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The History of Mathematics: A Source-Based Approach (1)
The History of A Source-Based Approach is a comprehensive history of the development of mathematics. This, the first volume of the two-volume set, takes readers from the beginning of counting in prehistory to 1600 and the threshold of the discovery of calculus. It is notable for the extensive engagement with original primary and secondary source material. The coverage is worldwide, and embraces developments, including education, in Egypt, Mesopotamia, Greece, China, India, the Islamic world and Europe. The emphasis on astronomy and its historical relationship to mathematics is new, and the presentation of every topic is informed by the most recent scholarship in the field. The two-volume set was designed as a textbook for the authors' acclaimed year-long course at the Open University. It is, in addition to being an innovative and insightful textbook, an invaluable resource for students and scholars of the history of mathematics. The authors, each among the most distinguished mathematical historians in the world, have produced over fifty books and earned scholarly and expository prizes from the major mathematical societies of the English-speaking world.
- GenresMathematicsHistory
488 pages, Hardcover
Published March 8, 2019
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May 22, 2025
This book gave me a lot of insight into how different cultures throughout history interpreted what it meant to "do mathematics". Some of us are probably aware of the difference between what it means to do math in high school or college (often very calculation-intense and with numbers), versus doing math at the graduate/research level (often very proof-focused with reasoning via logic and words). Some of us might even attach a normative stance to each regarding what's better or worse, or more applied or more pure, etc. However, throughout history sometimes what was considered "properly doing math" fluctuated between calculating things (using a purely verbal / text-based medium of reasoning and no numbers at all!), to calculating things with numbers, to reasoning with symbols, to visual geometric proofs, to a back-and-forth dialogue-like argument, to mechanical methods, to "merely" translating older works from one language to another, and to providing commentary and critique, etc.
Overall, this book depicted some great examples of methodological pluralism throughout the history of maths. I think it would be wise for current students and members of the mathematical community to be somewhat versed in the history of their field such that they don't potentially adopt a particular perspective that one way of exploring mathematical concepts is strictly better than another (not to say that there might exist such a strictly better method, just that it doesn't seem likely given the path dependence of the field and some historical lessons imparted by this book).
Additionally, it was very exciting to be reading the accounts of historical mathematicians side-by-side with copies of their actual works and their various translations, their struggles, reactions to past mathematicians and concepts, and ultimately the philosophical, theological, cultural, economic, and otherwise non-mathematical influences that shaped the trajectory of mathematical ideas and concepts throughout time and geography.
The "source-based approach" advocated and used by this book immersed and embedded me into those historical moments, and I often felt like I was some combination of Indiana Jones deciphering an arcane document mixed with a classical monk translating, reviving, and trying to keep alive the thread of mathematical discourse traveling through time across cultures. As a person who studies mathematics at the amateur-level, as well as academically at the graduate-level, and professionally in the applied industry setting, this made me feel like I was actually *taking part in the Grand Conversation* across time, and me feel very thankful for being part of that.
Overall, this book has *shaped me* and as such I rank it highly.
Overall, this book depicted some great examples of methodological pluralism throughout the history of maths. I think it would be wise for current students and members of the mathematical community to be somewhat versed in the history of their field such that they don't potentially adopt a particular perspective that one way of exploring mathematical concepts is strictly better than another (not to say that there might exist such a strictly better method, just that it doesn't seem likely given the path dependence of the field and some historical lessons imparted by this book).
Additionally, it was very exciting to be reading the accounts of historical mathematicians side-by-side with copies of their actual works and their various translations, their struggles, reactions to past mathematicians and concepts, and ultimately the philosophical, theological, cultural, economic, and otherwise non-mathematical influences that shaped the trajectory of mathematical ideas and concepts throughout time and geography.
The "source-based approach" advocated and used by this book immersed and embedded me into those historical moments, and I often felt like I was some combination of Indiana Jones deciphering an arcane document mixed with a classical monk translating, reviving, and trying to keep alive the thread of mathematical discourse traveling through time across cultures. As a person who studies mathematics at the amateur-level, as well as academically at the graduate-level, and professionally in the applied industry setting, this made me feel like I was actually *taking part in the Grand Conversation* across time, and me feel very thankful for being part of that.
Overall, this book has *shaped me* and as such I rank it highly.
Displaying 1 of 1 review