Projects work well for this course because they force you to connect proof, explanation and argument. Choose one narrow problem and take it seriously, rather than writing a broad survey of “maths and philosophy”.
A good project should leave you with something you can discuss under questioning. The best evidence is often a written solution, a short essay, or a corrected notebook showing how your thinking developed.
How to present a project:
- Why you did it.
- What the project is.
- How you did it.
- What went wrong.
- What you did about it.
- What you learned.
A proof portfolio could compare direct proof, contradiction, induction and construction across three mathematical results.
An infinity, paradox and foundations project could examine Cantor’s diagonal argument, Hilbert’s hotel, Russell-style paradoxes or Gödel’s incompleteness theorems.
A philosophy of mathematics case study could compare platonism, formalism, logicism or structuralism through a concrete example such as natural numbers, sets, limits, imaginary numbers or induction.