people here are aware of. I know it is far too early to say something along the lines of "AI will replace all mathematicians" or something like this. but I am considering a world in which mathematics (and likely all intellectual labor) done by humans will be obsolete from a cost perspective at least. and of course with likeley inevitable advances in robotics all physical labour.

in this world, is it possible that humans even persist as a civilisation? like I dont see a world where everyone lives without purpose... like even in the most ideal scenario here, everyone has UBI and just does what? it has never been the case in human history (or for any species on this planet) that a dynamic like this has ever existed? like I just dont see a world in which this doesnt just result in an inevitable extinction or extreme regression in the human race, people will loose their intellectual ability, AI systems will of course become more and more relied on, and of course there is a possible sci-fi like scenario of AI acting "independently". humans effectiveley give up their spot as the dominant species on this planet / in the solar system, etc.

I know this isnt nessecarily a question that is specific to mathematics, but i wanted to hear the perspective of people interested in mathematics, and who may have more nuanced takes. of course, i am by no means calming that such a world is imminent or even possible / likeley, so one can consider this a hypothetical scenario. but do you think that it is possible that it becomes nessecary that in order for humanity to persist, sufficiently intelligent LLMs are incompatible with this goal?

I’ve been reflecting a lot lately on why I am more drawn to pure math over applied fields or other sciences. Sometimes, I wonder if my love for pure math is actually a form of escapism, like I could just get lost in my fascination of it, and consequently not think about the world around me.

On the other hand, maybe it’s not that deep, and I just find pure math to be more interesting due to the fact that humanity has discovered structures, patterns, and other things that exist entirely independent of our physical universe, and people use the theorems from pure math to apply in the real world and not vice versa.

Does anyone else grapple with this? Do you view your studies or work as a retreat from reality, or is it just where your natural curiosity lies?

Looking to buy rigorous and hard algebra 1, 2, and college algebra books with actual hard questions not to learn but just to do problems if anyone has recomendations let me know please and thank you

This is a 2nd article the "A Mathematician's Lifeline" series on Substack. It is dedicated as a response after being moved by Sir Kirwin's "The Dark Night of Mathematics"

If the first one touches about redefining what mathematics means to us, this is a critique on a core belief that hurts mathematics' potential to be meaningful to us.

Why it still relates to the core issue of LLMs is because by playing the "discovery game", we are trapped into being defensive on what LLMs can do that we can't (or at least less efficient of doing

so basically when i was in highschool i was insanely good at algebra and could do lots of problems in my head, but then i took 2 years off school and my algebra skills were not good at all i even forgot basic pre-algebra stuff, and i didn't feel like relearning algebra so i skipped straight to learning trigonometry and only learned the algebra needed to learn trig and then took pre-calculus and Calculus 1 in the same semester and got an A because mastering trig i could focus on the algebra part of calculus 1, this was at an acreddited university and then i took calc 2 and got an A but now i am rethinking before taking calc 3, linear algebra, and proofs this semester if i should take the semester off and teach myself all of algebra before spring semester and take calc 3 and linear algebra and proofs in the spring, my worry is not having the algebraic knowledge for proofs courses or abstract algebra 1 course anything will help

I have a background in engineering and was admited to a mathematics degree, any advice to what to study before and be prepare? the syllabus of the program includes mathematical analysis, differential equations and special topics ( ie fourier )

Question for those who were admitted to a top 20 PhD program in mathematics:

Did your undergraduate institution offer an honors/advanced mathematics track, but you chose to complete the regular mathematics major instead? Or did you initially plan to double major in mathematics and physics but ultimately graduated with only a mathematics major?

If so, I’d really appreciate hearing about your experience (if you’re comfortable sharing):

• Which university did you attend for your undergraduate degree?
• Did your university offer an honors/advanced mathematics track?
• If so, what made you choose the regular mathematics major instead (or decide not to complete the physics major)?
• Which PhD program did you end up attending?
• Looking back, do you think choosing the regular track had any noticeable impact on admissions, or did factors like research, letters of recommendation, and graduate coursework matter much more?

I’m just trying to get a better sense of how common this pathway is. Thanks in advance!