Most practically-useful mathematics does not need the strength of a theory such as ZFC. The reverse mathematics programme shows that many notable theorems can be stated in $RCA_0$, which is a finitistic system. Most other systems studied in revese mathematics (such as $WKL_0$, $ACA_0$ or $ATR_0$) are subsystems of second-order arithmetic, and also enjoy conservativity properties over $RCA_0$.