1h ago

OpenAI Model Disproves Erdős Unit Distance Conjecture

5
Original post

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

12:04 PM · May 20, 2026 View on X
Reposted by

An OpenAI model has achieved a major breakthrough in mathematics, by disproving a central conjecture in discrete geometry that was first posed by Paul Erdős in 1946.

This is the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:32 PM · May 20, 2026 · 112.8K Views

Today, we’re sharing that a general-purpose internal @openai model achieved a breakthrough on one of the best-known combinatorial geometry problems. Less than 1 year ago frontier AI models were at IMO gold-level performance. I expect this pace of progress to continue.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:14 PM · May 20, 2026 · 53.8K Views

This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves.

Noam BrownNoam Brown@polynoamial

Today, we’re sharing that a general-purpose internal @openai model achieved a breakthrough on one of the best-known combinatorial geometry problems. Less than 1 year ago frontier AI models were at IMO gold-level performance. I expect this pace of progress to continue.

7:14 PM · May 20, 2026 · 53.8K Views
7:18 PM · May 20, 2026 · 16.2K Views

Today, we’re sharing that a general-purpose internal @openai model achieved a breakthrough on one of the best-known combinatorial geometry problems. Less than 1 year ago frontier AI models were at IMO gold-level performance. I expect this pace of progress to continue.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:11 PM · May 20, 2026 · 24.7K Views

Excellent thread from mathematician Tim Gowers on the significance of the @OpenAI model’s breakthrough on the Erdos Unit Distance Problem!

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

If you are a mathematician, then you may want to make sure you are sitting down before reading further.

7:04 PM · May 20, 2026 · 194K Views
7:21 PM · May 20, 2026 · 3.7K Views

@BorisMPower Congrats to the result, still disagreeing with the sentiment.

Boris PowerBoris Power@BorisMPower

A general purpose model made this breakthrough at the heart of geometry. Exciting time ahead and probably no need for specialized models here!

7:42 PM · May 20, 2026 · 9K Views
8:39 PM · May 20, 2026 · 56 Views

Whatever the definition of "superhuman AI mathematician" is, I think my original prediction of June 2026 is not too far off the mark.

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:04 PM · May 20, 2026 · 87K Views
7:50 PM · May 20, 2026 · 10K Views

@tunguz I am getting less and less confident about predicting. I think we have just entered the prediction event horizon where all bets are off.

Bojan TunguzBojan Tunguz@tunguz

@ChrSzegedy Yup, I think you nailed that prediction. What are some of your other predictions?

8:34 PM · May 20, 2026 · 113 Views
8:37 PM · May 20, 2026 · 87 Views

Once AI starts making solving open problems in novel ways it won’t stop.

We are entering the final stage of human solutions to open problems like this.

Feels weird, doesn’t it?

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:28 PM · May 20, 2026 · 8.2K Views

June 2024: The latest general-purpose LLMs could not count the r's in strawberry. July 2025: The latest general-purpose LLMs get gold in the International Math Olympiad. May 2026: The latest general-purpose LLM solve one of the "best-known questions in combinatorial geometry"

8:04 PM · May 20, 2026 · 9.5K Views

More on the solution: https://openai.com/index/model-disproves-discrete-geometry-conjecture/

Ethan MollickEthan Mollick@emollick

June 2024: The latest general-purpose LLMs could not count the r's in strawberry. July 2025: The latest general-purpose LLMs get gold in the International Math Olympiad. May 2026: The latest general-purpose LLM solve one of the "best-known questions in combinatorial geometry"

8:04 PM · May 20, 2026 · 9.5K Views
8:09 PM · May 20, 2026 · 3.7K Views

The frontier is still jagged though (here is Gemini 3.5 Flash messing up counting letters in words)

8:20 PM · May 20, 2026 · 3.2K Views

Its The Graph again (not the METR graph, the one from the o1 launch).

Although no logarithmic decay of ability with increasing compute...

Noam BrownNoam Brown@polynoamial

This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves.

7:18 PM · May 20, 2026 · 16.2K Views
8:30 PM · May 20, 2026 · 3.6K Views

Very striking, as is the linked post:

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:04 PM · May 20, 2026 · 87K Views
7:38 PM · May 20, 2026 · 4.5K Views

Let's break this down, step by step [...]

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:25 PM · May 20, 2026 · 9.2K Views

it’s kind of fucking ridiculous (and quite frightening) we‘re this far — the models are solving long standing problems in discrete geometry — yet the models do this still by thinking to themselves in plain english? that is easily interpretable? what the hell man

will depuewill depue@willdepue

what a moment. wow. a bit in shock

8:16 PM · May 20, 2026 · 12K Views
8:22 PM · May 20, 2026 · 3.3K Views

what a moment. wow. a bit in shock

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
8:16 PM · May 20, 2026 · 12K Views

i’m so curious who on seb’s team just YOLOed planer unit distance into the latest checkpoint one night. doesn’t seem like anyone actually expected the model to solve it

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
8:30 PM · May 20, 2026 · 3.9K Views

AIs are gaining momentum, and "human level" is an inexistent milestone.

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:04 PM · May 20, 2026 · 87K Views
8:03 PM · May 20, 2026 · 3.7K Views

So it took 20 months to go from making these plots on AIME problems to making them on 80 year old conjectures in combinatorial geometry…

7:59 PM · May 20, 2026 · 3K Views

A general purpose model made this breakthrough at the heart of geometry.

Exciting time ahead and probably no need for specialized models here!

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:42 PM · May 20, 2026 · 9K Views

A monumental achievement for AI. The wall falls first brick by brick, and then all of a sudden

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:04 PM · May 20, 2026 · 87K Views
8:49 PM · May 20, 2026 · 23 Views

1/ Ten months ago, I was ecstatic that AI could win IMO gold.

Today, that excitement feels quaint: an internal @OpenAI model has refuted Erdos’s unit distance conjecture—a research result that one could recommend “acceptance without any hesitation” to the Annals of Mathematics.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:33 PM · May 20, 2026 · 46.6K Views

2/ Why does this matter?

First, that we are here less than a year after IMO gold is a surprise to me. As bullish as I’ve been on AI math, I thought it would have taken longer to go from the 1.5 hour horizon of IMO proofs to the hundreds of hours needed for breakthrough research.

Alexander WeiAlexander Wei@alexwei_

1/ Ten months ago, I was ecstatic that AI could win IMO gold. Today, that excitement feels quaint: an internal @OpenAI model has refuted Erdos’s unit distance conjecture—a research result that one could recommend “acceptance without any hesitation” to the Annals of Mathematics.

7:33 PM · May 20, 2026 · 46.6K Views
7:33 PM · May 20, 2026 · 2.1K Views

3/ In hindsight, it's not crazy that AI can shortcut these time horizons significantly: LLMs have superhuman knowledge bases and are primed to make insights that span research communities e.g. applying modern class field theory to discrete geometry in our case. Progress is fast!

Alexander WeiAlexander Wei@alexwei_

2/ Why does this matter? First, that we are here less than a year after IMO gold is a surprise to me. As bullish as I’ve been on AI math, I thought it would have taken longer to go from the 1.5 hour horizon of IMO proofs to the hundreds of hours needed for breakthrough research.

7:33 PM · May 20, 2026 · 2.1K Views
7:33 PM · May 20, 2026 · 1.8K Views

5/5 This of course hits close to home: I’ve certainly seen my own research workflow transform over the past ~6 months.

For further commentary and contextualization on the math, check out the companion paper by the experts: https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-remarks.pdf

Alexander WeiAlexander Wei@alexwei_

4/ Second, math is a leading indicator of what is to come. Soon—perhaps sooner than we all think—AI will begin autonomously producing landmark results in CS, physics, econ, bio, … We should be prepared for a new world where the nature and methods of science will have changed.

7:33 PM · May 20, 2026 · 3.2K Views
7:33 PM · May 20, 2026 · 1.7K Views

4/ Second, math is a leading indicator of what is to come. Soon—perhaps sooner than we all think—AI will begin autonomously producing landmark results in CS, physics, econ, bio, … We should be prepared for a new world where the nature and methods of science will have changed.

Alexander WeiAlexander Wei@alexwei_

3/ In hindsight, it's not crazy that AI can shortcut these time horizons significantly: LLMs have superhuman knowledge bases and are primed to make insights that span research communities e.g. applying modern class field theory to discrete geometry in our case. Progress is fast!

7:33 PM · May 20, 2026 · 1.8K Views
7:33 PM · May 20, 2026 · 3.2K Views

Smile: a renaissance is upon us.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:43 PM · May 20, 2026 · 5.6K Views

Frog should apologize to caterpillars

Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

AI has now solved a major open problem -- one of the best known Erdos problems called the unit distance problem, one of Erdos's favourite questions and one that many mathematicians had tried. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:04 PM · May 20, 2026 · 87K Views
8:09 PM · May 20, 2026 · 1.3K Views

From the post. 'The proof came from a new general-purpose reasoning model' 'An internal OpenAI model' And what might the name of this model be?

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:16 PM · May 20, 2026 · 10.2K Views

Proof PDF: https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf

Andrew CurranAndrew Curran@AndrewCurran_

From the post. 'The proof came from a new general-purpose reasoning model' 'An internal OpenAI model' And what might the name of this model be?

7:16 PM · May 20, 2026 · 10.2K Views
7:19 PM · May 20, 2026 · 1.5K Views

'This result marks an important moment in the interaction between AI and mathematics: an AI system has autonomously resolved a longstanding open problem at the center of an active field. It also offers an early glimpse of a new kind of collaboration between AI and human mathematicians. In this case, the companion work by external mathematicians paints a substantially richer picture than the original solution alone.'

Andrew CurranAndrew Curran@AndrewCurran_

Proof PDF: https://cdn.openai.com/pdf/74c24085-19b0-4534-9c90-465b8e29ad73/unit-distance-proof.pdf

7:19 PM · May 20, 2026 · 1.5K Views
7:20 PM · May 20, 2026 · 1.6K Views
Noam BrownNoam Brown@polynoamial

Today, we’re sharing that a general-purpose internal @openai model achieved a breakthrough on one of the best-known combinatorial geometry problems. Less than 1 year ago frontier AI models were at IMO gold-level performance. I expect this pace of progress to continue.

7:14 PM · May 20, 2026 · 53.8K Views
7:27 PM · May 20, 2026 · 922 Views

'This is a general-purpose LLM. It wasn't targeted at this problem or even at mathematics. Also, it's not a scaffold.'

Emergent, like Mythos.

Noam BrownNoam Brown@polynoamial

This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves.

7:18 PM · May 20, 2026 · 16.2K Views
7:30 PM · May 20, 2026 · 2.8K Views
Thomas BloomThomas Bloom@thomasfbloom

An internal OpenAI model has disproved one of the most well-known Erdős problems: the unit distance problem. This is, without doubt, the most impressive achievement of AI in mathematics so far. https://openai.com/index/model-disproves-discrete-geometry-conjecture/

7:10 PM · May 20, 2026 · 10.4K Views
7:33 PM · May 20, 2026 · 912 Views

'math is a leading indicator of what is to come. Soon-perhaps sooner than we all think-Al will begin autonomously producing landmark results in CS, physics, econ, bio, ... We should be prepared for a new world where the nature and methods of science will have changed.'

Alexander WeiAlexander Wei@alexwei_

4/ Second, math is a leading indicator of what is to come. Soon—perhaps sooner than we all think—AI will begin autonomously producing landmark results in CS, physics, econ, bio, … We should be prepared for a new world where the nature and methods of science will have changed.

7:33 PM · May 20, 2026 · 3.2K Views
7:36 PM · May 20, 2026 · 1.3K Views
Timothy Gowers @wtgowersTimothy Gowers @wtgowers@wtgowers

If you are a mathematician, then you may want to make sure you are sitting down before reading further.

7:04 PM · May 20, 2026 · 194K Views
7:41 PM · May 20, 2026 · 1.5K Views
Sebastien BubeckSebastien Bubeck@SebastienBubeck

http://x.com/i/article/2057150538202976256

7:53 PM · May 20, 2026 · 15.7K Views
7:54 PM · May 20, 2026 · 1.3K Views

Narrators voice 'The name of this model? GPT-5.6'

Andrew CurranAndrew Curran@AndrewCurran_
7:54 PM · May 20, 2026 · 1.3K Views
7:59 PM · May 20, 2026 · 691 Views

@deanwball 'Rejoice, my friends, or weep with sorrow. What California is today, the world will be tomorrow.'

Dean W. BallDean W. Ball@deanwball

Smile: a renaissance is upon us.

7:43 PM · May 20, 2026 · 5.6K Views
7:45 PM · May 20, 2026 · 425 Views

@polynoamial @OpenAI Congrats!

Noam BrownNoam Brown@polynoamial

Today, we’re sharing that a general-purpose internal @openai model achieved a breakthrough on one of the best-known combinatorial geometry problems. Less than 1 year ago frontier AI models were at IMO gold-level performance. I expect this pace of progress to continue.

7:11 PM · May 20, 2026 · 24.7K Views
8:08 PM · May 20, 2026 · 85 Views

@_aidan_clark_ Great time to be alive. Congrats!

Aidan ClarkAidan Clark@_aidan_clark_

Let's break this down, step by step [...]

7:25 PM · May 20, 2026 · 9.2K Views
8:22 PM · May 20, 2026 · 181 Views

waiting with bated breath for Gary’s take

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:34 PM · May 20, 2026 · 3.6K Views

OpenAI for research!

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:13 PM · May 20, 2026 · 216 Views

Yeah, this is now getting real.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:41 PM · May 20, 2026 · 21.4K Views

@ChrSzegedy Yup, I think you nailed that prediction. What are some of your other predictions?

Christian SzegedyChristian Szegedy@ChrSzegedy

Whatever the definition of "superhuman AI mathematician" is, I think my original prediction of June 2026 is not too far off the mark.

7:50 PM · May 20, 2026 · 10K Views
8:34 PM · May 20, 2026 · 113 Views

Where were you when AI disproved the Erdős planar conjecture?

8:02 PM · May 20, 2026 · 1.2K Views

@_aidan_clark_ > After verifying the initial proof, we investigated the success rate of our models on this problem with varying amounts of test-time compute. The results are shown here.

this is the verification accuracy here right? or derivation of the proof again?

Aidan ClarkAidan Clark@_aidan_clark_

Let's break this down, step by step [...]

7:25 PM · May 20, 2026 · 9.2K Views
8:42 PM · May 20, 2026 · 62 Views

ask your codex what is extraordinary about this proof to feel it

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:18 PM · May 20, 2026 · 2.6K Views

wtf wtf wtf

Hongxun WuHongxun Wu@HongxunWu

🧵(1/8) An @OpenAI internal reasoning LLM achieved an AI Math milestone: solving an open problem central to its mathematical subfield— in this case, the unit distance problem of discrete geometry. We came across it in a side quest to truly push our model on the hardest problems.

7:07 PM · May 20, 2026 · 18.7K Views
7:51 PM · May 20, 2026 · 5.1K Views

Probably the best summary of OpenAI latest math breakthrough: "first example of a result produced autonomously by an AI that I find exciting in itself, as opposed to as a leading indicator." Feels like they’re really scaling search rather than solutions to bounded problems.

Daniel LittDaniel Litt@littmath

(What I wrote is screenshotted below.)

7:24 PM · May 20, 2026 · 7.3K Views
8:34 PM · May 20, 2026 · 613 Views

An internal general-purpose reasoning model at OpenAI just made a huge breakthrough.

Here is how Fields Medalist Timothy Gowers puts it: "What's significant about this moment is that it's the first really clear example of AI solving — not just an unsolved math problem — but a really well-known math problem."

7:36 PM · May 20, 2026 · 6.2K Views

the model was probably something like GPT-5.6-Pro-xhigh

Lisan al GaibLisan al Gaib@scaling01

An internal general-purpose reasoning model at OpenAI just made a huge breakthrough. Here is how Fields Medalist Timothy Gowers puts it: "What's significant about this moment is that it's the first really clear example of AI solving — not just an unsolved math problem — but a really well-known math problem."

7:36 PM · May 20, 2026 · 6.2K Views
7:36 PM · May 20, 2026 · 1.3K Views

@polynoamial not a scaffold => not a Pro model ?

Noam BrownNoam Brown@polynoamial

This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves.

7:18 PM · May 20, 2026 · 16.2K Views
7:57 PM · May 20, 2026 · 575 Views

What a time

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
8:30 PM · May 20, 2026 · 384 Views

Congratulations to the team! The visualization is also so elegant

Hongxun WuHongxun Wu@HongxunWu

🧵(1/8) An @OpenAI internal reasoning LLM achieved an AI Math milestone: solving an open problem central to its mathematical subfield— in this case, the unit distance problem of discrete geometry. We came across it in a side quest to truly push our model on the hardest problems.

7:07 PM · May 20, 2026 · 18.7K Views
7:56 PM · May 20, 2026 · 740 Views

It’s a really special time to be alive…some thoughts from training this model 🧵

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:09 PM · May 20, 2026 · 14.9K Views

2/n Last year AI models achieved IMO gold level performance, but the jury was still out on whether they could do novel research. Today, our model has produced work that leading mathematicians like Tim Gowers said they would accept into Annals of Mathematics “without any hesitation.”

Sheryl HsuSheryl Hsu@SherylHsu02

It’s a really special time to be alive…some thoughts from training this model 🧵

7:09 PM · May 20, 2026 · 14.9K Views
7:10 PM · May 20, 2026 · 1.4K Views

3/n Sometimes from the outside, it seems like we focus a lot on math. That's because math is a field where it is easy to share landmark results of this sort. However, the model that produced this is a general purpose model - it was not trained with the goal of doing math research.

Sheryl HsuSheryl Hsu@SherylHsu02

2/n Last year AI models achieved IMO gold level performance, but the jury was still out on whether they could do novel research. Today, our model has produced work that leading mathematicians like Tim Gowers said they would accept into Annals of Mathematics “without any hesitation.”

7:10 PM · May 20, 2026 · 1.4K Views
7:10 PM · May 20, 2026 · 1.1K Views

6/n It only took 10 months to go from IMO gold to original math research. Working on this model and seeing what it can do every day has been very AGI-pilling for me, can’t wait to see where we are next year and time to lock tf in to make it happen!

7:10 PM · May 20, 2026 · 1.6K Views

I gave a talk with this slide less than two weeks ago and now I already have to update it. Crazy!!!

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:33 PM · May 20, 2026 · 4.4K Views

another

Daniel LittDaniel Litt@littmath

(What I wrote is screenshotted below.)

7:24 PM · May 20, 2026 · 7.3K Views
8:01 PM · May 20, 2026 · 85 Views
OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:33 PM · May 20, 2026 · 4.3K Views

someone should probably turn this into a proper benchmark, same w mythos exploit cherrypicking

bilalbilal@bilaltwovec
7:33 PM · May 20, 2026 · 4.3K Views
7:35 PM · May 20, 2026 · 135 Views

unfortunately openai didn't publish the unsummarized chain of thought, but the summary is 125 pages!

the model reaches the crucial idea (which it describes as 'frightening,' i would love to read the unabridged chain of thought here...) on page 39

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
8:36 PM · May 20, 2026 · 495 Views
Timothy NguyenTimothy Nguyen@IAmTimNguyen

A new AI milestone today: "If a human had written the paper and submitted it to the Annals of Mathematics and I had been asked for a quick opinion, I would have recommended acceptance without any hesitation. No previous AI-generated proof has come close to that.” - Tim Gowers 1/

7:42 PM · May 20, 2026 · 2.3K Views
7:42 PM · May 20, 2026 · 303 Views

the time is almost here.

OpenAIOpenAI@OpenAI

Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul Erdős in 1946. For nearly 80 years, mathematicians believed the best possible solutions looked roughly like square grids. An OpenAI model has now disproved that belief, discovering an entirely new family of constructions that performs better. This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics.

7:06 PM · May 20, 2026 · 893.3K Views
7:40 PM · May 20, 2026 · 10.1K Views

@polynoamial please do.

Noam BrownNoam Brown@polynoamial

This is a general-purpose LLM. It wasn’t targeted at this problem or even at mathematics. Also, it’s not a scaffold. We have not pushed this model to the limit on open problems. Our focus is to get it out quickly so that everyone can use it for themselves.

7:18 PM · May 20, 2026 · 16.2K Views
7:29 PM · May 20, 2026 · 477 Views
OpenAI Model Disproves Erdős Unit Distance Conjecture · Digg