OGC TOK: Mathematics

Knowledge Questions & Mathematics

Scope

• Is absolute certainty attainable in mathematics?
  • How Imaginary Numbers were Invented, video
  • Godel's Incompleteness Theorem, video
  • Math is the Hidden Secret to Understanding the World, video
• Is mathematics better defined by its subject matter or its method?
  • Do Numbers EXIST? video
  • The Complete Fun to Imagine with Fenyman, video
• Does mathematics only yield knowledge about the real world when it is combined with other areas of knowledge?
  • Why you can't say "Math is certain", video
  • Is Mathematics Invented or Discovered? video
  • The Map of Mathematics, video

Perspectives

• What is it about mathematics that enables mathematical results to remain unchanged over time?
  • Different Cultures, Different Math? video
• What is the role of the mathematical community in determining the validity of a mathematical proof?
  • Mathematics is about Progress, Adventure, and Emotion
• If mathematics is created by humans, is it still possible to accept mathematical truths as objective facts about the world?
  • What's the difference between Math and Physics? video

Methods & Skills

• What is meant by the term “proof” in mathematics, and how is this similar to, or different from what is meant by this term in other areas of knowledge?
  • Why algorithms are called algorithms, video
• How do mathematicians reconcile the fact that some conclusions seem to conflict with our intuitions?
• How is an axiomatic system of knowledge different from, or similar to, other systems of knowledge?
  • Euclid's First Four Postulates, video

Ethics

• On what criteria could we decide whether mathematicians should be held responsible for unethical applications of their work?
• How are unethical practices, such as “data dredging”, used by statisticians to deliberately manipulate and mislead people?
• Do mathematical judgments and ethical judgments face similar challenges in terms of the evidence available to support them?
  • Math's Fundamental Flaw, video
  • Ethics in Maths, video channel

Want more questions? See HERE via the IBO

Key Concepts for Mathematics

Proof

• What is "proof" to mathematicians?  Is this different from proof in other AOKs?
  • An Introduction to Mathematical Theorems, video