Some tricky conversations this evening about the impending social media ban.
‘I don’t even know who this government guy is’
‘Keir Starmer’
‘Keir Starmer, what does that mean’
@woke8yearold Also worth considering before making such claims that people are going to be even more angry if they get lied to about this before it happens
The funniest outcome atp is that Keiko finishes ahead but by such a microsopic margin that the election gets thrown out, and afterwards she loses the rerun
@sanherms Tienes razón, pero investir a un candidato técnico bajo la condición de que convoque elecciones es la única forma (chapucera) para salir de la situación ridícula que fuerza Sánchez bajo el sistema actual
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 This isn’t a literature review that found a previously unpublished human solution, or a slight improvement to an existing human solution, or a solution to some minor subproblem that no one cares about.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.