Mathematical Thought from Ancient to Modern Times

Morris Kline

Get ready to dive into the intriguing history of mathematics with Morris Kline’s captivating book. Unlike philosophy or literature, mathematics doesn’t have a conventional history, making this neglected field of study all the more fascinating.

Kline takes a unique approach by striking a balance between depth and accessibility. He gives the Greeks only 15% of the spotlight, briefly mentioning the Egyptians, Arabs, and Renaissance, before focusing on the revolutionary René Descartes.

Kline’s passion for synthetic geometry shines through as he brings Greek geometry to life. Instead of overemphasizing the human aspects, he expertly translates the brilliance of Greek geometry into modern language. He even highlights the often overlooked figures like Apollonius.

The book reaches its climax with the chapters on nineteenth-century analysis. Kline’s expertise in the subject makes this section a joy to read. His blending of historical development with a clear, linear description gives readers a comprehensive overview of mathematics up to the turn of the century.

While the book excels in many ways, there are some limitations. The chapters on differential geometry may be difficult for students trained in recent years, as they lack contemporary notation. Kline also takes a conservative approach to functional analysis and topology, which differs from current practices in graduate courses.

Despite any criticisms, this 1200-page treasure deserves a spot on your shelf. It is, without a doubt, the best book on mathematical history available.