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The Growth of Mathematical Knowledge

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"The Growth of Mathematical Knowledge" by Emily Grosholz, Herbert Breger is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

This book draws its inspiration from Hilbert, Wittgenstein, Cavaillès and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences.

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Best For: Readers interested in the philosophy and history of mathematics
Focus: Examining the growth of mathematical knowledge through historical and logical analysis
Covers: Philosophical theses inspired by Hilbert, Wittgenstein, Cavaillès, and Lakatos presented in dialogical form
Why It Matters: It shifts the focus from foundations to the development of mathematical rationality over time

"The Growth of Mathematical Knowledge" by Emily Grosholz, Herbert Breger is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.

Topic: Core Mathematics

Author: Emily Grosholz, Herbert Breger

Who this is for:

  • Teachers and classroom instructors
  • Students building subject mastery
  • Readers looking for practical learning support

Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.

This book draws its inspiration from Hilbert, Wittgenstein, Cavaillès and Lakatos and is designed to reconfigure contemporary philosophy of mathematics by making the growth of knowledge rather than its foundations central to the study of mathematical rationality, and by analyzing the notion of growth in historical as well as logical terms. Not a mere compendium of opinions, it is organised in dialogical forms, with each philosophical thesis answered by one or more historical case studies designed to support, complicate or question it. The first part of the book examines the role of scientific theory and empirical fact in the growth of mathematical knowledge. The second examines the role of abstraction, analysis and axiomatization. The third raises the question of whether the growth of mathematical knowledge constitutes progress, and how progress may be understood. Readership: Students and scholars concerned with the history and philosophy of mathematics and the formal sciences.

AuthorEmily Grosholz, Herbert Breger
PublisherBoom Koninklijke Uitgevers
Published2000-01-31
ISBN-139780792361510
BindingHardcover
Pages480
LanguageEnglish
SubjectsHistory
TopicCore Mathematics
SeriesSynthese Library

Format: Hardcover

Length: 480 pages

Language: English

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