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Maths › 01. History and Biography ›

1.2 Number Concepts

From objects to ideas Early counting connects directly to objects. People count three stones, five animals, or ten tools. Each number stays tied to a specific collection. Over time, a shift occurs. The idea of “three” starts to exist on its own, independent of what is being counted. This shift matters. Once you understand “three” as a general idea, you can apply it anywhere. Three apples, three days, and three...

Maths › 01. History and Biography ›

1. Prehistoric and Early Counting

Chapter 1. Prehistoric and Early Counting Mathematics begins in practical activity. Early humans needed to track quantity, compare sizes, and organize their environment. These needs produced the first forms of counting and measurement. This chapter examines how these basic ideas appeared and how they shaped later mathematics. At this stage, mathematical thinking stays close to daily life. People count animals, measure land, track time, and divide resources. Each task requires...

Maths › 01. History and Biography ›

1.1 Tally Systems

Counting with marks The earliest way to count uses marks. A person makes one mark for each thing they want to count. If there are three animals, they draw three lines. If there are ten, they draw ten lines. Each mark stands for one object. You can see the total just by looking at the marks. This idea is simple but important. You match each object with one mark. This...

Maths › 01. History and Biography ›

Preface

Mathematics is often presented as a finished structure: definitions, theorems, proofs, and formal systems arranged in logical order. This presentation is useful for learning results, but it hides an essential aspect of the subject. Mathematical ideas did not appear fully formed. They emerged gradually, in response to concrete problems, cultural needs, and intellectual traditions. This volume focuses on that process. The scope follows the classification MSC 01, which concerns the...

Maths ›

01. History and Biography

This volume traces the evolution of mathematical ideas, methods, and communities. The scope follows MSC 01: historical development, primary sources, and biographies of mathematicians. The emphasis stays on how concepts emerged, stabilized, and influenced later work. Part I. Origins of Mathematics Chapter 1. Prehistoric and Early Counting 1.1 Tally systems and artifacts 1.2 Emergence of number concepts 1.3 Measurement and geometry in early societies 1.4 Oral vs written transmission 1.5...

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1.2 Number Concepts

1. Prehistoric and Early Counting

1.1 Tally Systems

Preface

01. History and Biography