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MIT FILMED THE PROFESSOR WHOSE STUDENTS WENT ON TO BUILD THE ALGORITHMS RUNNING INSIDE EVERY HOSPITAL, EVERY BANK, AND EVERY AI SYSTEM ON THE PLANET - AND THIS IS THE LECTURE THEY ALL SAY CHANGED HOW THEY THINK FOREVER
This is Denis Auroux, MIT 18.02 Multivariable Calculus, lecture 22. He opens with one claim - if you have a closed curve, you never have to compute the line integral along it. Compute a double integral over the region inside instead. Same answer. Completely different calculation.
He starts with the example. The line integral of ye to the minus x dx plus something involving x and e to the minus x dy, along a circle of radius one centered at 2, 0. Direct approach: parameterize, substitute, integrate from zero to 2pi. You immediately hit e to the minus x terms that make it unsolvable by hand.
Green's theorem: take the curl instead. N sub x minus M sub y. The e to the minus x terms cancel each other out. What remains is just x. The impossible line integral becomes the double integral of x over a unit disk.
Then the shortcut. The double integral of x over any region is the area times the x coordinate of the center of mass. The disk has area pi. Its center sits at x equals 2. Answer is 2pi. No parameterization. No substitution. Thirty seconds.
Then the proof. He cuts it into two steps. First prove it for a vertically simple region where y runs between two functions of x. The boundary has four pieces. Two vanish because dx equals zero. The remaining two combine into exactly the double integral of negative M sub y. Then glue regions together, add the y component, Green's theorem in full generality.
Watch the moment he shows a planimeter - a mechanical arm from the 1800s that measures area by tracing only the boundary. It never touches the inside. It computes a line integral and reads off the area from a dial. Green's theorem built into metal a century before anyone proved it rigorously.
A fluid dynamics engineer I know rewatched this before their first CFD project. Said it was the first time circulation felt like geometry rather than computation.
Free on YouTube, MIT OpenCourseWare, Creative Commons license.
bookmark this and watch later - after this lecture every closed curve you see will feel like a boundary hiding a double integral inside it
A Coronal flux rope erupts through the Sun's magnetic field.
The animation is driven by reduced resistive magnetohydrodynamics using coupled non-linear PDEs for plasma flow and magnetic flux. We use the Arakawa Jacobian, SSP-RK3 time integration, a spectral Poisson solver.
Machines learn by repeatedly stepping opposite the slope of their own errors.
The cost function averages the squared difference between prediction and truth. Its partial derivative with respect to each weight tells the direction of steepest ascent; subtracting a fraction of that derivative moves the model downhill.
In practice this rule trains everything from house-price predictors to the linear stages inside deep networks. The shortest path to better answers is often just the average gradient.
Booking Tony Robbins today costs $1 million for a single day. this is a 21-minute tape from inside his own house, filmed over 30 years ago, where he breaks down exactly how to get anyone to say yes. same $1 million material. completely free.
this is a rare, unfiltered tape from decades before this man started charging billionaires just to be in the room with him.
people give you two excuses when they say no, he says. not enough time. not enough money. neither is true. the real reason is they don't believe it's worth it yet, and that's not a money problem, that's a state problem.
so he teaches something he calls attack and confess. instead of arguing with the objection, you confess your own. "I had a chance to go to this thing six months ago and I didn't go until two months ago," he tells the room. "I can't even imagine the time I lost." the room goes quiet. nobody argues back.
he calls it getting someone on the yes train. every small yes you get compounds into the next one, until saying no to the final ask feels harder than saying yes. by the time he asks someone to sign, he says, they've already agreed to it five times over without realizing it.
21 minutes. that's all it takes to walk away knowing the exact two moves people pay $1 million a day to learn: how to read anyone's state, and how to move it. most people spend years in sales guessing at this. he wrote it down on a flip chart in his living room in under half an hour.
a seat in that room cost $125 back then. today it's a $1 million-a-day to sit in front of him.
The tape is free right now, and the answer is in this video.
The three-quark model of a proton may be elegant, but this simplicity comes with shortcomings. Physicists have known for decades that the proton is much more than three quarks. https://t.co/SU1SYg2rAh
3D artists are focusing on the wrong threat.
The scary part is not that AI can make a pretty render.
The scary part is that GPT + Intangible MCP can already turn a prompt into something that looks like a full cinematic 3D scene: architecture, environment, mood, lighting, reflections, camera movement, the whole thing.
That changes the conversation fast.
Because once AI starts operating the workflow instead of just spitting out a lucky image, “knowing the software” stops being the moat people thought it was.
The bottleneck shifts somewhere much more dangerous: taste.
And taste is a much smaller moat than most 3D people want to believe.
We implemented @karpathy 's microgpt from scratch in pure C.
Runs at:
> 6.9M tok/s on a Ryzen 5 5600H CPU
> 10.1M tok/s on an Apple M5 Pro
Optimized with hand-written AVX2 and NEON kernels, column-major weights that eliminate horizontal reductions, a precomputed (token, pos) prefix table and Schraudolph's fast exponential approximation.
https://t.co/d9sgqnp56k
I open-sourced the Sylva three.js site and the skills behind it.
I started with one reference and asked Opus 5 to recreate it in Three.js as a single HTML file (looped for 2 hours). The moss root is procedural geometry with around 130,000 instanced blades, and all the code is under 1 MB.
Live site: https://t.co/R1EGBqYDWT
Repo: https://t.co/lJwCp13tra
I turned the main interactions into three reusable skills:
- threejs-wireframe-scan-reveal
- threejs-pointer-orbit
- threejs-gpu-particle-spray
Skills repo: https://t.co/gMuw2gt9FJ
Depth-aware light injection in TypeGPU
I got a 448x448 monocular depth model down to ~8 ms on my M4 Pro across ~250 dispatches, which is fast enough to use in realtime :D
Since the inference is written directly in TypeGPU, I can just feed the depth buffer straight into the lighting pass. It never has to leave the GPU or go through any extra synchronization/interop step
Inference, lighting and draw all go through the same command encoder.
What if every time you looked at an equation, it could be intuitively color-coded and linked to clear explanations of what each part meant and the role it played within the physical process represented by the equation? Well, at least you can now on https://t.co/Ff4ChZ0eKT!
🚨ESTO ES UNA LOCURA
Un desarrollador chino acaba de lanzar una herramienta GRATUITA capaz de crear vídeos automáticamente para TikTok, Reels y YouTube Shorts.
Se llama MoneyPrinterTurbo.
Y ya ha superado las 100.000 estrellas en GitHub.
Así funciona:
1. Introduces un tema o una palabra clave
2. La IA genera el guion, la narración y los subtítulos
3. Busca el material visual, edita el vídeo y te entrega el resultado final
Todo ocurre en un único flujo de trabajo.
Guárdate esta herramienta.
Estoy seguro de que puedes sacarle muchísimo partido.
Enlace abajo👇
PSA: If you are tired of Claude-lish or Chat-lish, tell your AI to read the Google Developer Docs Style Guide and build a skill that follows it
It’s like magic. Suddenly your AI will make sense again!
I’ve tried both and this is much better than the ASD-STE100 Simplified Technical English skill
And friends at the labs: please invest more in AI comms skills!
A brilliant agentic AI that cannot speak English is dramatically less useful and undermines the utility of RLVR
https://t.co/xUbgHn0xpg
2d moments frozen in time. Turned into 3d holograms. Left exactly where they happened in the real world. The geospatial memory palace coming to life.
Excited baby deer startles mama deer momentarily, who then chills out after :) Can you imagine when your entire camera roll comes to life like this?
If you want to go deeper down this rabbit hole of reconstructing the world from your own captures and random internet photos - this deep dive (also on my yt channel) will get you grounded in this lineage of computer vision research https://t.co/Wqvg1VWCk3
Running Qwen 3.8 27B Q4 on a single RTX 4060 (8GB VRAM) gaming laptop shouldn’t be physically possible.
You can now run this 27B dense beast locally with a massive 64,000 token context window (minimum requirement by hermes agent) on budget consumer hardware, without crashing into OOM hell.
A model that bests claude opus 4.6 in several benchmarks, now runs on a $300 GPU!
after benchmarking it on rtx 4090 (24 GB VRAM) yesterday, today i tested on an Intel i7 12700H rig with an 8GB VRAM card and only 16GB dual channel DDR4 RAM, PCIe 4.
The breakthrough is using the new IQ4_XS quant by Unsloth (occupies just 14.6 GB on disk vs 16.7 GB for standard Q4_K_XL).
By tuning hybrid CPU/GPU offloading and quantized KV cache, we unlocked deep context with usable generation speeds.
Here are the numbers from a 4.5k real world prompt test:
- Context Window: 64,000 tokens (-c 64000)
- Prefill Speed: 150 tokens/sec
- Decode Speed: 5 tokens/sec (steady generation via native MTP)
The exact llama.cpp flags to run it right now:
.\llama-server -m Qwen3.8-27B-IQ4_XS.gguf -c 64000 --port 8080 -ngl 25 -ctk q4_0 -ctv q4_0 --threads 6 --threads-batch 8 --spec-type draft-mtp --spec-draft-n-max 2 --spec-draft-p-min 0.7
this occupies the vram completely.
Why this works:
1. `-ngl 25` offloads just enough layers to fill your 8GB VRAM without memory spillover.
2. `-ctk q4_0 -ctv q4_0` crushes the KV cache memory footprint.
3. Native MTP (`draft-mtp`) drafts candidate tokens ahead to keep CPU bound decode at a readable pace.
Complete stress test benchmark suite for this setup drops tomorrow.
Unsloths's Hugging Face GGUF link in the replies.
fire it up on your 8GB rig tonight. What budget GPU are you testing this on?