Theory of Knowledge
13
Chapters
165
Notes
Chapter 1 - Knowledge & The Knower(Core)
Chapter 2 - Knowledge & Technology(Optional)
Chapter 3 - Knowledge & Language(Optional)
Chapter 4 - Knowledge & Politics(Optional)
Chapter 5 - Knowledge & Religion(Optional)
Chapter 6 - Knowledge & Indigenous Societies(Optional)
Chapter 7 - History(AoK)
Chapter 8 - The Human Sciences(AoK)
Chapter 9 - The Natural Sciences(AoK)
Chapter 10 - The Arts(AoK)
Chapter 11 - Mathematics(AoK)
Chapter 12 - ToK Exhibition
Chapter 13 - ToK Essay
Theory of Knowledge
Chapter 11 - Mathematics(AoK)
The Allure of Numbers: Beauty in Mathematics Unveiled
745 words
4 mins read
Last edited on 5th Nov 2024
Introduction
- Definition of Beauty: Beauty, especially in mathematics, is subjective. Just as someone might appreciate Beethoven’s Ninth Symphony, mathematicians find beauty in numbers and equations. If you can't see the beauty in them, it's difficult for someone else to explain it to you.
Mathematical aesthetics
- Mathematics and Beauty: Mathematicians often recognize beautiful proofs or results. For instance, Euler’s formula (e^iπ + 1 = 0), has been labeled "our jewel" and "the most remarkable formula in mathematics". It ties together five key mathematical constants: 0, 1, π, e, and i.
- Real-world example: Consider a perfect soccer game where everything seems to fall in place - the passes, the shots, the teamwork. Just as soccer lovers may find such a game beautiful, mathematicians find beauty in well-constructed proofs and equations.
Beauty in the brain
- Science of Aesthetics: A 2014 study using functional magnetic resonance imaging (fMRI) found that experiencing mathematical beauty correlates with emotional activity in the brain in the same way as beauty from other sources. This suggests that an aesthetic sense is universal among practicing mathematicians.
- Real-world example: It's like getting goosebumps when you listen to a beautiful piece of music - your brain is responding emotionally to something it finds aesthetically pleasing.
Deeper beauty
- Deep Beauty: Deep beauty in mathematics refers to results or methods that provide unexpected insights into mathematical structures. Beauty arises from the "inevitability", "unexpectedness", and "economy" of a work.
- Real-world example: Imagine creating a complex LEGO structure without instructions, and it unexpectedly turns out to look like a masterpiece. That surprise and uniqueness are akin to the deep beauty in mathematics.
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Theory of Knowledge
Chapter 11 - Mathematics(AoK)
The Allure of Numbers: Beauty in Mathematics Unveiled
745 words
4 mins read
Last edited on 5th Nov 2024
Introduction
- Definition of Beauty: Beauty, especially in mathematics, is subjective. Just as someone might appreciate Beethoven’s Ninth Symphony, mathematicians find beauty in numbers and equations. If you can't see the beauty in them, it's difficult for someone else to explain it to you.
Mathematical aesthetics
- Mathematics and Beauty: Mathematicians often recognize beautiful proofs or results. For instance, Euler’s formula (e^iπ + 1 = 0), has been labeled "our jewel" and "the most remarkable formula in mathematics". It ties together five key mathematical constants: 0, 1, π, e, and i.
- Real-world example: Consider a perfect soccer game where everything seems to fall in place - the passes, the shots, the teamwork. Just as soccer lovers may find such a game beautiful, mathematicians find beauty in well-constructed proofs and equations.
Beauty in the brain
- Science of Aesthetics: A 2014 study using functional magnetic resonance imaging (fMRI) found that experiencing mathematical beauty correlates with emotional activity in the brain in the same way as beauty from other sources. This suggests that an aesthetic sense is universal among practicing mathematicians.
- Real-world example: It's like getting goosebumps when you listen to a beautiful piece of music - your brain is responding emotionally to something it finds aesthetically pleasing.
Deeper beauty
- Deep Beauty: Deep beauty in mathematics refers to results or methods that provide unexpected insights into mathematical structures. Beauty arises from the "inevitability", "unexpectedness", and "economy" of a work.
- Real-world example: Imagine creating a complex LEGO structure without instructions, and it unexpectedly turns out to look like a masterpiece. That surprise and uniqueness are akin to the deep beauty in mathematics.
Unlock the Full Content!
Dive deeper and gain exclusive access to premium files of Theory of Knowledge. Subscribe now and get closer to that 45 🌟