Youtor
Why Theres No Quintic Formula proof without Galois theory
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=BSHv9Elk1MU
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!) • 00:00 Introduction • 01:58 Complex Number Refresher • 04:11 Fundamental Theorem of Algebra (Proof) • 10:28 The Symmetry of Solutions to Polynomials • 22:47 Why Roots Aren't Enough • 28:29 Why Nested Roots Aren't Enough • 37:01 Onto The Quintic • 41:03 Conclusion • Paper mentioned: https://web.williams.edu/Mathematics/... • Video mentioned: • Short proof of Abel's theorem that 5t...
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