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What is BookofProofs?

BookofProofs (BoP) is an open online book dedicated to mathematics, physics or computer science, which is completely written by the Internet community. It can be browsed (and downloaded - working on it) completely for free and for educational purposes. It is also our policy to keep the book as a pure educational resource, which is free of advertising.

Mission statement

The mission of BoP is to promote the competency of thinking logically and formulating proofs as basic skills rather than something reserved for academia, to broaden the knowledge of the axiomatic method, and to drive awareness of its supreme importance for any kind of scientific progress.

Unlike article-based wikis structuring all information by categories, BoP is structured more like an open book, in which you can create parts, chapters, sections, and subsections, and develop the theories by adding theorems, proofs, definitions, examples, explanations, exercises, and solutions. The book contains only tagged entries, i.e. each entry has a unique id, which makes it referenceable independently from the structure of the book.

BoP's unique features

A unique feature of BoP is that some hyperlinks - those, which are contained in proofs and in definitions - are not only used to better navigate through the book but have a special meaning and follow a strict pattern: The pattern allows for tracking the logical predecessors and the logical successors of all theorems and definitions. This feature strictly follows the axiomatic method, enabling the reader to recognize, which theorems or definitions follow logically from which other theorems or definitions, and to track this logical chain back to the axioms, upon which a theory is based. It is also possible to follow a theory the other way round - starting with axioms, and identifying one-by-one all the theorems or definitions derived from them in a theory.

To make this pattern work, it is important that each theorem, lemma, proposition, and corollary has at least one proof and that its text body contains exactly those hyperlinks, which are necessary for the logical conclusions in the proof. The same restrictions apply for hyperlinks which have to be included in the text body of each definition. Other types of hyperlinks, i.e. those contained in the text body of the theorems themselves, in examples, in explanations, in exercises, won't do the trick, and will be ignored when tracking the logical chain. Nevertheless, you are encouraged to set also such hyperlinks to make it easier for the reader to navigate through the book.

As the same mathematical theories and concepts can be derived from different sets of axioms, only one of these possibilities could be depicted in the logical structure of BoP. In accordance with the mission statement, it is not the goal of the book to provide means of deriving mathematical theories from any possible sets of axioms but rather to focus on one valid way and on promoting and demonstrating the power of the axiomatic method as a tool and achievement of human thinking.

Another important feature of BoP is that it does not consist of separate self-contained open books, one for each discipline. This means for you as a co-author that it is not necessary (and not allowed) to reintroduce mathematical concepts already defined in the book (like e.g. sets, functions, numbers, ...), just because you need using the concepts in the branch of mathematics you are currently working on. This means for you as a reader that, throughout all disciplines of BoP, all mathematical concepts are introduced and defined only once. Thus, they remain always referenced consistently and, if needed, can quickly be re-stated/corrected at a central place. Every catalog entry has been thoroughly reviewed to ensure high quality and avoid such redundancies. Unless it is absolutely necessary (for instance in case of branch-specific conventions), we also pay particular attention to keeping a unique notation of all mathematical concepts throughout the whole book.

How to contribute?

The BoP project is a collaborative effort. With your help, this book will become more comprehensive and cover at least all main branches of modern mathematics, theoretical physics, and computer sciences. The growing library of BoP currently consists of 5669 entries, contributed since 1 May 2014 (launch of the project) by 85 author(s). Last updates were provided 1 month ago. There is a list of people who have contributed so far, according to badges collected for contributing. While browsing the site please provide feedback by leaving a comment. Please correct any errors you encounter directly in the online version of the book. Another option is to post new or edit existing results. For more details please visit our help page.

You can also support us by giving us backlinks, or like us on social media!

Register to get free access to all contents and to contribute! Currently, we are e.g. looking for contributors in the following parts and chapters of the book:

rss Project Log

19 February 2017

Euclid's “Elements” - all 13 books now available on bookofproofs.org!

Euclid's “Elements” - a modern translation of all 13 books of this masterpiece prototype of the axiomatic method is now available on bookofproofs.org.

More Project Log

1 September 2016

BoP meets Python!

We decided to replace the original pseudo code algorithm engine by Python syntax highlighting. Python is a great, powerful and easy-to-learn programming language and comes out with thousands of free libraries. Now you can share your awesome Python algorithms under the CC-BY-SA license.

1 February 2016

BoP goes mobile!

We have improved the user friendliness and availability of our site on mobile devices, including smartphones and tablets.

24 May 2015

BoP goes interactive!

Bring mathematics to life and enjoy our documents containing interactive demonstrations on devices running iOS, Android, firefoxOS, Windows 8 (at least). If you are a BoP author (or want to become one), its now very easy to embed your or other people's own mathles into your articles, based on JSXGraph (project of the University of Bayreuth, Germany).

1 December 2014

Contribute to BoP as a Guest

You do not need to register in order to edit the contents of BookOfProofs. Contributing to BoP's Initiative is now easier than ever before! Check it out!

17 August 2014

A step-by-step introduction for adding your content provided

Adding or editing content of BookOfProofs is very easy, but slightly different from blogs or other wikis you might find on the Internet. Learn in a short step-by-step introduction how.

4 June 2014

BookOfProofs introduces an experimental visualization of the axiomatic method.

Proofs are the strength of mathematics and the axiomatic method is what makes them so powerful - based on simple axioms and using logical reasoning one proves theorems, and based on these theorems one proves even more theorems, and so forth - like a snow ball. BookOfProofs introduces a visualization of this principle by attaching clickable graphics to each axiom, definition and theorem (learn more in "The Axiomatic Approach on BookofProofs"). These structures are dynamic. This means that adding a hyperlink to a proof of a theorem A, which refers to a theorem B, will be visualized by showing that the theorem B logically proceeds the theorem A. This logical chain can be followed backward to simple axioms and definitions or forward to more and more deep theoretical results.

1 May 2014

Going life.

The site's mission statement is to be an open community project to create a cartography of existing mathematical results ("what follows from what?"). The site aims to bring the mathematical ways of approaching and solving problems to a broader public. It contains a first draft top-down table of contents of mathematical topics, which can also be used for easy navigating the site. Some of the topics contain first definitions, theorems, proofs and examples. All interested visitors are kindly invited to contribute to the project.

7 February 2014

The site bookofproofs.org (BookOfProofs) is born.

Working on a proof of concept, the site is not publicly available yet.


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