Video/Why There's 'No' Quintic Formula (without Galois theory)
Turner, Carl (Jul 5, 2021). Why There's 'No' Quintic Formula (without Galois theory). local page: not all wrong.
The transcript by Assembly AI is here:Transcript
Excerpts from Youtube Page
Feel free to skip to 10:28 to see how to develop Vladimir Arnold's amazingly beautiful argument for the non-existence of a general algebraic formula for solving quintic equations! This result, known as the Abel-Ruffini theorem, is usually proved by Galois theory, which is hard and not very intuitive. But this approach uses little more than some basic properties of complex numbers. (PS: I forgot to mention Abel's original approach, which is a bit grim, and gives very little intuition at all!)
Must see video on this subject
For those of you who have seen this video, you must also watch the video[1] by Trevor Cheung of Mathemaniac.
Critical Connection to Petri Net
In the famous Dinning Philosopher problem, it is standard to start with at least five participants. The reason is obvious that any number below this, will have trivial behavior. However, there was rarely a document that I have found on the web that directly answers why this is the case.
The Quintic Formula
It is until I saw the explanations[2][3][4] of why there are no solutions for Quintic Formula, that finally gave me the convincing argument. It has to do with the infinite combinatorial possibilities generator by five commutators.
References
- ↑ Cheung, Trevor (Jul 3, 2022). Why can't you solve quintic equations? - Galois theory explained intuitively. local page: Mathemaniac.
- ↑ Turner, Carl (Jul 5, 2021). Why There's 'No' Quintic Formula (without Galois theory). local page: not all wrong.
- ↑ Aleph 0, ed. (Feb 21, 2021). The Insolvability of the Quintic. local page: Aleph 0.
- ↑ Cheung, Trevor (Jul 3, 2022). Why can't you solve quintic equations? - Galois theory explained intuitively. local page: Mathemaniac.
Related Pages
Organized by:not all wrong Presented by:Carl Turner