The problems from IMO 2009 are now available. I haven’t had much time to work on them, though.

There are two classical geometry problems, which I already know I won’t attempt. While I am well aware that classical geometry often requires a great deal of ingenuity, I am also aware of the existence of the field of automatic geometric theorem proving. On this subject I largely agree with Doron Zeilberger: it is more interesting to find an algorithm to prove classes of theorems than to prove individual theorems. The sooner we see areas like classical geometry as “low-level,” the sooner we can work on the really interesting “high-level” stuff. (Plus, I’m not very good at classical geometry.)

Zeilberger’s typical example of a type of theorem with a proof system is the addition or multiplication of very large numbers: it is more interesting to prove symbolically than it is to prove individual “theorems” such as . Zeilberger himself played a significant role in the creation of another proof system, but for the far less trivial case of hypergeometric identities (which includes binomial identities as a special case).

But so I can make my point concretely, I’d like to discuss some examples based on the types of problems most of us had to deal with in middle or high school.

(more…)

Read Full Post »