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South Africa
Joined October 2018
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great embodiment of chaos. retweeted
ALL THE HATE ON FAKER LMAOOO THESE RAGEBAITERS GOT ME BRUH THIS IS THE FIRST TIME FAKER IS THE PROTAGONIST HE WAS ALWAYS THE VILLAIN
HE DESERVED THIS TRIBUTE A LONG TIME AGO FK OFF TRUE DAMAGE "FANS" HATING ON THE ESPORTS AND LOL GOAT.. HE IS THE REASON TD EVEN EXISTS 🤬😠🤬😠💢
great embodiment of chaos. retweeted
I work in CRISPR discovery research. This is one of the most exaggerated nothing-burgers ever and would be laughed out of the room if a human scientist attempted to publish something like this. (cont.)
great embodiment of chaos. retweeted
T′ᵢⱼₖ = (∂xᵃ/∂x′ᵢ)(∂xᵇ/∂x′ⱼ)(∂xᶜ/∂x′ₖ) Tₐᵦ𝑐
Woldemar Voigt gave the objects their modern name in 1898 while studying the stresses that stretch a crystal; the same transformation law later let Einstein describe how matter stretches spacetime.
A cube of numbers becomes a tensor only when its components obey this exact product of partial derivatives under every change of coordinates. A scalar needs none of them; a vector needs one Jacobian factor; a matrix needs two.
Each extra index multiplies the transformation so that the entire array continues to describe the same geometric or physical quantity, independent of the axes chosen.
great embodiment of chaos. retweeted
Anita and I are doing a wedding themed subathon this month! Tune in starting 9/14 10:00AM pst for collab lobbies, special guests, giveaways and more!
great embodiment of chaos. retweeted
"A Mathematical Explanation of Transformers" is a recent paper that develops a rigorous mathematical framework for understanding the architecture behind Transformers and large language models.
It interprets the Transformer as a discretization of a continuous integro-differential equation, with self-attention represented as a non-local integral operator, layer normalization as a projection onto a constrained set, and feedforward layers and activation functions incorporated into the same mathematical framework, then uses operator splitting and numerical discretization to recover the standard Transformer architecture and extend the formulation to multi-head attention, Vision Transformers, and convolutional Transformers.
I've already shared several resources on the mathematics behind neural networks, Transformers, and LLMs, but there always seems to be something new and interesting to explore in this area.
arxiv.org/pdf/2510.03989
great embodiment of chaos. retweeted
Some thoughts on the Navier-Stokes news from a professor of aerospace engineering:
1) take a deep breath
2) posts indicating we "solved Navier-Stokes" are incorrect and overblown. A very specific mathematical proof involving a niche scenario for Navier-Stokes has *potentially* been shown (that a perfectly smooth incompressible initial condition with finite energy could produce a singularity--note the assumptions here piled on to an equation set that already involves some assumptions).
3) there is no general closed form solution for N-S and that's not what this news is about
4) this is more of a mathematical curiosity than anything else and could matter a lot to mathematicians but basically changes nothing in the way N-S are used in practice
5) there are already very useful exact solutions to Navier-Stokes that greatly simplify the equation set with the right boundary conditions/geometry like laminar flow through a pipe or a 2D Taylor-Green vortex
6) in aerospace, we already treat N-S as an approximation in many instances and are well aware of its limitations. we don't outright solve these equations anyway and regularly chop off terms or simplify parts (at the expense of accuracy) to make them easier to deal with.
7) to be honest I have never found this specific problem to be particularly interesting because we know a core assumption of N-S is a "continuum" fluid where you ignore molecules and assume hydrodynamic scales >>> molecular scales. We know a real fluid cannot have infinite velocity or energy. But clearly you can push equations outside of their bound of validity and make them produce funky results and singularities.
great embodiment of chaos. retweeted
I’m about to give a lecture to the Columbia Math Dept, but honestly I just wanna ask THE STUDENTS how they feel about AI frontrunning their life’s work & each other. 😂 Here’s what happened in plain English:
2 groups of mathematicians made a lifetime breakthrough one of the most famous problems that had gone unsolved for almost 100 years.
But they only solved a much easier version of the problem w/lots of AI assistance, & then a false rumor went around that Anthropic had solved the problem because one of the authors was working at Anthropic lmao.
So then OpenAI decided to frontrun them & spend $20 million of compute to solve the problem. 😏
And since it’s a famous problem there’s a $1M prize for it like the Nobel.
Then the OpenAI dude told the group leader you can share the prize with us & we’ll even let you claim first authorship but you need to drop the name of your Anthropic coauthor from the paper.
Then the group leader got mad because that’s super unethical & felt like they secretly used his ChatGPT data to figure out what he was working on to frontrun him. At least that’s the Anthropic perspective.
The problem is so hard that the original two authors would’ve gotten a top math prize & generational prestige for just solving the easier version.
But OpenAI just brute forced it while seemingly stealing their idea and being unethical and everything.
If not for the drama the scientific achievement would’ve been comparable to curing a form of cancer in their field‼️
But instead no one’s questioning that it got solved, & instead it devolved into this shitshow. 😌
Now a lot of mathematicians are saying the hardest problems that they spend a lifetime working on are gonna get solved in a year or two. 🙃
And some mathematicians are now saying it’s like doping and they should ban using AI on some types of problems to “maintain the challenge.”
We’re sharing a solution to the Navier-Stokes Millennium Prize Problem, one of the deepest problems at the frontier of mathematics.
The proof was produced by a group of agents, using an OpenAI next-generation model significantly more capable than GPT-6 Astra.
The problem concerns whether the description of smooth three-dimensional fluid motion modeled by the Navier-Stokes equations can break down. It has remained unresolved for roughly 90 years.
great embodiment of chaos. retweeted
I can't speak for them obviously but in academia it is almost always official policy to never put anything confidential or new into LLMs unless they are institutionally made because WE KNOW the corporations HAVE, CAN AND WILL steal intellectual property / confidential research.