Korner wrote a lovely book on this topic, "The Pleasures of Counting." Among the ideas he discusses not already mentioned,

• how statistics helped early epidemiologists discover how cholera was transmitted
• how mathematicians developed radar in WWII, saving Britain from the Luftwaffe
• also in WWII: the development of sonar & cryptography
• how basic ideas in operations research were developed to optimize convoys in WWI to elude submarines