Russia has demonstrated the delivery of nuclear warheads to the territory of Belarus.

The Russian Defense Ministry reported that nuclear munitions have been delivered to the storage points of the missile brigade in Belarus.

This is happening as part of exercises, where Belarusian military personnel are practicing the equipping of missile carriers with "special munitions", the covert deployment of units, and preparation for launches.

Recall that Belarus and Russia are currently conducting nuclear exercises, including with the use of "Iskander" missiles, designed for strikes on Europe.

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

Sauron lurks.

It’s not over until the Ring is destroyed.

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

These houses in San Francisco are actually straight

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

With the ordeal that women are going through in Afghanistan, with the things the men there are subjecting them to you would expect them to be flooding into western countries. Oh hold on a minute

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

We used to be a proper country

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

Getting off the bus to avoid the floods in NYC didn't quite work out as planned for her

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

They removed this passage from his book after he died.

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

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

Women commit 70% of domestic violence

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

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 This isn’t a literature review that found a previously unpublished human solution, or a slight improvement to an existing human solution, or a solution to some minor subproblem that no one cares about.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.

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

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.

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

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.

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

Math grad student friend comments on the recent Erdős proof

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶

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…

🄳🄾🄾🄼🄿🤖🅂🅃🄸🄽🄶