# An Elegant and Insightful Direct Combinatorial Proof of the Arithmetical Identity 4+5=2+7

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Doron Zeilberger, Rutgers University
Fine Hall 110

There are no trivial theorems, only trivial mathematicians (those who believe that there exist trivial theorems). Being a non-trivial mathematician myself, I will present a new, elegant, and very insightful direct combinatorial proof of the seemingly (to most people) "trivial" arithmetical theorem that states that four plus five equals two plus seven. More important, the methodology should extend to give insightful direct combinatorial proofs of even deeper identities, like (4+6+200+6+50)+(3+10+30+5)=300+4+10.