# Hilbert's Second Dream: Making Science Itself Computable

> Why mechanizing scientific reasoning is the unfinished project behind a new kind of AI for the physical sciences.

[Watch on YouTube](https://www.youtube.com/watch?v=gSH50n-9ZLk)

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## Two Dreams, One Century Apart

At the turn of the twentieth century, the mathematician David Hilbert set out an agenda that would shape the next hundred years of thought. One strand of that agenda has become so woven into everyday life that we rarely notice it: the ambition to mechanize mathematical reasoning, to take the language of abstract thought and make it something a machine could manipulate without human intuition at every step.

That first dream was, in a real sense, achieved. Efforts to formalize logic and computation gave us the theory of what machines can calculate, and from that theory flowed computers, programming languages, and the proof assistants that let us check mathematical arguments mechanically. These are not footnotes to modern AI; they are its foundations. When a system can generate and verify code or chase down a proof, it is standing on the ground Hilbert's program cleared.

David Hilbert had a dream. Actually, he had two.

![The talk opens with a deceptively simple claim about Hilbert's two ambitions.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t005.jpg)
*[0:05] The talk opens with a deceptively simple claim about Hilbert's two ambitions.*

## The Dream That Was Never Finished

The second dream is less famous and, until recently, far less finished. Hilbert also wanted to mechanize scientific reasoning — the language not of abstract thought but of physical thought. Where mathematics asks what follows from axioms, science asks what the world is actually doing, and that is a harder thing to pin down in symbols.

This is why progress in AI has been lopsided. We have watched systems improve themselves recursively in mathematics and in software, domains where the rules are explicit and an answer can be checked against those rules. The physical sciences have not seen the same compounding gains. There was no formal language of physical reasoning for machines to reason in, and so no comparable engine of self-improvement.

> **KEY** — The central thesis: AI has raced ahead in math and code because those fields were already formalized. Science lagged because scientific reasoning itself had never been mechanized.

## What It Means to Verify a Piece of Physics

To close that gap, the people building this system argue, you first have to say precisely what it would even mean to formalize science. Most of us have an intuition for formalizing a theorem — rendering it in a logic a computer can check — or verifying software against a specification. But what does it mean to formalize a scientific model, or to verify a piece of physics? That question turns out to have three distinct layers.

![The team frames formalizing physics as a problem with several stacked layers of consistency.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t090.jpg)
*[1:30] The team frames formalizing physics as a problem with several stacked layers of consistency.*

The first layer is mathematical: is the model internally consistent, free of contradictions on its own terms? The second is theoretical: is the model consistent with the other things we already hold to be true about the world? A model can pass the first test and fail the second — it may be perfectly coherent yet quietly violate a principle we are confident about.

These demands are subtle because consistency is rarely all-or-nothing. A model might conserve energy in one regime and silently break it in another. It might respect thermodynamics at one scale and not at every scale. And a model that is theoretically flawless can still collapse the moment it is discretized for a numerical simulation, where the approximations introduced by a computer undo the very properties that made the physics sound.

The third layer is experimental, and it is the one that keeps science honest: does the model match physical reality as we can actually observe and measure it? A model can clear every internal and theoretical hurdle and still disagree with the instruments.

## Bridging Symbols and the World

Confronting the experimental layer forces a harder design problem than pure logic ever poses. To touch real experiments, a formal language cannot merely encode theories. It must also encode observations and measurements, and — crucially — the models of perception, analysis, and interpretation that sit between a raw instrument reading and a scientific claim. Data never arrives theory-free; how we measure already assumes something about what we are measuring.

![Whiteboard work linking mathematical, physical, and numerical notions of consistency.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t180.jpg)
*[3:00] Whiteboard work linking mathematical, physical, and numerical notions of consistency.*

The approach draws deliberately on two traditions that rarely meet. From twentieth-century philosophy of science it borrows the idea that our semantics and even our perceptions are 'theory-laden' — that observation is shaped by the theories we bring to it. From twenty-first-century scientific machine learning it borrows concrete tools, in particular neural networks that carry bounded error and can be composed algebraically, so that assembling pieces does not let uncertainty spiral out of control. The aim is to let these two ideas meet in the middle and bridge the gap between an AI's internal reasoning and the world it is reasoning about.

## Lanyon: Reasoning in a Formal Language

The product of this thinking is a model called Lanyon, and its headline claims are about efficiency as much as capability. On scientific modeling tasks the team reports that Lanyon runs more than 200 times faster and roughly 250 times cheaper than frontier large language models, while making fewer errors. Those are not marginal improvements; they describe a different operating regime.

![The founders position Lanyon against general-purpose frontier models on scientific work.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t150.jpg)
*[2:30] The founders position Lanyon against general-purpose frontier models on scientific work.*

The mechanism behind the numbers is the interesting part. Rather than having a language model reason in ordinary prose and hope the physics comes out right, the Lanyon agent reasons in an ultra-compact formal language of its own. From that representation, symbolic code generation and theorem-proving algorithms produce proofs and implementations deterministically and at the same time — so an answer arrives together with a machine-checkable argument that it is correct.

> **KEY** — Reasoning in a purpose-built formal language, then compiling to proofs and code deterministically, is what lets the system be both fast and trustworthy rather than trading one for the other.

## Why a Custom Language Changes the Economics

A domain-specific language buys more than speed. Because the agent expresses physics in a constrained formalism rather than free text, it cannot 'misformalize' in the way a general model might — it is far harder to accidentally write down a statement that doesn't mean what you intended. The same constraint sharply reduces hallucination, since the language will not express ill-formed claims in the first place.

The payoff compounds. Within this formalism the system can emit thousands of lines of verified code and proof per second, generating implementation and justification in lockstep. And once discovery and verification are both automatic, you can run reinforcement learning over models themselves — letting the system propose scientific models, theories, and algorithms and check them at machine speed, fully autonomously.

![The project is pitched as an infrastructure play as much as a single model.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t005.jpg)
*[0:02] The project is pitched as an infrastructure play as much as a single model.*

## Networks and Proof Assistants for Physical Reality

The same compositional formalism that keeps physics honest also doubles as a way to build neural networks. Because the pieces compose with provable error bounds, the team describes constructing feedforward networks, recurrent networks, and even transformers within the formalism in a mathematically principled way — architectures whose correctness properties are enforced rather than hoped for.

Around the core model sits a broader research ambition: a next generation of type systems built specifically for scientific modeling, and a next generation of proof assistants aimed not at pure mathematics but at physical reality. Delivering those means opening fresh research programs across applied mathematics, computational physics, and theoretical computer science at once — the project treats the science and the engineering as the same undertaking.

![Scientific computing work sits at the heart of the effort.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t060.jpg)
*[1:00] Scientific computing work sits at the heart of the effort.*

## Where This Is Headed

The intended destinations are deliberately demanding fields: energy, aerospace, and defense, alongside semiconductors, advanced manufacturing, and other industries where being wrong is expensive and verification genuinely matters. These are domains where a model that comes with a proof of its own correctness is not a luxury but a requirement.

Delivery runs through partnerships with universities, government agencies, and federal contractors — the institutions that already live at the intersection of hard science and high stakes. The framing throughout is less about a chatbot and more about infrastructure for doing science itself.

![The founding team presents the work as the opening move, not the finished product.](http://farzipedia.com/jobs/ios-1793600021372-6dc7e6/screenshots/t240.jpg)
*[4:00] The founding team presents the work as the opening move, not the finished product.*

The pitch closes on the ambition that organizes everything else: to finish the second of Hilbert's dreams and make scientific reasoning something machines can genuinely do.

If you're excited by our mission to make the universe computable, we want to hear from you.

## Key takeaways

- Hilbert imagined mechanizing both mathematical and scientific reasoning; the first was achieved and underpins modern computing, but the second was never completed.
- AI has compounded fastest in math and code precisely because those domains were already formalized and checkable, leaving the physical sciences behind.
- Formalizing physics requires three stacked kinds of consistency — internal/mathematical, theoretical, and experimental — and models can pass one while failing another.
- A faithful formal language for science must encode not just theories but observations, measurements, and the theory-laden processes of perception and interpretation.
- Lanyon reasons in a compact domain-specific formal language and compiles to proofs and implementations deterministically, claiming ~200x faster and ~250x cheaper performance than frontier LLMs on scientific tasks with lower error.
- Constraining reasoning to a formal language reduces misformalization and hallucination and enables verified code and proof generation, autonomous model discovery, and provably bounded neural architectures.


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