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M5 delivers incredible performance for everything users want to tackle, from everyday productivity to creative workflows. MacBook Air with M5 features a 10-core CPU with the world’s fastest CPU core for even more responsiveness.1 Combined with an up-to-10-core GPU with a powerful Neural Accelerator in each core, MacBook Air with M5 delivers up to 4x faster performance for AI tasks than MacBook Air with M4, and up to 9.5x faster than MacBook Air with M1.2 This makes it an incredibly capable platform for AI — whether using Apple Intelligence across apps and system experiences at home, or running LLMs on device in an enterprise.3
The ProblemHow densely can identical spheres be packed in n-dimensional space? In one dimension, the problem is trivial, and in two dimensions, elementary proofs have existed for decades. In three dimensions, a solution was conjectured by Kepler in 1611, but it was not proved until Thomas Hales settled it in 1998, in a heavily computer-assisted proof that subsequently took over a decade to formally verify.
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