Theory of Knowledge
Theory of Knowledge
13
Chapters
165
Notes
Chapter 1 - Knowledge & The Knower(Core)
Chapter 1 - Knowledge & The Knower(Core)
Chapter 2 - Knowledge & Technology(Optional)
Chapter 2 - Knowledge & Technology(Optional)
Chapter 3 - Knowledge & Language(Optional)
Chapter 3 - Knowledge & Language(Optional)
Chapter 4 - Knowledge & Politics(Optional)
Chapter 4 - Knowledge & Politics(Optional)
Chapter 5 - Knowledge & Religion(Optional)
Chapter 5 - Knowledge & Religion(Optional)
Chapter 6 - Knowledge & Indigenous Societies(Optional)
Chapter 6 - Knowledge & Indigenous Societies(Optional)
Chapter 7 - History(AoK)
Chapter 7 - History(AoK)
Chapter 8 - The Human Sciences(AoK)
Chapter 8 - The Human Sciences(AoK)
Chapter 9 - The Natural Sciences(AoK)
Chapter 9 - The Natural Sciences(AoK)
Chapter 10 - The Arts(AoK)
Chapter 10 - The Arts(AoK)
Chapter 11 - Mathematics(AoK)
Chapter 11 - Mathematics(AoK)
Chapter 12 - ToK Exhibition
Chapter 12 - ToK Exhibition
Chapter 13 - ToK Essay
Chapter 13 - ToK Essay
IB Resources
Chapter 11 - Mathematics(AoK)
Theory of Knowledge
Theory of Knowledge

Chapter 11 - Mathematics(AoK)

The Evolution of Mathematical Thought: From Enlightenment to Today

Word Count Emoji
586 words
Reading Time Emoji
3 mins read
Updated at Emoji
Last edited on 14th Jun 2024

Table of content

Mathematics & its cultural evolution

  • Mathematical knowledge may seem timeless, yet its creation and development is embedded in cultural contexts and has significantly changed over time.

  • For instance, during the 18th-century Europe, mathematicians were perceived as 'natural men', thought to unveil the hidden mathematical structure of the universe. They were appreciated for their simplicity, purity, and detachment from societal rivalries and jealousies.

Real-world example: Think of Sir Isaac Newton, whose mathematical and scientific contributions during the Enlightenment era were significant and widely accepted.

Shifts in the mathematical perspective

  • Over time, perspectives on mathematics shift with the norms and values of mathematical communities.

  • During the 19th century, a new generation of mathematicians emerged. They were more concerned with the internal architecture of mathematics itself - its interconnections and the precise meaning of its statements. They saw mathematics as its own self-contained world, judged by mathematical standards alone.

Real-world example: Consider Georg Cantor, a 19th-century mathematician. He delved deep into abstract mathematical concepts, focusing on the concept of infinity, a perspective considered radical at the time.

Mathematics & disagreements

  • Despite the potential for differences in perspective, disagreements in mathematics seem to be easier to resolve than in other fields.

  • This could be due to the nature of mathematical practices or the efficiency of the mathematical community in resolving conflicting perspectives.

Real-world example: In most scientific debates, there are multiple competing theories. However, in math, once a theorem is proven, it's universally accepted - like Pythagoras' theorem.

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IB Resources
Chapter 11 - Mathematics(AoK)
Theory of Knowledge
Theory of Knowledge

Chapter 11 - Mathematics(AoK)

The Evolution of Mathematical Thought: From Enlightenment to Today

Word Count Emoji
586 words
Reading Time Emoji
3 mins read
Updated at Emoji
Last edited on 14th Jun 2024

Table of content

Mathematics & its cultural evolution

  • Mathematical knowledge may seem timeless, yet its creation and development is embedded in cultural contexts and has significantly changed over time.

  • For instance, during the 18th-century Europe, mathematicians were perceived as 'natural men', thought to unveil the hidden mathematical structure of the universe. They were appreciated for their simplicity, purity, and detachment from societal rivalries and jealousies.

Real-world example: Think of Sir Isaac Newton, whose mathematical and scientific contributions during the Enlightenment era were significant and widely accepted.

Shifts in the mathematical perspective

  • Over time, perspectives on mathematics shift with the norms and values of mathematical communities.

  • During the 19th century, a new generation of mathematicians emerged. They were more concerned with the internal architecture of mathematics itself - its interconnections and the precise meaning of its statements. They saw mathematics as its own self-contained world, judged by mathematical standards alone.

Real-world example: Consider Georg Cantor, a 19th-century mathematician. He delved deep into abstract mathematical concepts, focusing on the concept of infinity, a perspective considered radical at the time.

Mathematics & disagreements

  • Despite the potential for differences in perspective, disagreements in mathematics seem to be easier to resolve than in other fields.

  • This could be due to the nature of mathematical practices or the efficiency of the mathematical community in resolving conflicting perspectives.

Real-world example: In most scientific debates, there are multiple competing theories. However, in math, once a theorem is proven, it's universally accepted - like Pythagoras' theorem.

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Dive deeper and gain exclusive access to premium files of Theory of Knowledge. Subscribe now and get closer to that 45 🌟