Historically, the development of mathematics has at least two clues. One is a formal clue of pure reason, and the other is a clue closely related to the development of physical science and engineering problems.
From Archimedes to Leonardo da Vinci, from Descartes to Euler, Newton, Lagrange, Laplace, even Gauss and von Newman. These masters combine mathematics with the development of solid science and engineering perfectly.
The high-tech after the emergence of computers is essentially mathematical technology. What we are concerned about here is how to apply mathematics to practice, not just intellectual games.