Book Reviewed: The Secret Lives of Numbers: A Hidden History of Math's Unsung Trailblazers by Kate Kitagawa and Timothy Revell

The marginalized voices who propelled mathematics This is a focused history of mathematics illuminating the marginalized voices across the globe who propelled the discipline of numbers that include thousands of years of untold stories. The history of mathematics is often associated with Europeans like Euclid, Pythagoras, and Newton. However, many pioneers who made significant contributions to the field are unsung heroes from non-European countries with diverse backgrounds such as India, China, and Mesopotamia (ancient Iraq). In the fourteenth century, a school of Mathematics in Kerala (a Southern state), India was a melting pot for mathematicians. Its founder, Madhava of Sangarnagrama was a brilliant mathematician, among his achievements was describing a theory of calculus. He explored the key ideas that make calculus possible which were then honed by successive mathematicians at the Kerala school. A long list of Indian mathematicians includes Aryabhata (476–550 CE) known for discovering decimal System, Place Value, and Pi (π) value, Brahmagupta (598–668 CE) first to establish clear rules for using zero in calculations, introduced the concept of negative numbers, solutions to quadratic equations, and proposed gravitational force. Bhaskara I (600–680 CE) gave more accurate approximation of the sine function, Bhaskara II (1114–1185 CE) worked on properties of cyclic quadrilaterals and differential calculus, and expanded on the ideas of gravity. Madhava of Sangamagrama (1340–1425 CE), the founder of the Kerala School of Mathematics (14th–16th century) worked on Infinite Series for trigonometric functions like sine, cosine, and arctangent. Srinivasa Ramanujan (1887–1920) was a self-taught Indian mathematician whose work has significantly influenced various areas of mathematics, including number theory, continued fractions, and infinite series. Though he did not work directly on string theory, his mathematical discoveries, particularly his insights into modular forms, partition functions, and special functions found relevance in theoretical physics. Despite having little formal training, his intuitive understanding of complex mathematical ideas earned him recognition by Cambridge mathematician G.H. Hardy. The Babylonians used mathematics for many practical purposes, including splitting plots of land and calculating tax. Some clay-tablet writers recorded revenues and budgets, and so familiarized themselves with numbers. Hypatia of Alexandria (360–415 CE) was long known as the earliest woman mathematician, in fact, that honor goes to Ban Zhao (45–116 CE) a Chinese historian, mathematician, and scholar during the Eastern Han dynasty best known for her work as a historian and also proficient in mathematics and astronomy. She assisted in the development of calendrical science and participated in projects related to the Han calendar. Pioneering women mathematicians like Sofya Kovalevskaya (1850–1891) and Mary Jackson found inspiration in the work of earlier women who had defied societal norms like Émilie du Châtelet, a French mathematician and physicist who translated and expanded upon the works of Isaac Newton. African American mathematicians like Elbert Frank Cox (1895–1969), William Schieffelin Claytor (1908–1967), Walter Richard Talbot Woodard (1874–1952), Mary Jackson (1921–2005), and Martha Euphemia Lofton Haynes (1890–1980) contributed significantly to mathematics when opportunities for African Americans were limited. These inspirations reflect a deep, interconnected web of intellectual and personal influences that crossed boundaries of geography, race, gender, and time. The author’s road to rediscovering the forgotten and ignored contributions of non-Europeans to mathematics could have included a little more history.