History and philosophy of maths · Solid · Dissertation

Maths and the breaking of Enigma: a maths EPQ idea

Why it works as an EPQ

The permutation mathematics behind Enigma is accessible, and weighing it against operator errors and captured material is a real historical judgement.

Scope and difficulty

Solid. Solid. Explain the mathematics of the machine and one method, such as the Polish work on permutations.

The maths

Builds on these A Level topics: Probability · Proof.

You would learn:

• Permutations and cycle structure
• Counting the key space
• Cribs

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

One possible plan

1. Count the machine settings and explain why brute force failed.
2. Explain one mathematical attack in detail.
3. Weigh the other factors using historical sources.
4. Judge mathematics' share of the success.

Pitfalls

• Film-based history.
• Counting settings without stating the assumptions.

Where to start reading

• The Code Book (Simon Singh)
• Search for: Rejewski permutation cycles Enigma

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

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All history and philosophy of maths ideas · all 93 ideas

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.