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Were going to talk about a classic problem in mathematics. This problem is 400 years old. Its about sphere packing. The question is, what is the best way to pack spheres? And by best I mean, what is the densest way of packing spheres. And its thought that the best way of packing spheres is 74.05%. So if you were packing a container, it would be 74 percent full. Now its been thought that is the best way of packing spheres for 400 years, and it was finally proven in the 1990s. However the referees, when they looked through the proof, thought they were 99% certain that the proof was right. So thats kind of, slightly unsatisfying. So then they started a, a 15-year project to really make sure that this is correct, and theyve rewritten the proof in very formal mathematical language which allows a computer to automatically check the proof, which was finally accepted in 2017. Finally proving the conjecture about how densely you can pack spheres. But the problem itself goes back to Sir Wa
