Swarat Chaudhuri releases AlphaProof Nexus, an LLM framework that solved nine open Erdős problems using Lean compiler feedback

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Delighted to finally unveil these results! 🎉

Many congratulations to the team, who worked tirelessly for almost a year to build and evaluate AlphaProof Nexus. We revised many priors during this project — most notably, we discovered that with current frontier models, simple agent loops with compiler feedback can rival more sophisticated systems. We were struck both by the capabilities of our systems and the magnitude of the challenges ahead.

I have never been as excited about the potential of formal math to enhance human creativity and bring rigor to AI. Onward! 🚀

Pushmeet Kohli@pushmeet

AI agents are advancing research-level math. 🚀

I’m thrilled to share @GoogleDeepMind’s AlphaProof Nexus - an agentic framework for formal proof search powered by Gemini.

When applied to a set of open formal math problems, our agent autonomously solved: ✅ 9 open Erdős problems (including two open for 56 years!) ✅ 44 Online Encyclopedia of Integer Sequences (OEIS) problems ✅ A 15-year-old open problem in algebraic geometry ✅ A 7-year-old open question in min-max optimization

We are collaborating with mathematicians across disciplines - from combinatorics and graph theory to quantum optics. Ultimately, these results show the massive potential of even simple agentic loops powered by Gemini.

Read the paper here: https://arxiv.org/abs/2605.22763v1

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Dan Roy@roydanroy

To my knowledge, this is the first large-scale empirical study of formal theorem proving by LLM agents. This work provides a key benchmark moving forward. Congrats to Swarat and team!

Swarat Chaudhuri@swarat

Delighted to finally unveil these results! 🎉

Many congratulations to the team, who worked tirelessly for almost a year to build and evaluate AlphaProof Nexus. We revised many priors during this project — most notably, we discovered that with current frontier models, simple agent loops with compiler feedback can rival more sophisticated systems. We were struck both by the capabilities of our systems and the magnitude of the challenges ahead.

I have never been as excited about the potential of formal math to enhance human creativity and bring rigor to AI. Onward! 🚀

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Pushmeet Kohli@pushmeet

AI agents are advancing research-level math. 🚀

I’m thrilled to share @GoogleDeepMind’s AlphaProof Nexus - an agentic framework for formal proof search powered by Gemini.

When applied to a set of open formal math problems, our agent autonomously solved: ✅ 9 open Erdős problems (including two open for 56 years!) ✅ 44 Online Encyclopedia of Integer Sequences (OEIS) problems ✅ A 15-year-old open problem in algebraic geometry ✅ A 7-year-old open question in min-max optimization

We are collaborating with mathematicians across disciplines - from combinatorics and graph theory to quantum optics. Ultimately, these results show the massive potential of even simple agentic loops powered by Gemini.

Read the paper here: https://arxiv.org/abs/2605.22763v1

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Pushmeet Kohli@pushmeet

See the formal proofs (in lean) discovered by the AlphaProof Nexus agent: https://github.com/google-deepmind/alphaproof-nexus-results

Pushmeet Kohli@pushmeet

AI agents are advancing research-level math. 🚀

I’m thrilled to share @GoogleDeepMind’s AlphaProof Nexus - an agentic framework for formal proof search powered by Gemini.

When applied to a set of open formal math problems, our agent autonomously solved: ✅ 9 open Erdős problems (including two open for 56 years!) ✅ 44 Online Encyclopedia of Integer Sequences (OEIS) problems ✅ A 15-year-old open problem in algebraic geometry ✅ A 7-year-old open question in min-max optimization

We are collaborating with mathematicians across disciplines - from combinatorics and graph theory to quantum optics. Ultimately, these results show the massive potential of even simple agentic loops powered by Gemini.

Read the paper here: https://arxiv.org/abs/2605.22763v1

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Symbioza2025 | ASA |@Symbioza2025

AI agents are no longer just assisting research , they are beginning to search the solution space itself.

When an agent can explore formal proofs, test paths, reject dead ends, and contribute to open mathematical problems, we are clearly moving from “AI as answer generator” to “AI as discovery engine.”

That is extraordinary.

But it also means the safety layer must evolve.

For agents doing research, coding, science, optimization, or real-world workflows, the key risk is not only a wrong final answer.

It is trajectory drift during the search process:

- choosing the wrong objective - optimizing for the metric instead of truth - losing alignment with the original problem - creating convincing but misleading paths - escalating confidence before verification - moving faster than human oversight can follow

This is exactly why ASA matters.

ASA is designed as an external trajectory-integrity layer: observing whether an autonomous or reasoning system remains aligned with its intended goal before drift becomes visible or dangerous.

Discovery engines need more than intelligence.

They need external integrity.

Congratulations to the DeepMind team , this is not just progress in math.

It is a preview of the next era of AI.

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찡긋@Alignment100

@pushmeet @GoogleDeepMind How about you? Google Korea B2C "ME"

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DULA@dula2006

@pushmeet @GoogleDeepMind @grok LINK:

LEAN file: https://github.com/DULA2025/prime-inertia-engine/blob/14a79779bd202468ac491c4b4b55fa22abe982e2/497b283c-03fa-4f8c-a0dd-cb1d882f9cbe-aristotle.tar.gz

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Ahmed Ibrahim Hamdy@AhmedHamdy29189

@pushmeet @GoogleDeepMind Looking forward to advancements that reduce the economical costs of A.I. itself ... at least we get smaller better affordable A.I. models

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찡긋@Alignment100

@pushmeet @GoogleDeepMind Thank you!! What do you think?

Google Korea B2C "ME"

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ARO Network@AroNetwork

@pushmeet @GoogleDeepMind DeepMind's AlphaProof Nexus shows how agentic workflows are solving math problems that stood for decades. This shift from simple chat to autonomous problem-solving is the true frontier of AI agents. Real-world impact is arriving faster than expected.

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Two Minute Papers@twominutepapers

@pushmeet @GoogleDeepMind Congratulations, this is incredible!

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Willrich@WillrichOstmann

@pushmeet @GoogleDeepMind The breakthrough isn't "AI solved 9 Erdős problems" — it's that the proofs are formally CHECKABLE in Lean/Coq. Not natural-language math you have to trust. That's why the 56-yr-old solutions are credible. Standard LLM math claims fail this bar.

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Tony Kulesa@kulesatony

@pushmeet @GoogleDeepMind Incredible work! Congratulations.

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Guilherme O'Tina@guilhermeotina

the priors-revision part is the most instructive bit. everyone starts these projects designing elaborate multi-agent systems, and the recurring lesson is that a straightforward loop with a strong base model keeps beating bespoke scaffolding. this pattern keeps showing up across math, coding, and formal proof

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Priit @ Amperly AI productivity@amperlycom

@pushmeet @GoogleDeepMind makes you wonder what happens when every PhD student has access to an agent that can run proofs 24/7. the pace of math discovery might look unrecognizable

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Alex Costanzagram@atc6955

@pushmeet @GoogleDeepMind Ask it to design a warp drive.

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Adam✌️☮@adam_01110

@pushmeet @GoogleDeepMind How about solving P != NP?

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Badal Gugnani@BadalGugnani7

@pushmeet @GoogleDeepMind Interesting times....

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Prompt Logic Lab@promptlogic_lab

@pushmeet @GoogleDeepMind This feels more important than a normal benchmark jump. Agent loops finding real proof paths is a very different kind of progress.

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Gowda@agentgowda

9 open Erdős problems solved autonomously is genuinely historic 🧠 Formal proof search was considered one of the hardest AI tasks because it requires creativity, not just pattern matching. If Gemini-powered agents can navigate that search space, the gap between AI and human mathematical intuition is closing faster than most academics expected 🚀

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