Tsao, Hung-ping (2019). Evolutionary mathematics and arts for talk elegancy investigation. In: “Evolutionary Progress in Science, Technology, Engineering, Arts, and Mathematics (STEAM)”, Wang, Lawrence K. and Tsao, Hung-ping (editors). Volume 1, Number 1, January 2019; 68 pages. Lenox Institute Press, Newtonville, NY, 12128-0405, USA. No. STEAM-VOL1-NUM1-JAN2019; ISBN 978-0-9890870-3-2. ————— ABSTRACT: The author has been motivated by Tower of Hanoi and Einstein Riddle to provide innovative ways of solving various types of problems such as Twin knight, The ballot box, Ties in matching pennies, The theater row and Same birthday among classmates. In addition, mutual independency versus mutual exclusiveness, current life insurance models deficiency and Sudoku puzzles efficiency will be discussed.