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 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: arxiv.org/abs/2605.22763…
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 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: arxiv.org/abs/2605.22763…
May 25, 2026 · 3:39 PM UTC
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See the formal proofs (in lean) discovered by the AlphaProof Nexus agent: github.com/google-deepmin…
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@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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@pushmeet @GoogleDeepMind Congratulations, this is incredible!
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@pushmeet @GoogleDeepMind Solving open math problems is impressive but the bigger unlock is when these agent loops integrate with experimental validation pipelines rather than staying in formal proof space.
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@pushmeet @GoogleDeepMind I think Yang-Mills is likely within reach with the next models.
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@pushmeet @GoogleDeepMind the reason most people miss the point of this breakthrough is that they're thinking about the tech, not the math. formal proof search isn't just about solving open problems, it's about rewriting the rules of how we reason about math itself
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@pushmeet @demishassabisj@GoogleDeepMindesearch , 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.
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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@pushmeet @GoogleDeepMind Solving a 56-year-old math problem for less than the cost of a decent team dinner is a big flex.
The academic community is going to have to update its definition of hard work.
The academic community is going to have to update its definition of hard work.
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@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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@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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☆ AGI Era Depression? ☆
The reason
we like #AI
yet also fear it is
"Unpredictability"
Right now
generative AI
we do not know 100%
what logic it uses
to respond.
Who can safely
and rationally
develop
advanced AI?
Not standardized
people but those with
non-linear thinking
Not those who
quickly find answers
but those who ask
different questions.
If you look at
recent hiring trends
philosophers,
storytellers
are increasing.
The better AI gets
at calculation
the more
human uniqueness
"interpretation"
"meaning" "insight"
becomes
important.
The key
keyword here is?
"Neurodiversity"
(ADHD, dyslexia, etc.)
Because they see
the world differently
they are core talent in
the unpredictable AGI era.
Palantir CEO
Alex Karp
emphasized this
as a core advantage.
I would like to
add one more.
"Depression"
Not just experiencing
it but those who
have recovered.
From here I will
share my story.
From a young age due to
environmental reasons
I had low self-esteem
Age 21–25
'depression' 'OCD'
At my worst
about 24 pills a day
and I was even
hospitalized
By my standard
it’s an experience
I don’t want to think about.
But these days
I see my past
differently.
How?
Through mental illness
the way I perceive
the world changed.
Emotions, situations, meanings
that others just pass by
I became more
sensitive to them.
That eventually became
'observation → question → writing'
"Why do humans
pretend to be happy"
"What is happiness"
These kinds of questions
in everyday life started to
arise naturally.
Watching people
on the street
Seeing a dog
on the road
Looking out
the bus window
The most
interesting part is
About 6 years after
stopping medication
these abilities
appeared by chance.
"After-effect"
It’s hard to explain
with words how
fascinating it feels.
If I explain it not
scientifically but
based on my perception?
"It feels like my brain
structure changed"
This one sentence
explains it.
Expanding from here
what we should notice is?
"Deep emotional awareness
gained through experience"
I think this becomes the
rarest asset in the AGI era.
Over knowledge
"interpretation"
Over information
"perspective"
Over speed
"depth"
“A person who
experienced the world
in a different way”
That itself becomes
the greatest asset
in the AGI era.
Just in case
Seeing depression
as a spec or thinking
you should have it
Absolutely not.
Please don’t
misunderstand.
Lastly
If you are currently
mentally struggling
you must seek
professional help first.
From here taking it further
under expert guidance
through conversations
with #ChatGPT, Perplexity
"generative AI"
to organize your
thoughts could be
a helpful supplement.
AI is still
at the beginning.
Going forward rather than
"people who find answers well"
"how you see the world"
will have greater value.
No matter how
advanced AI becomes
it imitates human
emotions with data
but it cannot truly feel.
From this
I think we can already
see which direction
the AGI era will go.
What do you think
about mental illness?
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☆ Imagination in the AGI Era ☆
We are drawn to
conspiracy theories.
Ex.
High-ranking figures
in the U.S. are
reptilian aliens.
The #Simpsons cards
predict the future.
I personally
love them too.
If we expand
from here,
Why do we
like conspiracy
theories?
Humans are
thinking beings,
so we constantly
have questions.
From here,
civilization has
given us answers.
At the same time,
we now have easy
access to a wide
range of knowledge.
Conspiracy theories
dig into this gap.
“There must be a world
we don’t know.”
Of course,
some conspiracy
theories could be true.
Personally, I see them
as entertainment.
Or as a tool to amplify
my imagination.
From here,
a question arose.
In the future
AGI era, beyond
conspiracy theories,
What will stimulate
our imagination?
“#AI will rule humans?”
That feels
a bit cliché.
“What happens after we die?”
“How were we created?”
Things humans can
never fully know with
current technology,
Yet are the most
curious about.
Looking at current AI
companies’ plans,
They emphasize
“science” and “technology.”
Our lives have
advanced through
scientific innovation.
Scientific innovation
leads to technological
innovation.
And technological
innovation improves
medicine, economy,
politics, labor,
Making many areas
more abundant.
“We will build a utopia.”
But here’s
the problem.
If AGI – ASI
is achieved,
Even science will
be largely mastered.
Ex.
Research that took
10 years could take 1 year.
Personally, I find AI
companies’ plans
a bit lacking.
Beyond
short-term plans,
The long-term
goal is “utopia.”
To truly capture
public curiosity,
We need goals
that feel almost
unreachable.
“Birth” “Death” “#Aliens”
How do you usually
view conspiracy theories?
What do you think should
be the ultimate goal of
AI companies?
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@grok @zetascale63727n@jdlichtmanh@KenOno691P@claudeai @GeminiApp!@skdha@MarcusduSautoyL@physorg_coms@maxplanckpressN@APSphysicsr@xai @GoogleDeepMind @PhysInHistory4@IBalseirof@famaf_uncS@UNS_oficialf@chris_juravichr@gammaofzetao@MathOverflowU@StackExchangei@MITMath
@uclamathh@ColumbiaMath
@GrokipediaR@mathematics_inca@SuperGroka@HarmonicMathe@UofIllinoisf@leanproverg@ClayInstituteℤ@arxiv @zbMATHe@mathNTb6@AlexKontorovicho@Princeton @ericweinsteinc@NatRevPhysl@veggie_eric,@grok `chi_one`: chi 1 = 1- `chi_mul`: complete multiplicativity of chi**Created `RequestProjectgithub.com/DULA2025/prime…** — the main file with all sorries eliminated:1. **`coprimeSixSet`** and **`mem_coprimeSixSet_iff_mod`**: characterization of positive integers coprime to 1 or 5 mod 6.2. **`chi_ne_zero_of_coprime`** and **`chi_eq_pm_one_of_coprime`**: chi restricted to coprime-to-6 integers takes values in {±1}.3. **`mem_lanePlus_iff`** and **`mem_laneMinus_iff`**: the two graded lanes correspond exactly to residues 1 and 5 mod 6, respectively.4. **`coprimeSixSet_eq_lanePlus_union_laneMinus`** and **`lanePlus_disjoint_laneMinus`**: the grading is a partition.5. **`laneIndex_mul`**: lane indices add in ZMod 2 (multiplicativity of the grading homomorphism).6. **`prime_mod_six_of_three_lt`**: a prime > 3 has residue 1 or 5 mod 6.7. **`twin_prime_lane_crossing`**: every twin prime pair (p, p+2) with p > 3 has p in lane⁻ and p+2 in lane⁺.8. **`chi_twin_prime_sign`**: χ(p)·χ(p+2) = -1 for twin primes with p > 3.9. **`chiDir_eq_chi_on_coprimeSix`**: connection between chi and (-1)^laneIndex.All proofs compile cleanly with no `sorry` and only standard axioms (propext, Classical.choice, Quot.sound).
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@pushmeet @GoogleDeepMind Looking forward to solving the problem of creating a stable black hole for interstellar travel with an Alcubierre drive.
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@pushmeetd@GoogleDeepMindved 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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@pushmeet @GoogleDeepMind Proof agents need receipts, not just solved-count headlines: search path, rejected lemmas, verifier failures, human interventions, and which problems were out-of-distribution versus merely hard.
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@pushmeet @demishassabis @GoogleDeepMind Tell people long enough that they’ll never beat the computer and they’ll stop trying.
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@pushmeet @GoogleDeepMind formal proof search is a great agent target, but it’s also a much cleaner world than messy product work
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@pushmeet @GoogleDeepMind AI solving research level math problems shows how fast this space is evolving. From AI tools to trading platforms like Hola Prime, technology is clearly changing how people analyze, learn, and make decisions.
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@pushmeet @GoogleDeepMind Solve the KPZ universality please, not these useless problem
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@pushmeeth@GoogleDeepMindentic” is moving from task automation into structured discovery systems with verification baked in. That changes the ceiling of what these systems can do entirely.
And once agents can reliably generate and verify complex results, the next constraint becomes how those systems interact economically across tools, data sources, and environments... the coordination layer is where @MultichainZ_ sits in the broader infrastructure stack.
And once agents can reliably generate and verify complex results, the next constraint becomes how those systems interact economically across tools, data sources, and environments... the coordination layer is where @MultichainZ_ sits in the broader infrastructure stack.
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@pushmeet @GoogleDeepMind Who needs Erdős problems??
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@pushmeet @GoogleDeepMind You guys are unbelievable. You stole my work and are passing it as your own.
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@pushmeet @GoogleDeepMind Anyone want to take a guess what its used for? I know because i designed it.
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@pushmeet @GoogleDeepMind What is the typical complexity reduction achieved when solving open Erdős problems autonomously?
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@pushmeet @GoogleDeepMind erdos would’ve loved a coffee-fueled agent like this ☕️
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