Jonathan Gorard

Updated my profile picture and (finally) got X Premium+ for… no particular reason. Expect nothing interesting to be coming from this account in the coming days and weeks.

@_AashishReddy @dwarkesh_sp @3blue1brown In the final stages now, but very soon I’ll actually have something to talk about, too…

@dwarkesh_sp @3blue1brown You should have @getjonwithit on

Always so much fun to chat with @3blue1brown AI has been making much faster progress in math than in other fields. As a result, mathematics is showing us, very concretely, what AI progress in other fields will look like. Even within mathematics, there's a jagged landscape. What does it look like? What is the nature of the most important conceptual breakthroughs in the history of mathematics, and how different are they from what AIs are currently able to do? Does AI (on net) increase or decrease human understanding of the field? How big is the overhang from having AIs systematically try to connect ideas already in the literature? And what advice does Grant have for aspiring mathematicians, coders, and other students who are passionate about fields that are being most transformed upon by AI? 0:00:00 – AI is discovering new proofs. Is that AGI? 0:11:32 – The verification loop on conceptual breakthroughs can be a century long 0:26:12 – Will we understand an AI proof of the Riemann hypothesis? 0:38:08 – Can AI find the hidden bridges between fields? 0:53:48 – Why real-world tasks don’t fit into RL environments 1:07:07 – Good writing requires theory of mind that AI still lacks 1:16:02 – Why learning will still depend on human curation Look up Dwarkesh Podcast on Spotify, Apple Podcasts, YouTube, etc.

@bznotes DM'd.

Every major foundation model company has a Physical AI effort ongoing. Will be very interesting to see what gets built by others to improve the stack, or on top of it. If you are working in this space, pls reach out. DMs are open! Or BZ at RedGlass dot vc.

@dearmadisonblue No. If a person is blind from birth and can’t experience visual qualia, that doesn’t diminish the first-person nature of their perspective on the world. Taken to its extreme, it’s easy to imagine a person who experiences *no* qualia, yet still maintains a first-person perspective

Sentience and consciousness are the same under these definitions. Well well well, not so easy to make a definition of these words huh?

@thePartyPartyUS Yes. I’m a panpsychist who believes that the relevant spectrum is one of communication/reporting and empathy (e.g. can a rock report to me what its first-person experience is like, in a manner that I can understand and empathize with?). Without that it’s pretty meaningless.

@getjonwithit You can shove a first person experience in anything. Are you a panpsychist then

Sentience (ability to experience subjective qualia) is not self-awareness (having a self-model that is distinct from one’s world-model) is not consciousness (existence of a first-person experience) is not intelligence (ability to perform complex computation) is not…

@jane_gatsby Good stuff

the one thing i wont shut up about is computational irreducibility

@corsaren Banger

Okay, I see how it is. So if you say that Claude has no feelings, all the AI folks will get upset. But if you criticize their CNC parties suddenly it’s all “a simulation of a thing is not the thing itself” 😒

@teortaxesTex Is there any place for Group C: people like me who think that AI is the most transformative technology of the last 1000 years, yet who consider the way that almost everyone (including Group A) uses it to be both aesthetically and philosophically repulsive?

In the last 12-18 months, a divergence has began among the global cognitive elite; both, I fear, have passed their respective point of no return. Group A can no longer be productive without AI. Group B has formed a stubborn reality bubble where AI doesn't work, and is ngmi.

@jessi_cata @maxhodak_ @cashewmake2 Potentially experimentally testable?

I am not a color qualia realist, but, I am rethinking my view that S_3 is the right symmetry group (for realists / for illusionists as fiction), as perhaps red could come from mixing supersaturated yellow and magenta. Thus O(2) would be the symmetry group (circular symmetry)

@wordgrammer The negations of any of these propositions would be *far* more weird, IMO.

If you think that LLMs are conscious you must accept a lot of weird conclusions. Like: - we can clone conscious experience - we can reverse time in conscious experience - we can pause and resume conscious experience - we can distribute conscious experience in space

@mathelirium This work is based on our existing DSL + theorem-prover work which axiomatized the IEEE-754 for floating-point arithmetic as an algebraic structure: arxiv.org/abs/2503.13877 All correctness theorems are proved up to machine precision.

@getjonwithit How do you plan to bridge the gap between the continuous math model and the discrete DSL without gettin stuck on floating point rounding and stanility issues

New project: a coding and formal verification agent for computational physics and applied mathematics. Auto-generate type-correct DSL code for equations and numerical schemes, autoformalize correctness properties in Lean/Isabelle/Rocq, then compile down to provably-correct C code

@IanSmith_HSA (1) The code-generation (e.g. variable name selection) is not performed by an LLM. An LLM is used only to convert the initial natural language prompt into a formal DSL specification. All else is deterministic. (2) There is no "training data" on formally-verified PDE solvers.

I don't believe in most "one shot examples" because it is likely pulling from GitHub or other sources. The "most likely answer" was already present in the training data. People are using LLM to "write code" but they are just paying per token for search results. Did you try searching for the variable names after the "one shot" test?

For reference, Lanyon can currently one-shot a provably-correct C implementation of a complex 3D nonlinear PDE solver (e.g. resistive MHD), and synthesize a ~10k-line Lean + Rocq proof of its mathematical and physical correctness, in ~3 minutes. And we're just getting started...

@justgrm It's not just the math that's (auto)verified: the algorithm + implementation is fully verified too, right the way down to the IEEE-754 axioms of floating-point arithmetic. The math verification is actually the easy part.

@getjonwithit what happens when it hits a bug that isnt in the math?

@PrazRama This project is essentially an extremely powerful agentic extension of arxiv.org/abs/2503.13877, which perhaps gives some insight into what formal verification means in the context of a numerical code.

@getjonwithit This might already be in one of your papers, but: I think the case for formal verification is clear wrt cryptography for example, or pure math. But I’m not sure I understand the case in physics. What does FV add in addition to the theory + experimentation loop?

@scheminglunatic Exactly. Racket DSL with a very lightweight custom theorem-prover for verifying numerical algorithms (based on arxiv.org/abs/2503.13877).

@scheminglunatic If you read some of my previous papers (of which this project is an extension), you'll see that I've also been a big advocate of developing fully bespoke theorem-provers for domain-specific software verification, in large part due to frustrations with formalizing IEEE-754 in Roq

@scheminglunatic No, you're not. I much prefer the type systems of Roq/Isabelle for software verification. This particular project contains a mix of pure math and software verification, though, and my current plan is to use Lean for the former and some combination of Roq/Isabelle for the latter.