They removed this passage from his book after he died.

"In a passage dropped from later published editions..."

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Women commit 70% of domestic violence

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SITUATION EXPLAINED: OpenAI solves a real math problem

In 1946, renowned mathematician Paul Erdős defined a simple problem: if you place n points in a plane, what is the maximum possible number of pairs of points that can be exactly 1 unit of distance apart? This problem, the planar unit distance problem, became one of the most well-known in the field of combinatorial geometry. Erdős conjectured that the “square lattice” solution shown below was more or less optimal.

An internal OpenAI model just disproved this conjecture, finding a more optimal solution. This is a big deal. This isn’t a literature review that found a previously unpublished human solution, or a slight improvement to an existing human solution, or a solution to some minor subproblem that no one cares about. It’s a fully AI-discovered novel solution to a well-known open problem central to a field of mathematics.

Just as crucially, the result came from a general-purpose reasoning model, not a model specifically designed for math like Google’s AlphaProof. It’s possible that this model is the next version of GPT-5.5 Pro, soon to be released to millions of ChatGPT subscribers worldwide. The dream of a genius in everyone’s pocket is one step closer to becoming a reality.

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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 Erdős 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 Erdős 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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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.

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Math grad student friend comments on the recent Erdős proof

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I have an opinion about the baby flamingo learning to paddle and its value vis-à-vis the majority of people inhabiting the world beyond the borders of Europe…

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BREAKING: South Korea’s KOSPI exploded +8% to 7,787 after Samsung reached a tentative labor union deal.

₩570,000,000,000,000 added in market value today.

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Malachy Steenson got thousands of people on the streets to protest against Ireland’s population replacement of migrants from all over the world.

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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NEW: Cuba braces for possible U.S. military escalation.

Air defense systems are said to be on heightened alert, while military ambush and rapid response operations are reportedly being tested across the island.

Tensions in the region appear to be rising fast as fears of a potential confrontation grow.

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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 “Los Shottas” cartel.

44-year-old Alexander Valencia Hernández and his 22-year-old son Nicolás were intercepted after the son accidentally entered a cartel-controlled “forbidden zone” while filming their fishing trip. When the father tried to defend his son, both were taken.

Hours later, authorities found Alexander’s body floating in a tidal area. His son Nicolás is still missing.

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Trying a switch from Firefox to Brave

let's see how it goes

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When politics divide a father and son: Riots in Bolivia enter their fourth week

Bolivia faces the worst economic crisis in 40 years, with high living costs, severe fuel shortage and an annual inflation of 14%

The workers are demanding the resignation of President Rodrigo Paz and immediate government action

"Even my son is here today. He's back there, and he's confronting me"

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$USDT.D just got rejected at its trendline resistance.

USDT market cap is sitting around $190 BILLION.

If $USDT.D starts to decline, BILLIONS in sidelined liquidity will flow into $BTC and alts.

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Bro just shaved his mustache and thinks nobody will recognize him?

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