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Erd\H{o}s Rado Sunflower Theorem for Shifted Families
Combinatorics [Submitted on 1 Jun 2026 (v1), last revised 8 Jun 2026 (this version, v2)] Title:Erdős Rado Sunflower Theorem for Shifted Families View PDF HTML (experimental)Abstract:Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$. The Erdős-Rado Sunflower Conjecture states that for every $s >2$, there is an constant $C=C(s)$ such that $f(k,s) \leq C^k$.
Erd\H{o}s Rado Sunflower (Conjecture) Theorem
Combinatorics [Submitted on 1 Jun 2026] Title:Erdős Rado Sunflower (Conjecture) Theorem View PDF HTML (experimental)Abstract:Let $f(k,s)$ denote the minimum integer $m$ such that any family $\mathcal{F}$ consisting of $k$-sized sets of cardinality at least $m$ always contain a sunflower of size $s$.
OpenAI makes breakthrough on 80-year-old maths problem
OpenAI has announced a significant advancement in AI reasoning after its technology successfully addressed an 80-year-old mathematical challenge. The breakthrough relates to the planar unit distance problem, which was first posed by mathematician Paul Erdős in 1946.
An OpenAI model solved a famous math problem that stumped humans for 80 years
In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 years. OpenAI gave several mathematicians early access to the result and published their reactions. Tim Gowers—who won the Fields Medal, the most prestigious prize in mathematics—wrote that “there is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics.”
Mathematical AI helps researchers crack 50-year-old problem
After an AI from OpenAI found a trick to solve an 80-year-old conjecture from Paul Erdős, mathematicians have borrowed the same technique to solve another important problem
An OpenAI model solved a famous math problem that stumped humans for 80 years
In mid-May, OpenAI announced that an internal AI model had disproved the Erdős unit distance conjecture, a famous problem in discrete geometry that had stumped human mathematicians for the last 80 years. OpenAI gave several mathematicians early access to the result and published their reactions. Tim Gowers—who won the Fields Medal, the most prestigious prize in mathematics—wrote that “there is no doubt that the solution to the unit-distance problem is a milestone in AI mathematics.”
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
A golden age of maths is dawning and mathematicians are freaking out
I am attempting to solve a mathematical conundrum that has stumped many of humanity’s greatest thinkers. I have zero mathematical training, apart from a distant undergraduate physics degree, which should put my odds of success at slim to none. But I also have a trick up my sleeve – a kind of mathematical genie that can conjure arcane secrets seemingly out of thin air.
The maths meme that has been distracting mathematicians for a century
Almost a century ago, a mathematician came up with a puzzle that was so seemingly simple and yet so fiendishly difficult that it has been distracting other mathematicians ever since. It has become a meme that jumps from brain to brain, with many people claiming to have solved it, only to have their hopes dashed as the proof unravels. And be warned – once I explain the rules, you will immediately want to start playing around with it yourself, and I take no responsibility for how much of your...