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Almost every aspect of our lives is touched by software. Where we live, who we meet, what we eat, how we work, what we learn, how we play are all influenced, directly or indirectly, by computer programs. Yet these programs are surprisingly fickle and unreliable: software failures cause enormous damage every day, from mundane to life-threatening. How did we come to trust our lives to such untrustworthy artifacts, and why is software so uniquely broken? In this talk, I will approach this question through the lens of formal methods, a field of computer science that studies programs as mathematical objects. I will argue that the practice of software construction owes too much to craft and too little to science, and I will present vignettes from my lab's research to illustrate the deep connection that unites software and mathematics: all software can be distilled into mathematical formulae that lend themselves to precise reasoning and proofs.