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    So what makes dimensions 8 and 24 so special? “Everybody asks what is special about dimensions 8 and 24 — I don’t know, it’s a mystery,” Viazovska told us in 2018. “In these dimensions we have these two extremely great configurations, which we don’t have in other dimensions. They are so good that methods which fail in all other dimensions, in these dimensions give a sharp estimate. If you ask me why, I don’t know.”

    This is remarkable to me. Someone, who’s among the very best in the world in her subfield and just made a historic breakthrough, eagerly admits that neither she nor anyone else has any insight into some obvious and straightforward question concerning it. There’s so much we don’t know!

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      There are some incredibly strange behaviors in higher dimensions which do not seem to have an intuitive explanation yet. Like exotic spheres, exotic R^4 and of course the leech lattice https://en.wikipedia.org/wiki/Exceptional_object#8_and_24_dimensions Another similar kind of thing is some work on 4d unknotting https://www.quantamagazine.org/graduate-student-solves-decades-old-conway-knot-problem-20200519/ There’s so much of this interesting and unique behavior that occurs in higher dimensions.