History and philosophy of maths · Solid · Dissertation

Is maths discovered or invented?: a maths EPQ idea

A title to start from

Is mathematics discovered or invented? Weighing Platonism against formalism

A starting point, not your title. Change the case, the data or the comparison until it is yours, then agree it with your supervisor. Check your title.

Why it works as an EPQ

A classic question that becomes an EPQ when every claim is tested against real mathematical examples.

Scope and difficulty

Solid. Solid. Two positions, three or four worked examples, a reasoned verdict.

The maths

Builds on these A Level topics: Proof.

You would learn:

Platonism, formalism and intuitionism
Non-Euclidean geometry as a test case
Imaginary numbers as a test case

Learning maths beyond the course is expected in a maths EPQ, but you must understand and explain everything you use.

One possible plan

Set out the main positions fairly.
Choose examples that each position explains well or badly.
Work through the mathematics of each example.
Reach a judgement and answer the strongest objection.

Pitfalls

An essay with no mathematics in it.
Strawman versions of a position.

Where to start reading

The Mathematical Experience (Philip Davis and Reuben Hersh)
Mathematics: A Very Short Introduction (Timothy Gowers)

Prefer books, lecture notes, journal articles and official data to a single website, and record every source as you read (how to reference).

Next steps

Check your title Plan your timeline

Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.

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