In 1969, Tony Hoare published a classical Communications' article, "An Axiomatic Basis for Computer Programming." Hoare's article culminated a sequence of works by Turing, McCarthy, Wirth, Floyd, and Manna, whose essence is an association of a proposition with each point in the program control flow, where the proposition is asserted to hold whenever that point is reach. Hoare added two important elements to that approach. First, he described a formal logic, now called Hoare Logic, for reasoning about programs. Second, he offered a compelling vision for the program-verification project: "When the correctness of a program, its compiler, and the hardware of the computer have all been established with mathematical certainty, it will be possible to place great reliance on the results of the program, and predict their properties with a confidence limited only by the reliability of the electronics."

Algorithms are already amongst us to a great extent. Some of them taking important decisions such as helping in the judiciary system to determine potential for recidivism, supporting decisions to renew or not a loan, or in which shares to invest our money, and even diagnosing whether our cell samples are malign or not, which determines the treatment we receive and the insurance we are offered. While their use has great potential to help us become more accurate and reach better decisions, they come with a series of problems including privacy issues, risk of bias, error, accountability questions and lack of transparency. The widespread adoption of artificial intelligence depends on trust. And we can only deem an algorithm trustworthy if we understand how it is reaching its decisions if we understand how it works.