I like this analogy:
“Programming without Mathematics is like Sex without Love.” 

Google Search is powerful because of Linear Algebra theory in finding core “EIGENVALUES” in order to manipulate the billion rows X billion columns matrices comprised of PageRanks (another formula invented by 2 Stanford Applied Math Masters degree students who co-founded Google.)

Facebook’s two Harvard undergrads Mark Zuckerberg and roommate Eduardo Savarin (now migrated to Singapore) created the prototype of Campus Facebook to rank Harvard girls with the Elo Formula (applied Normal Distribution Theory, used as standard in Chess and Sport rating). 

Other examples: 
RSA Encryption using Prime number factorization with a public and a private key.

Black-Sholes Formula (won 1997 Nobel Prize in Economics) for Derivatives trading software used by stock traders worldwide. The abuse of this formula was the main culprit of the 2010 Sub-prime global financial crisis.