Emile Silvis

Maths is now the best part of my day emilesilvis.com/maths-is-now-t…

@prasanna_says @raphaeltraviss @justinskycak MF I and II took be about 2 years I think.

@raphaeltraviss @emilesilvis @justinskycak how long did that take you?

Pro tip: you can point Deep Research at The Math Academy Way by @justinskycak to generate a learning system for nearly any skill domain. I'm using mine to learn traditional art (I'm following it and actual results shown)--put the time in and do the reps!

@davidbessis I'm actually listening to your book at the moment! Good stuff. Can you tell us a bit why you find this idiotic?

Am I the only one to find this story completely idiotic?

Any MA people on Bluesky?

My Mathematical Foundations III progress so far. It's slow going but satisfying as heck.

@ninja_maths I recall reading something about MA wanting to split MF III into two parts - do I recall correctly and is that still the plan?

@BRKBERG @TivadarDanka Maybe we have different definitions of “root”, but that doesn’t look like the root to me.

Exactly. Gradient descent sits at the root of the entire ML graph. SCT takes it one step further: every weight stays in truncated SVD factors (U diag(s) V^T). Exact gradients via standard backprop. QR retraction keeps U and V orthonormal after every step. Result: 172x memory reduction on 70B-class models. Full training step runs on Steam Deck CPU. Repo: github.com/EctoSpace/SCT

I built the full knowledge graph of machine learning, and it’s fucking awesome. Check where gradient descent is: (Graph is hierarchical. Lower nodes are fundamental, top nodes are advanced. Yellow edges lead to prerequisites, blue to concepts building on gradient descent.)

@3blue1brown Oh man, my favourite content creator makes a video about my favorite artist?!

This video was a complete joy to make. Here's a short preview, but next time you're looking to sit down for 45 minutes of math and art, take a look at the full version on YouTube.

@ninja_maths You guys are on fire 🔥

Link to the full course description below. mathacademy.com/courses/mathem…

I'm happy to announce that we've just released a major update to our Mathematics for Machine Learning course! Here’s a summary of what's new.👇

@Propriocetive 😅

@Propriocetive Hmm 🤔

I just published a 459-page book. Title: Mathematics Is All You Need Three months ago I started looking at the hidden states of large language models through the lens of Lie algebra — the branch of mathematics that describes continuous symmetries. What I found was not what I expected. Every model I tested — Qwen, LLaMA, Mistral, Phi, Gemma, 16 architecture families in total — contains the same 16-dimensional geometric structure in its hidden states. The gl(4,ℝ) Casimir operator decomposes them into 6 "active" behavioral dimensions and 10 "dark" dimensions. The dark dimensions are erased every single layer by normalization. The model rebuilds them every single layer from its weights. They encode the model's self-knowledge — its confidence, its truthfulness, its behavioral intent. And until now, nobody knew they were there. Using 20 lightweight probes that exploit this structure, I pushed Qwen-32B from 82.2% to 94.4% on ARC-Challenge. No fine-tuning. No prompt engineering. No chain of thought. Pure mathematics. The probes transfer across architectures without retraining. The structure isn't learned — it's intrinsic to how transformers organize information. I did this on a single NVIDIA RTX 3090 in my office. 190 patent applications filed. Proprioceptive AI, Inc. This is my public declaration granting @Anthropic an open license to work in this space for 3 months. They are currently the first and only company I've extended this to. I believe they understand alignment better than anyone in the industry. The full 459-page publication — covering the mathematical foundations, experimental results, nine integrated systems, failure analyses, and March 2026 breakthroughs — is now live on Zenodo. I welcome collaboration inquiries. Full publication: zenodo.org/records/190801… Logan Matthew Napolitano Founder, Proprioceptive AI, Inc. logan@proprioceptiveai.com proprioceptiveai.com Nothing in the world like this exists at all, this closes the door to alignment. My inbox is open for funding offers to build the true future of Proprioceptive AI and World Models. Not a theory but a full reproducible guide, existing products and a true mission on Alignment @grok @elonmusk @xai @AnthropicAI

@_kaitodev @karpathy I did the same thing for Europe: emilesilvis.com/job-market-tre… Same pattern: if you stare at screens all day, it's not looking great.

5 minutes ago, @karpathy just dropped karpathy/jobs! he scraped every job in the US economy (342 occupations from BLS), scored each one's AI exposure 0-10 using an LLM, and visualized it as a treemap. if your whole job happens on a screen you're cooked. average score across all jobs is 5.3/10. software devs: 8-9. roofers: 0-1. medical transcriptionists: 10/10 💀 karpathy.ai/jobs

@julianboolean_ Yeah that’s right! Courses are just (sometimes overlapping) bits of the single graph!

oooh this looks fun the cool thing is that under the hood courses are not a primitive in MA - it's all just a sea of individual topics in one giant directed graph - which reflects the fact that (esp in math) course boundaries are an illusion and all the knowledge is connected so an MA course (assuming you have developed all the necessary topics) is simply a curated playlist that picks out topics from the graph

@ninja_maths @_MathAcademy_ Amazing! Would MF I to III set me up for this?

I'm delighted to announce that @_MathAcademy_ has released two courses in Mathematical Methods for the Physical Sciences. Designed for students who want the mathematical tools needed for undergraduate-level study in physics, engineering, and other STEM fields. Details below👇

@Tim_Qian Oh it could be because feeds.pub is down :)

@Tim_Qian cool repo, but I see the RSS feed is broken. github.com/headllines/hac…

I got tired of memorising trigonometry by rote so I built an interactive unit circle — I think I get it now! emilesilvis.com/interactive-un…

@predict_addict I am immediately buying this.

My translation preserves the original mathematical structure while adapting language and examples for modern students. 214 sections. Whole numbers through proportional quantities. valeman.gumroad.com/l/arithmetic

Performing math vs knowing math. That's the difference between modern textbooks and one written in 1884. A.P. Kiselev was a Russian schoolteacher who got tired of watching students struggle with verbose, overcomplicated textbooks that taught procedures without understanding.

@bruce_v3 That’s exactly what AI Bruce would say…

Bots will get close, but not replace human connection.

Actually pretty excitied for this one @joshuastarmer!

@obsdmd CLI + @claudeai Code + $5 and I have an *organised vault*.