Short answers, pulled from the story.
Muhammad ibn Musa al-Khwarizmi wrote the text called Kitab al-Hisab al-Hindi around 825 AD. This book introduced the Hindu-Arabic numeral system to the Islamic world and later to Europe through Latin translations in the early 12th century.
John of Seville produced Liber Alghoarismi de practica arismetrice during the early 12th century. The work began with the phrase Dixit Algorismi, meaning Thus spoke Al-Khwarizmi, which established the root for the word algorism by the year 1225.
Archaeologists found a Sumerian clay tablet in Shuruppak near Baghdad that describes the earliest known division algorithm. This artifact dates back to Babylonian mathematics from around 2500 BC and contains algorithms for computing formulas and predicting astronomical events during the Hammurabi dynasty.
Al-Kindi developed the first cryptographic algorithm in his manuscript On Deciphering Cryptographic Messages during the 9th century. This work introduced frequency analysis as the earliest codebreaking method within Indian and Arab mathematical traditions.
Babbage's analytical engine is considered history's first Turing-complete computer rather than just a calculator. Ada Lovelace created the first algorithm intended for processing on this machine during the mid-19th century based on earlier concepts of weight-driven clocks and mechanical devices.
Alan Turing developed his Turing machines during 1936-37 and again in 1939 while Alonzo Church introduced lambda calculus in 1936. These theoretical frameworks established the mathematical foundation for effective calculability through Gödel-Herbrand-Kleene recursive functions published between 1930 and 1935.