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Group theory, abstraction, and the 196,883-dimensional monster

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Further reading 1

When does a pattern in a picture become a proof? →A tiling suggests a conjecture, a new encoding turns rectangles into collisions, and a plotting rule creates spirals before primes even enter the picture. What work does each picture actually do?This video helps answer · Which relationship must survive a change of picture?

Caption notes

Cube rotations and permutations of four objects can realize the same group structure. A correspondence must preserve what happens when two operations are composed.

Video or transcript source ↗
Original passages · 2
the multiplication table still captures the inner structure of the group
Group theory, abstraction, and the 196,883-dimensional monster · ▶ 8:58–9:14
which preserves composition
Group theory, abstraction, and the 196,883-dimensional monster · ▶ 11:42–11:51

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