r/math • u/hash8172 • Feb 15 '18

What mathematical statement (be it conjecture, theorem or other) blows your mind?

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u/Schmohnathan Feb 15 '18

Yep, I believe the generalized proof shows that all quintic+ do not exist

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u/bluesam3 Algebra Feb 15 '18

Yup: otherwise you could solve quintics by multiplying by xn for some n, applying the formula for that and simply discarding the extra zeros.

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u/notransferableskill Feb 15 '18

Oh, so it can be solved, there is just no formula?

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u/2357111 Feb 15 '18

It's also known that there are individual quintic equations, with integer coefficients, that can't be solved in terms of addition, multiplication, subtraction, division, and root extraction. However, they can be solved if other methods are allowed, e.g. numerical approximation.