TITLE: Why is the "Buffalo Way" considered inelegant?
QUESTION [7 upvotes]: I was going through an "article" on the "Buffalo Way", where the author said that one should NEVER use the Buffalo Way for proving inequalities in actual real-time contests as it is "highly inelengant". What is the reason behind this notion ? In Mathematics, there are a whole lot of ways to attempt a given question. If the BW provides a proof for some inequality, then why it is given the downvote ?

REPLY [8 votes]: I think we can not delete BW from all methods, with there help we can prove polynomial inequalities.
This method is very useful. See here: http://www.artofproblemsolving.com/community/c6h522084 
There are polynomial inequalities, which we can prove by nice way, 
but to find this way during a competition is very hard. 
By the way, BW can give a quick proof sometimes.
There are polynomial inequalities for which there is a proof by BW only.
See here:  Olympiad Inequality $\sum\limits_{cyc} \frac{x^4}{8x^3+5y^3} \geqslant \frac{x+y+z}{13}$
By the way, there are  polynomial inequalities for which BW does not help.
See here: Inequality $\sum\limits_{cyc}\frac{a^3}{13a^2+5b^2}\geq\frac{a+b+c}{18}$