An Informed Guide to Exploring the History of Mathematics: Alternative Recommendations to Kitagawa & Revell’s The Secret Lives of Numbers
The 2024 release by Kate Kitagawa and Timothy Revell, titled The Secret Lives of Numbers: A Global History of Mathematics & Its Unsung Trailblazers, has garnered both praise and criticism from readers and historians alike. While the authors aimed to create a comprehensive, approachable, and “global” narrative on mathematics, the book has faced backlash (notably here and here) for its dramatic flair, inaccuracies, and dubious historical interpretations. This has prompted numerous readers and math aficionados to wonder: If this isn’t suitable, what alternatives exist?
For those in search of a meaningful and precise introduction to the history of mathematics—be it general or regionally focused—there exists a rich array of literature. Some titles appeal to the inquisitive general reader, while others necessitate a more rigorous academic exploration. Below is a thoughtfully curated selection of some of the most esteemed, dependable, and enlightening works that delve into the worldwide advancement of mathematics, spanning from ancient times to the present.
1. Classic General Histories
Carl B. Boyer – A History of Mathematics (3rd ed., with Uta C. Merzbach, Wiley, 2011)
Boyer’s text is considered one of the earliest extensive modern histories of mathematics. It encompasses civilizations such as Mesopotamia, Egypt, Greece, China, India, the Islamic world, and the evolution of European mathematics. It is academically robust, accessible to informed laypersons, and increasingly acknowledges non-European contributions in its latest edition. Although it focuses on Greek and Western advancements, it maintains a global perspective.
Carl B. Boyer – History of the Calculus and Its Conceptual Development (Dover, 1959)
Perfect for those intrigued by the progression of calculus as a concept, despite largely overlooking the Indian Kerala School—a topic recently highlighted. The book remains a rigorous and accurate historical account.
Morris Kline – Mathematical Thought from Ancient to Modern Times (Oxford, 1972)
Kline’s extensive and intricate work is often deemed overly Eurocentric, lacking a nuanced discussion of non-Western traditions. Its encyclopedic format may be overwhelming for newcomers to the subject.
Victor J. Katz – A History of Mathematics (3rd ed., Pearson, 2014)
Now regarded as a fundamental reference, Katz’s text excels in its extensive global inclusivity. It integrates comprehensive examinations of Indian, Chinese, and Islamic mathematics into the broader narrative. For those seeking a more concise version, his Brief Edition (Pearson, 2003) provides a shorter yet still meaningful introduction.
2. Sourcebooks and Reference Works
Victor J. Katz (ed.) – The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Princeton, 2007)
This impressive anthology offers direct access to translated ancient texts, complete with expert analysis. It’s an invaluable tool for committed enthusiasts or students.
Victor J. Katz et al. – Sourcebooks on Greek, Islamic, and Medieval European Mathematics
Additional source collections include:
– Sourcebook in the Mathematics of Ancient Greece (Princeton, 2024)
– Sourcebook in the Mathematics of Medieval Europe and North Africa (Princeton, 2016)
These volumes present contextual excerpts, ideal for those wishing to grasp original mathematical ideas within their historical contexts.
Ivor Grattan-Guinness – The Rainbow of Mathematics (W. W. Norton, 1997)
More of a thematic bibliography than a narrative, Rainbow is perfect for readers eager to explore the academic realm. It’s particularly useful for advanced readers looking for varied themes or methodologies.
Ivor Grattan-Guinness (ed.) – Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (2 volumes, Johns Hopkins, 1994)
A vast academic reference filled with thematic essays and bibliographies. It’s a great resource for consultation but decidedly not for beginners.
3. Specialized Academic Works (Regional or Thematic)
Eleanor Robson – Mathematics in Ancient Iraq: A Social History (Princeton, 2008)
This remarkable volume traverses three millennia of mathematical traditions in Mesopotamia, providing cultural and social insights into the evolution of cuneiform mathematics.
Kim Plofker – Mathematics in India (Princeton, 2009)
A must-read for anyone fascinated by the rich mathematical heritage of ancient and medieval India. Plofker’s narrative is thorough, balanced, and devoid of exaggeration—an essential corrective to several popular misconceptions.
J. L. Berggren – Episodes in the Mathematics of Medieval Islam (Springer, 2003)
A scholarly yet engaging examination of mathematicians and philosophical schools from the Islamic Golden Age. Berggren is recognized as one of the leading experts in this domain.
S. Cuomo – Ancient Mathematics (Routledge, 2001)
Explores the motivations, inquiries, and conceptual frameworks behind Greek and Roman mathematics, challenging modern “presentist” inclinations to impose contemporary views.