20 Mathematicians Whose Invisible Work Powers Daily Life, From GPS to Encryption

Key facts

• Al-Khwarizmi's ninth-century treatise on calculation, written around 820 CE, gave both algebra and the algorithm their names.
• René Descartes introduced the coordinate system in 1637, which now underlies every digital map and GPS calculation.
• Gottfried Leibniz worked out the modern binary number system in a 1703 paper, which became the operating language of all digital hardware.
• George Boole published 'An Investigation of the Laws of Thought' in 1854, introducing true/false logic that runs every microchip.
• Clifford Cocks invented a working system of public-key cryptography in 1973, four years before RSA was published, but his work remained classified for 24 years.
• Katherine Johnson calculated the trajectory for Alan Shepard's 1961 flight and later contributed to Apollo 11; John Glenn requested she personally verify his 1962 trajectory calculations over an early computer's output.
• The 20 mathematicians span more than 1,000 years and four continents, from ninth-century Baghdad to 20th-century NASA.
• The article emphasizes direct, traceable links between one person's proof and one piece of daily life, not a ranking of history's greatest mathematicians.