Scope
- Is absolute certainty attainable in mathematics?
- Is mathematics better defined by its subject matter or its method?
- Does mathematics only yield knowledge about the real world when it is combined with other areas of knowledge?
Perspectives
- What is it about mathematics that enables mathematical results to remain unchanged over time?
- What is the role of the mathematical community in determining the validity of a mathematical proof?
- If mathematics is created by humans, is it still possible to accept mathematical truths as objective facts about the world?
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?
- 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?
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?
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