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Cambridge Elements in the Philosophy of Mathematics
A Concise History of Mathematics for Philosophers
This Element aims to present an outline of mathematics and its history, with particular emphasis on events that shook up its philosophy. It ranges from the discovery of irrational numbers in ancient Greece to the nineteenth- and twentieth-century discoveries on the nature of infinity and proof. Recurring themes are intuition and logic, meaning and existence, and the discrete and the continuous. These themes have evolved under the influence of new mathematical discoveries and the story of their evolution is, to a large extent, the story of philosophy of mathematics.
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Published June 30, 2019
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About the author
John Stillwell
51 books60 followersJohn Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University
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Displaying 1 - 2 of 2 reviews
August 20, 2025
How can we think about unfamiliar ideas and fields in our non-mother-tongue language? This review reveals my answer to this situation!
In A Concise History of Mathematics for Philosophers by John Stillwell, which is one of the Cambridge Elements in the Philosophy of mathematics series, the author tries to show us a brief history of mathematics in a landscape that connects mathematical problems and concepts to philosophical terms and ideas.
Every person has their own curiosity, and our internal desire drives us to read such a challenging book, like the one I am reading now (the present book I am talking about)! My first and most important motivation for reading this book is philosophical concerns, but that is not the only one.
One of my personal ideas about reading is that some people must be the translators of one subject to another. A person who takes this role for themselves must be deeply drawn into every field they try to translate!
Reading this book is one of my attempts to walk a path toward that purpose.
وسطنوشت: البته فکر کنم دیگه ادامهاش ندم این مسیر خاص رو. مصداق بارز ثبات قدم هستم :)
In his book, Stillwell's aim is to present a brief history of mathematics in one introduction and nine chronological chapters:
Irrational Numbers and Geometry
Infinity in Greek Mathematics
Imaginary Numbers
Calculus and Infinitesimals
Continuous Functions and Real Numbers
From Non-Euclidean Geometry to Arithmetic
Set Theory and Its Paradoxes
Formal Systems
Unsolvability and Incompleteness
In the beginning of the reading, I supposed that the last chapters (for instance, "Set Theory and Its Paradoxes" and "Formal Systems") would be the most engaging to me. But because of the author's tricks, the presentation of topics in the book had its charms from the beginning and was not limited to a few attractive chapters.
What are those tricks?
In every chapter, the author tries to satisfy two major dualities:
intuition vs. logic
discrete vs. the continuous
I mean that at the end of every chapter, Stillwell tries to connect the mathematical concerns to philosophical concerns by tracing answers to these dualities through the history of mathematics!
I think It must be OK for my first try to write book review in English!
In A Concise History of Mathematics for Philosophers by John Stillwell, which is one of the Cambridge Elements in the Philosophy of mathematics series, the author tries to show us a brief history of mathematics in a landscape that connects mathematical problems and concepts to philosophical terms and ideas.
Every person has their own curiosity, and our internal desire drives us to read such a challenging book, like the one I am reading now (the present book I am talking about)! My first and most important motivation for reading this book is philosophical concerns, but that is not the only one.
One of my personal ideas about reading is that some people must be the translators of one subject to another. A person who takes this role for themselves must be deeply drawn into every field they try to translate!
Reading this book is one of my attempts to walk a path toward that purpose.
وسطنوشت: البته فکر کنم دیگه ادامهاش ندم این مسیر خاص رو. مصداق بارز ثبات قدم هستم :)
In his book, Stillwell's aim is to present a brief history of mathematics in one introduction and nine chronological chapters:
Irrational Numbers and Geometry
Infinity in Greek Mathematics
Imaginary Numbers
Calculus and Infinitesimals
Continuous Functions and Real Numbers
From Non-Euclidean Geometry to Arithmetic
Set Theory and Its Paradoxes
Formal Systems
Unsolvability and Incompleteness
In the beginning of the reading, I supposed that the last chapters (for instance, "Set Theory and Its Paradoxes" and "Formal Systems") would be the most engaging to me. But because of the author's tricks, the presentation of topics in the book had its charms from the beginning and was not limited to a few attractive chapters.
What are those tricks?
In every chapter, the author tries to satisfy two major dualities:
intuition vs. logic
discrete vs. the continuous
I mean that at the end of every chapter, Stillwell tries to connect the mathematical concerns to philosophical concerns by tracing answers to these dualities through the history of mathematics!
I think It must be OK for my first try to write book review in English!
September 21, 2023
This history of math sure is concise! I never get tired of this story. It's very accessible and doesn't go past the middle of the 20th century.
Displaying 1 - 2 of 2 reviews