Mathematics is of two kinds, Rigorous and Physical. The former is Narrow: the latter Bold and Broad. To have to stop to formulate rigorous demonstrations would put a stop to most physico-mathematical inquiries. Am I to refuse to eat because I do not fully understand the mechanism of digestion?
DA Edge (1983). "Oliver Heaviside (1850-1927) - Physical mathematician". Teaching mathematics and its applications 2: 55-61.