  In this article, we use Lindstr\"om Gessel Viennot Lemma to give a short,
combinatorial, visualizable proof of the identity of Schur polynomials -- the
sum of monomials of Young tableaux equals to the quotient of determinants. As a
by-product, we have a proof of Vandermonde determinant without words. We also
prove the cauchy identity. In the remarks, we discuss factorial Schur
polynomials, dual Cauchy identity and the relation beteen Newton interpolation
formula.
