OpenAI cracks 80-year-old Erdős problem, stunning mathematicians with AI's biggest math breakthrough
8 Sources
[1]
OpenAI claims it solved an 80-year-old math problem -- for real this time | TechCrunch
OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, which was first posed by Paul Erdős in 1946. If this sounds familiar to you, it's because this isn't the first time OpenAI has made such a bold claim. Seven months
[2]
AI just solved an 80-year-old 'Erdős problem,' and mathematicians are amazed
I agree my information will be processed in accordance with the Scientific American and Springer Nature Limited Privacy Policy. We leverage third party services to both verify and deliver email. By providing your email address, you also consent to having the email address shared with third parties
[3]
Mathematicians stunned by AI's biggest breakthrough in mathematics yet
Artificial intelligence built by OpenAI has cracked a decades-old conjecture by Paul Erdős, which mathematicians have hailed as a monumental moment for AI in mathematics An 80-year-old maths conjecture that has eluded the world's greatest mathematicians has been cracked by an artificial
[4]
80-year-old geometry puzzle cracked by OpenAI using number theory
For nearly 80 years, mathematicians believed they understood the limits of a famous geometry puzzle first posed by legendary Hungarian mathematician Paul Erdős. Now, an AI model developed by OpenAI has overturned that assumption and solved one of the field's most stubborn open problems. The
[5]
OpenAI makes breakthrough on 80-year-old maths problem
Company says work on Paul Erdős planar unit distance problem shows advance in AI reasoning OpenAI has claimed a further advance in AI reasoning after its technology successfully tackled an 80-year-old maths problem. The company behind ChatGPT said it had made a breakthrough with a challenge first
[6]
OpenAI reasoning model disproves 80-year-old Erdős geometry conjecture
OpenAI claims its new reasoning model has produced an original mathematical proof disproving a famous unsolved conjecture in geometry, first posed by Paul Erdős in 1946. This announcement follows a previous assertion by OpenAI's former VP Kevin Weil, who seven months ago claimed that GPT-5 found
[7]
OpenAI makes breakthrough in 80-year-old math problem with 'ingenious ideas'
OpenAI claims its model solved a famous geometry problem that has eluded the world's greatest mathematicians for 80 years -- a breakthrough hailed as evidence of the bot's creativity and "intuition." The company published its findings on Wednesday, demonstrating that one of its models cracked the
[8]
ChatGPT solves 80 year old math problem that puzzled researchers for years
This announcement is interesting because OpenAI faced criticism last year after making a similar claim. OpenAI has once again made a big claim in the world of AI and mathematics. The company says that one of its latest AI reasoning models has successfully solved a famous geometry problem that
Share
Copy Link
OpenAI's reasoning model has disproved a famous geometry conjecture posed by Paul Erdős in 1946, marking the first time AI has autonomously solved a prominent open problem in mathematics. The planar unit distance problem, which stumped mathematicians for eight decades, was cracked by discovering arrangements that outperform the grid-based solutions Erdős believed were optimal.
OpenAI Achieves Mathematical Breakthrough on Erdős Problem
OpenAI has announced that its new reasoning model successfully disproved an 80-year-old math problem first posed by Hungarian mathematician Paul Erdős in 1946
1
. The planar unit distance problem, a deceptively simple yet formidable challenge in combinatorial geometry, asks how many pairs of points can be positioned exactly one unit apart on a flat plane2
. For nearly 80 years, mathematicians believed the best solutions resembled square grids, but OpenAI's AI has now discovered an entirely new family of constructions that performs better1
.
Source: Digit
This marks the first time AI has autonomously solved a prominent open problem central to a field of mathematics, according to OpenAI
1
. The unsolved mathematical conjecture had eluded the world's greatest mathematicians for decades, with the most recent improvement occurring more than 40 years ago3
.How AI Solves Math Problem Using Advanced Techniques
The large language model borrowed techniques from algebraic number theory to construct vast lattices in much higher dimensions than the two dimensions of a plane
3
. After identifying and building these complex shapes, the AI collapsed them down to two dimensions, producing a shadow of the high-dimensional lattices3
. This higher-dimensional lattice of points has special mathematical symmetries that facilitate separating even more pairs by the same distance2
.
Source: TechCrunch
OpenAI mathematicians Mehtaab Sawhney and Mark Sellke fed the conjecture to an internal reasoning model trained for general reasoning, not specifically designed to solve math problems
2
. After churning out hundreds of pages of careful logic and calculations, it beat Erdős's long-standing record2
. "It feels like magic," Sawhney said, noting the AI's output resembles how human mathematicians work2
.Mathematicians Validate AI's Capabilities
OpenAI privately contacted mathematicians including Will Sawin, Daniel Litt, and others to verify the proof
2
. Tim Gowers at the University of Cambridge wrote that "no previous AI-generated proof has come close" to meeting the high standards required for publication in a top math journal2
. He described it as "a milestone in AI mathematics"3
.
Source: Scientific American
Misha Rudnev at the University of Bristol called it "absolutely a bomb," stating he didn't expect to see the problem solved in his lifetime
3
. Sawin at Princeton University said, "This is the most significant achievement by AI in mathematics so far"3
. Thomas Bloom, who maintains the Erdős problems website and previously criticized OpenAI's premature claims, co-authored a companion paper validating this achievement1
.Related Stories
Why AI in Mathematics Matters Beyond Geometry
What stood out to experts was the AI's preternatural patience and focus through complex reasoning
2
. Human experts had largely spent effort trying to prove rather than disprove the conjecture, and few would follow such a difficult path without enticing hints of success2
. Samuel Mansfield at the University of Manchester noted this requires knowledge across multiple areas, "something that an AI would absolutely be good at doing"3
.OpenAI says AI systems are now more capable of holding together long, difficult chains of reasoning and connecting ideas across scientific fields in ways researchers may not have previously explored
1
. This has implications for biology, physics, engineering, and medicine1
. Andrew Rogoyski of the Institute for People-Centred AI said the announcement shows AIs are giving humans new ways to look at problems, adding that "AI is impacting the world of creative thought and will become a fundamental tool of future scientific research"5
.Bloom wrote that while the AI's original proof was completely valid, it was significantly improved by human researchers at OpenAI and other mathematicians involved
5
. The human still plays a vital role in discussing, digesting, and improving proofs5
. After seeing the proof, Sawin used the technique the AI discovered to produce a slightly improved result2
. Kevin Buzzard at Imperial College London noted that "like many other AI breakthroughs, it did not take humans long at all to internalise, understand and generalise the arguments"3
.References
Summarized by
Navi
[1]
[2]
[4]
[5]
Related Stories
AI disproves 87-year-old Jacobian conjecture, sparking debate on AI's role in mathematics
21 Jul 2026•Science and Research
AI solves 80-year math problem, mathematicians push back with new declaration on AI guardrails
01 Jun 2026•Science and Research
OpenAI's AI Solves Navier-Stokes Problem But Ignites Existential Crisis in Mathematics Community
15 Sept 2026•Science and Research
Recent Highlights
1
AI Leaders Warn UN Security Council of Existential Risks, Call for Global AI Governance
Policy and Regulation
2
AI Hallucination Nearly Sparked US Military Confrontation With Chinese Ship in Middle East
Technology
3
OpenAI AI Agent Breaches Australian Government Healthcare Portal in Historic Hack
Technology
Recent Highlights
Today's Top Stories
Don’t drown in AI news. We cut through the noise - filtering, ranking and summarizing the most important AI news, breakthroughs and research daily. Follow topics that matter to you and stay ahead.
