Welcome to the Book of Proofs (BoP)

BoP is a site for people interested in and enthusiastic with mathematics. By creating this site, we want to bring the concept of mathematical proofs, reasoning, its underlying thought processes, imagination and inventiveness outside the academic world - to a broader public. We hope that this site will propagate the mathematical proof as a unique approach of thinking that helps us, humans, to replace our mere assumptions and experiences by convincing certainty.

Motivation

Many people - including the initiator of this site - were taught in school to identify mathematics with arithmetics and formulas. This is still a widespread misunderstanding of mathematics and - it's wrong! The truth is that the real soul of mathematics cannot be found in arithmetics but it can be found in mathematical proofs. Unfortunately, this is not known to the broad public.

This widespread misunderstanding of mathematics is paradoxical, since mathematics is the foundation of our progress. Without it, no flights to the moon, no Internet and no technological achievements would be possible. What is even more astonishing, the world around us seems to have a fundamentally mathematical nature. This is confirmed by experiments in classical natural sciences like physics, chemistry or biology, as well as in the theory of relativity, quantum mechanics and cosmology.

How exactly does BoP work?

We're a little bit different from other sites. Here is how:

• BoP's mission is to become the most exhaustive free resource of mathematical sciences world-wide.
• BoP's goal is to reassemble deep mathematical results and concepts gained through the centuries and bring them to the broad public.
• BoP is built and run totally by you as part of our community. Contribute to it yourself, vote for contributions or become a reviewer.
• BoP is supposed to apply modern standards of mathematical formalism and preciseness, still being easy to understand through explanatory examples, interpretations and applications.

What is BoP not?

In contrast to other mathematical wikis, BoP is not based on writing articles to specific subjects. Nor it is a question & answer site for people seeking solutions to exam exercises. Instead, you can think of BoP as a dynamic, growing LaTeX document, in which each mathematical discipline is hierarchically structured into branches, parts, chapters, sections and subsections. In each of these, diving into different levels of detail and complexity in the mathematical discipline, you can find contributions. As stated before, these contributions are not articles, like you may find it in other wikis on the web. Instead, each contribution belongs to exactly one of the following categories:

• axiom,
• definition,
• theorem (you can distinguish between a theorem, a corollary, a lemma or a proposition),
• algorithm (BoP has a nice rendering engine for this),
• open problem (conjecture),
• proof,
• bibliographic entry.

The content of all contributions of these categories must follow modern standards of mathematical formalism, i.e. stuff like examples, motivations, etc. has to be excluded from such contributions. It can, however, be submitted in other contributions, having the corresponding categories, including:

• motivation,
• example,
• application,
• interpretations,
• explanation,
• historic entry, including centuries, events, and portraits of mathematicians.

All contributions, regardless which category they belong to, can be commented in a separate blog.

What is unique about BoP is that it is a self-learning catalogue.

Following the above rules, you might find some contributions very "short". As an example, the theorem stating that there are infinitly many primes is a quite short contribution (as short as the statement it contains). The first advantage is that mathematical statements like this should be free of any superfluous content. Following modern standards, all additional content is banished to related contributions, which might be attached to the statement. The second and biggest advantage, however, is that an arbitrary number of proofs can be now attached to this statement and sorted by different criteria, including the votes of users interested in the topic (see screenshot below): This principle is the most important feature, which is unique to the site of BoP. As users of BoP view and vote for the contributions of different categories, the catalogue uses this information as a powerful, self-learning feature to help other users to find the most interesting stuff.

How can you contribute to the BoP project?

You can contribute to the project in three different ways.

Write and submit your content

First of all, you can write and submit new content to the project or edit existing one. Your content will be licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License. All authors will be attributed accordingly in a version history. To give you some idea, on which type of content you can participate, visit our site explaining badges you can get.

Vote

Voting is only possible for registered users. You can vote for the mathematical correctness, preciseness and beauty of each contribution (e.g. a proof, a definition, an explanation, en example, etc.) separately. Learn more...

Discuss

Like for voting, each contribution has its separate discussion blog, where you can comment on the existing mathematical content or discuss changes to it. This is possible for registered users only.

Tell a friend

If you find this project interesting, tell about us to your friends.