Solved cryptogram
There is a formula that solves any cubic, and there can never be one for the fifth degree.
Mathematics Facts, sourced to MacTutor History of Mathematics.
Solve it yourself
This fact is a cryptogram here: 71 letters over 19 different ones, graded medium.
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What it means
Not that nobody has found one. That no such formula, built from the coefficients using arithmetic and roots, can exist. Abel proved it in 1824 and Galois explained why, by attaching to each equation a group that records how its solutions can be shuffled without disturbing the arithmetic between them. For degree five that group is too tangled to be unwound in steps, and the impossibility follows from its structure.
The claim comes from MacTutor History of Mathematics.
- SourceMacTutor History of Mathematics
- CollectionMathematics Facts
- Difficultymedium
- Length71 letters, 19 of them different
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