ProofZoom welcomes essays from mathematicians who want to make foundational mathematical concepts and important proofs clearer to a broad mathematical audience.
A ProofZoom essay should explain a foundational concept, present a main result, include supporting results leading to it, and give clear proofs. The main exposition should aim for elegance and readability, while optional zoom-ins may be used to resolve local pain points in the proofs.
One source to begin the essay is your own carefully written class notes on a foundational topic. Clearly, you can also begin the essay on a topic you feel is fundamental for mathematics in your area of specialty.
Contributions are of two kinds: one is a complete essay on a foundational topic. The other is Peer Review—a comment or revision on an essay that is already published on ProofZoom; in this case, please refer to the essay number—for example, entry-0009. Your initials and date of submission will be posted in the ‘Updated’ section above the abstract.
Contributors do not need to prepare web pages, Markdown files, YAML headers, HTML, or site formatting. ProofZoom will handle the web presentation.
To submit an essay or peer review, send the following two files:
Submissions may be sent to:
editor@proofzoom.org
A submitted essay should include the following parts.
The title should identify the foundational concept or main result clearly.
The abstract should briefly explain the central idea of the essay and the result or proof being clarified.
The body of the essay should develop the concept carefully and present the main result, supporting results, and proofs.
A ProofZoom essay is not merely a statement of a theorem and proof. It should help the reader see why the result matters, what idea drives the proof, and where the proof’s difficult steps occur.
References should include both historical and modern sources where appropriate.
Historical references help show where the idea came from or how it first emerged. Modern references help the reader locate clear contemporary treatments or standard formulations.
A short, well-chosen list of references is preferred over a long bibliography.
ProofZoom entries may include optional zoom-ins for proof pain points.
A pain point is a step in a proof where a reader may reasonably pause and ask:
When submitting an essay, the author may identify such pain points and provide the corresponding sub-proofs.
These pain points and sub-proofs should be submitted as a separate document, also prepared in LaTeX, together with a compiled PDF.
Thus a full submission may include:
The author may decide initially which proof steps should be treated as pain points. These optional zoom-ins should not clutter the main proof. Their purpose is to keep the main exposition elegant while making difficult local steps available to readers who want them.
Essays should ideally be under 15 pages.
If a foundational concept requires more space, it may be split into more than one ProofZoom essay.
To respect author privacy, ProofZoom does not list institutional affiliation.
Published essays will identify the author by a string formed from the first letters of the parts of the author’s name.
Present foundational concepts elegantly. Provide optional zoom-ins where proofs become painful.