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OpenAI made history today.
An internal reasoning model autonomously disproved a famous conjecture in mathematics that stood for nearly 80 years.
The problem: In 1946, Paul ErdΕs asked how many pairs of points can be exactly 1 unit apart if you place n points on a flat surface. The best known answer came from square grid constructions, and ErdΕs himself conjectured you can't do meaningfully better. Mathematicians believed this for decades.
The AI proved him wrong. It found entirely new point configurations that beat the square grid by a fixed polynomial factor, not a marginal improvement, a real mathematical gap.
The proof uses methods from algebraic number theory, a completely different branch of math, Class field towers, Golod-Shafarevich theory, tools nobody expected to be relevant to a geometry problem about distances in the plane (reminds me of move 37, AlphaGo tbh).
Fields Medalist Tim Gowers calls it "a milestone in AI mathematics." The proof was verified by leading external mathematicians.
According to OpenAI, this is the first time AI has independently solved a prominent open research problem in mathematics!
Caveat: Obviously OpenAI chose which problems to test the model on. So "autonomous" means the model generated the idea and wrote the proof, not that it wandered into the problem on its own.
But if reasoning models can reliably make cross-domain connections like this, finding paths that experts didn't prioritize, this changes research far beyond math. Biology, physics, materials science, medicine.
This isn't AI reproducing human knowledge anymore. This is AI producing new knowledge. That's a qualitative shift.
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An internal reasoning model autonomously disproved a famous conjecture in mathematics that stood for nearly 80 years.
The problem: In 1946, Paul ErdΕs asked how many pairs of points can be exactly 1 unit apart if you place n points on a flat surface. The best known answer came from square grid constructions, and ErdΕs himself conjectured you can't do meaningfully better. Mathematicians believed this for decades.
The AI proved him wrong. It found entirely new point configurations that beat the square grid by a fixed polynomial factor, not a marginal improvement, a real mathematical gap.
The proof uses methods from algebraic number theory, a completely different branch of math, Class field towers, Golod-Shafarevich theory, tools nobody expected to be relevant to a geometry problem about distances in the plane (reminds me of move 37, AlphaGo tbh).
Fields Medalist Tim Gowers calls it "a milestone in AI mathematics." The proof was verified by leading external mathematicians.
According to OpenAI, this is the first time AI has independently solved a prominent open research problem in mathematics!
Caveat: Obviously OpenAI chose which problems to test the model on. So "autonomous" means the model generated the idea and wrote the proof, not that it wandered into the problem on its own.
But if reasoning models can reliably make cross-domain connections like this, finding paths that experts didn't prioritize, this changes research far beyond math. Biology, physics, materials science, medicine.
This isn't AI reproducing human knowledge anymore. This is AI producing new knowledge. That's a qualitative shift.
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This AI pretended to be a student π
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π¨ One tiny biteβ¦ and your body could reject meat FOREVER.
Doctors say the Lone Star Tick can trigger Alpha-Gal Syndrome β a condition linked to severe allergic reactions to red meat, dairy, and more.
But now the internet is asking a darker questionβ¦
Why are these ticks suddenly spreading EVERYWHERE? ππ·οΈ
Some people think itβs natural.Others think something much bigger is going on.
Coincidence⦠or experiment? #lonestartick #alphagal #conspiracy #creepy #brainrotreels
Doctors say the Lone Star Tick can trigger Alpha-Gal Syndrome β a condition linked to severe allergic reactions to red meat, dairy, and more.
But now the internet is asking a darker questionβ¦
Why are these ticks suddenly spreading EVERYWHERE? ππ·οΈ
Some people think itβs natural.Others think something much bigger is going on.
Coincidence⦠or experiment? #lonestartick #alphagal #conspiracy #creepy #brainrotreels
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Today, we share a breakthrough on the planar unit distance problem, a famous open question first posed by Paul ErdΕs 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.
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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.
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Forwarded from DoomPosting
Math grad student friend comments on the recent ErdΕs proof
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Malachy Steenson got thousands of people on the streets to protest against Irelandβs population replacement of migrants from all over the world.
Vote Malachy Steenson 1 in Dublin Central on May 22
MalachySteenson
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Vote Malachy Steenson 1 in Dublin Central on May 22
MalachySteenson
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Woman blows through a stop sign in her white SUV. Dude calls her out and she immediately jumps out screaming, then shoots the back window of his car before speeding off
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In Colombia, two tourists, a father and his son, were abducted in broad daylight on a beach in Buenaventura by armed members of the βLos Shottasβ cartel.
44-year-old Alexander Valencia HernΓ‘ndez and his 22-year-old son NicolΓ‘s were intercepted after the son accidentally entered a cartel-controlled βforbidden zoneβ while filming their fishing trip. When the father tried to defend his son, both were taken.
Hours later, authorities found Alexanderβs body floating in a tidal area. His son NicolΓ‘s is still missing.
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44-year-old Alexander Valencia HernΓ‘ndez and his 22-year-old son NicolΓ‘s were intercepted after the son accidentally entered a cartel-controlled βforbidden zoneβ while filming their fishing trip. When the father tried to defend his son, both were taken.
Hours later, authorities found Alexanderβs body floating in a tidal area. His son NicolΓ‘s is still missing.
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>Be so fat you have to be kept under house arrest and constant supervision.
>Somehow manage to escape.
>Start eating food from a dumpster behind a supermarket.
>Eat so much spoiled food you die.
Why are fats like this?
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>Somehow manage to escape.
>Start eating food from a dumpster behind a supermarket.
>Eat so much spoiled food you die.
Why are fats like this?
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NOW - Former New Zealand PM says misinformation is reducing vaccine uptake, cites GAVI, that found over 1 in 4 top vaccine-related facebook videos, about Pakistan's HPV vaccine rollout, contained 27% misinformation and that the comments were 40% negative and 17% supportive
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"Big, bad, black b&tch" almost gets arrested in Japan. Documents herself breaking at least two laws
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