History and philosophy of maths · Accessible · Dissertation

How zero became a number: a maths EPQ idea

Why it works as an EPQ

Place value, arithmetic rules and the problem of dividing by zero, traced through several cultures.

Scope and difficulty

Accessible. Accessible. Two or three key stages and the mathematical difficulty at each.

The maths

Builds on these A Level topics: Algebra and functions · Proof.

You would learn:

• Place-value systems
• Early rules for zero
• Why division by zero is undefined

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

One possible plan

1. Compare number systems with and without zero.
2. Study early written rules for arithmetic with zero.
3. Show why 0 ÷ 0 and a ÷ 0 cannot be defined consistently.
4. Judge what the delay shows about how mathematics develops.

Pitfalls

• Unsourced claims about who was 'first'.
• Using only one culture's story.

Where to start reading

• MacTutor History of Mathematics (University of St Andrews)
• Search for: Brahmagupta rules for zero

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.