The purpose of this article is five-fold: (1) to elaborate on mathematical pedagogy, the application of mathematics, the misunderstanding and the myth around this powerful language; (2) to explain the differences between theoretical solutions and constructive solutions; (3) to explain the influence of technology and its pivotal--in many cases, indispensable--role in teaching, and research, and solving real-world problems; (4) to give examples that show the failure of technology to solve several well-posed problems that possess (constructive) solutions, and to give examples indicating that widely-used software sometimes provides the wrong answer; and (5) to discuss the misuse of technology in teaching mathematics, a trend that unfortunately will have adverse effects on learning mathematics. (Contains 2 figures.)