ProofZoom entries are concise mathematical expositions that clarify a single idea, theorem, or mathematical mechanism. The emphasis is on conceptual understanding, geometric insight, and structural clarity.

Entries should aim to make an important idea transparent to a reader who has appropriate mathematical background but may not be a specialist in the topic.

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Recommended Structure

A typical ProofZoom entry follows this structure.

1. Overview

   Introduce the central idea of the entry.

2. Key Idea

   Present the conceptual insight behind the result.

3. Mathematical Formulation

   Provide necessary definitions and notation.

4. Main Theorem

   State the principal result.

5. Proof

   Provide a clear proof emphasizing the central mechanism.

6. Discussion or Remarks

   Explain the significance of the result.

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References Philosophy

ProofZoom references are not merely “further reading.” They are intended to serve as a map of how an idea came into being and how it has been most clearly understood.

References should reflect the intellectual evolution of the concept, rather than a convenient list of modern sources.

In selecting references, contributors are encouraged to consider three roles:

• Origin — Who first grappled with the idea in a recognizable form?
• Structure — Who clarified and developed the idea into a coherent theory?
• Understanding — Who presents the idea most clearly for today’s reader?

Whenever possible, include at least one source that reflects the early development of the concept. As the founder of ProofZoom observed:

“We benefit from the groppings of the person who first discovered the concept.”

At the same time, include carefully chosen modern sources that provide clarity, precision, and accessibility.

A short, well-justified list of references is preferred over a long bibliography. Each reference should earn its place by illuminating the idea from a distinct perspective.

ProofZoom entries aim to preserve not only mathematical results, but also the path by which they were discovered, refined, and understood.

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Reference Selection Checklist

Before finalizing references, ask:

• Does at least one reference reflect the origin of the idea?
• Is there a source that captures the modern canonical formulation?
• Is there a source that best supports clarity for the intended reader?
• Does each reference contribute something distinct?

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Figures

Figures are encouraged whenever they clarify the structure of an argument.

The preferred format is TikZ, which ensures that diagrams render cleanly in both the PDF and web versions.

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Download Template

A starter LaTeX file for ProofZoom entries can be downloaded here:

Download template:
proofzoom-template.tex

This file already includes the ProofZoom style package and the recommended section structure.

You will also need the ProofZoom style file:

Download style file:
proofzoom.sty

Place both files in the same folder when preparing your entry.

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LaTeX Template