vasc's inequality
2025 March 17
Consider the following inequality.
\[(a^2+b^2+c^2)^2\ge 3(a^3b+b^3c+c^3a)\]
An 'easy' standard approach like Muirhead doesn't work on it (it's not symmetric). And yet an astounding one-liner kills it instantly (of the sum of squares type).
But what of it? A devilish puzzle of the mind, hidden away forever unless you hear of it. The world keeps on turning...
If something so idealized can slip and twist between our hands, evading solution, what about a problem in the real world, where variables aren't counted in single digit integers, and equality cases aren't strictly defined?
World domination is such an ugly phrase. I prefer to call it world optimization.