Some of the mathematical advances that influenced people's life in XX century are:
Fast Fourier Transform (applications to signal processing, in particular, image processing. Without it modern computer revolution would be impossible).
Radon transform (which makes computer tomography possible).
Progress in probability theory (all insurance industry is based on it. And "financial math" as well. Trading in derivatives is a relatively recent innovation. Based on non-trivial math, stochastic differential equations).
Progress in control theory (automatic control devices are literally everywhere).
Remarkable progress in coding theory in the end of XX century.