arXiv subjects
Publications and source records attributed to Doron Zeilberger.
Weinstein's[2] brilliant short proof of de Branges'[1] theorem can be made yet much shorter(modulo routine calculations), completely elementary (modulo Löwner theory), self contained(no need for the esoteric Legendre polynomials' addition theorem), and motivated(ditto), as follows.
The Vandermonde-Chu Binomial Coefficients Identity is shown to imply Bombieri's deep norm inequalities, via identities of Beauzamy-Dégot, and Reznick.
Ramanujan's series for Pi, that appeared in his famous letter to Hardy, is given a one-line WZ proof.
The future of mathematics is described, by using the WZ algorithmic proof theory as a parable.
The method of rational function certification for proving terminating hypergeometric identities is extended from single sums or integrals to multi-integral/sums and ``$q$'' integral/sums.
A short and elementary proof, and a finite-form generalization, are given of Jacobi's formula for the number of ways of writing an integer as a sum of four squares (that implies Lagrange's famous 1777 theorem.)