7/22/2025

 nvm google deepmind also got gold on the imo. they should test these models on the ioi too 🤔

tori!

in diff geo we are learning about parametrized surfaces! this site says that a torus can be covered with one surface patch  and thought of like a rectangular piece of rubber stretched around...



but in our exercise we parametrize it like so and we need 4 patches to make sure we're working with open sets. i saw some other websites saying you need at least 2 patches?!? so idk. btw this 3d plotting calculator is great for visualizing things - https://c3d.libretexts.org/CalcPlot3D/index.html


there are also different types of tori


frenet-serre equations

these just seem a normal triplet of equations that form the orthonormal basis for the curve (called the frenet-serre frame), but they're incredibly useful for solving problems to investigate properties for curves.


t = tangent vector, n = normal vector, b = binormal vector

rubiks cubing

i've been trying to cube recently :) and i'm getting the beginner algorithms down now lol. thanks jane street for the cube! interesting that how such a simple cube can be so much fun to solve. there's a rubiks cube group (as with all symmetric things) and it actually can just be generated by just two (insanely complicated) elements -- see here for a discussion


having ai run a business

ppl at anthropic turned claude into a little ai business called claudius and they would NOT recommend it to control a business lol, it's too "righteous" such that it's unable to exploit valuable profiting deals. furthermore coincidence or not on april 1st, it had strange behavior all of a sudden and hallucinated a bunch. honestly this sounds like a really fun experiment though it wouldn't be fun if we found out AI can now make its own startups :skull: anyways interested in seeing what further advancements project vend makes!

the ai did a bad job handling finances

new geometry for physics

this is relevant since i'm studying diff geo rn! the condition for differentiability is troublesome when there are sharp anomalous things like black holes. these physicists wanted to calculate curvature without calculus for einstein's equations, so they borrowed the practice of looking at triangles drawn on the surface using a definition for distance in terms of time, helping prove singularity theorems (smth smth ricci curvature and optimal transport). "this program might one day help establish a mathematical foundation for a theory of quantum gravity" -- !!!

Comments

Post a Comment

Popular posts from this blog

no more ap exams ever!

i've officially closed out one chapter of my high school career - ap exams! which means now i have a lot of time on my hands to do things i'm interested in :) last week i read this article  except i didn't understand a lot of it. but topology is cool! and it's pretty sad if you write a whole book on something that is only a few months later proved to not exist a lot of cool quanta articles popped up in my newsletter so i hope i can read them all and update this. in terms of other tech-related news, i heard about alphaevolve, which has been causing a lot of stir on the internet recently! in a later post i hope to dive further into the developments of google deepmind which are very relevant to the intersection of math and cs. i also heard about vibe-coding, a term coined by andrej kaparthy. there are tools like cursor.ai that help with writing code; i hope i can test it out soon and show you the results. i feel like it is still important for us to not be so reliant on ai ...
Read more

happy may

 i guess i'm just a girl who loves half-baked things. go to maybe an about page i'll create with some more info about myself. here goes a low quality blog that hopefully doesn't reveal too much about myself while accomplishing what i want, mainly to share what i've learned and what hobbies i like i guess i hope i can write something out everyday, and this will be a good motivator for me to continue exploring what i love i just read this quanta article on how the physics principle of spin glass contributed to the idea of a hopfield network, which is a form of an rnn that has "associative memory." hopfield networks influenced the boltzmann machine and modern neural networks. their creators, geoffrey hinton and his colleagues, won the nobel prize in physics this year for their work in this area. this article  is a good refresher on some ai concepts.  this other article on the fusion of math and cs for proofs is especially interesting because that is sort of what...
Read more

may 25 2025

 5/25/2025 is a pretty date :) okay so i'm getting back into posting half-baked things i guess i discovered curius and was thinking of using that other than this but i'm better at conveying myself on a blog? perhaps i read this quanta article on superdiffusion  and it's super cool how mathematicians are able to formalize the chaoticness of things like rubber ducks floating in a river. i'll include the gif from the article here because it's very aesthetic :O soap bubbles!  also the article emphasized the methods  involved in proving the superdiffusion conjecture, mainly renormalization (which i don't really understand) and homogenization (which the mathematicians emphasize is more important that they showed these techniques are very useful).  quantum field theory in general is pretty interesting because it's like modern physics + math, and some high schoolers are doing research in the math part of it ;D which brings me to the next thing i read which was an ar...
Read more