love this introduction on density plots from @mdahardy, thorough and intuitive. it also shows the power of visualization to understand complex data
i’m bullish on formalization. so glad @axiomai is doing this. we owe it to math.
Today Axiom formalized the proofs of the celebrated Weil conjectures, foundational pillars of algebraic geometry.
This took us less than a day.
Had the Stacks project not been formalized with high code quality, this success would've not been possible.
What we hope to show is that Stacks is a reusable, foundational library.
With the underlying theory built the right way, formalization of acclaimed results naturally fell, just like "a land mass being silently swallowed by the rising sea."
This is just the first example of such paradigm shift. From machine-assisted *formal proving* of individual theorems, to autonomous swarms **library building** of entire theories.
We are witnessing Grothendieck's vision come to life in Lean.
a first-order logic thinker 🤝 a first-order logic programming language
beautifully written @erfan_mhi
"the act of creation". the complete opposite of larping (TIL that word)
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The third SOTA wife has entered the chat, and this one is fresh off his exit at Anthropic.
Sarah (Head of DevX at Cerebras, @MilksandMatcha) and Vivian (GP at Y Combinator, @vivianmshen) sit down with @trq212 right after his last day at Anthropic.
What was supposed to be a quiet start to his funemployment era turned into getting outed on Twitter, CEOs in his DMs, and a next-day debrief on the pod.
01:16 Meet the third member: leaving Anthropic
03:15 YC's COVID batch
05:17 Over-raising and shutting down Multiverse
08:58 Toronto, Bay Area high schools and raising kids
12:39 First impressions of SF and tech Twitter
18:32 Going viral with Claude Code content
20:26 Why Anthropic, and idolizing the labs
22:33 Can startups survive the labs?
29:53 Labs as Hogwarts houses, and friendly rivals
35:21 Honeypots, spies and the apocalypse
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rigor rigor rigor
We will all be learning in coming weeks & months, that most human-made software:
▫️ Was really slow
▫️ Had many security vulnerabilities
▫️ Was under-specified and incorrect
AI will rewrite it all. Many times. It will make it fast, cost-efficient, and secure. It will think about failure modes we couldn't wrap our heads around.
It will prove, formally verify, load test, harden. It will turn memory-unsafe foundations into robust, optimized ones. If you ask, it'll thoroughly document it, teach you about it, make diagrams, animations, and slide decks.
In many ways, we are witnessing the true birth of software engineering.
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can't wait for more AI-scaled formal verification
New on our Frontier Red Team blog: using Claude to formally verify software at large scale.
Formal verification can prove that code is free of certain bugs, but historically it has only been feasible for small codebases (or required a lot of expert time).
With AI models, however, this is beginning to change. In collaboration with @theoremlabs, we used Claude to prove security properties in over one hundred real-world open-source libraries over the span of a few weeks.
Read our research in full here: anthropic.com/research/forma…
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