TITLE: Is there a "mathematical" definition of "simplify"?
QUESTION [29 upvotes]: Every mathematician knows what "simplify" means, at least intuitively. Otherwise, he or she wouldn't have made it through high school algebra, where one learns to "simplify" expressions like $x(y+x)+x^2(y+1+x)+3(x+3)$. 
But is there an accepted rigorous "mathematical" definition of "simplify" not just for algebraic expressions but for general expressions, which could involve anything, like transcendental functions or recursive functions? If not, then why? I would think that computer algebra uses this idea.

REPLY [2 votes]: There is a theory called Kolmogorov Complexity(KC,also called algorithmic information) which has been initiated by Chaitin,Solomonoff,and Kolmogorov.Roughly speaking,an object is simple if it's KC is shorter,it is related to recursive function or computability theory,or uncomputabilty ,See Kolmogorov complexity and it's application by Ming Li and Vitanyi for the exact definition and examples.or http://www.scholarpedia.org/article/Algorithmic_complexity. It may be what you are looking for.
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