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Wikipedia provides one of the more prominent resources on the Web for factual information about contemporary mathematics, with over 20,000 articles on mathematical topics. It is natural that many readers use Wikipedia for the purpose of self-study in mathematics and its applications. Some readers will be simultaneously studying mathematics in a more formal way, while others will rely on Wikipedia alone. There are certain points that need to be borne in mind by anyone using Wikipedia for mathematical self-study, in order to make the best use of what is here, perhaps in conjunction with other resources.
General points
- Wikipedia is a reference site, not a website directly designed to teach any topic.
- Wikipedia may supplement a textbook by explaining key concepts, but it does not replace a textbook.
- Wikipedia is organized as hypertext, meaning that the information you require may not be on one page, but spread over many pages.
- In technical subjects, the material may also be technical: there is no restriction on the depth of coverage. The lead section of each article is supposed to give a summary accessible to the general reader.
- Wikipedia is a work in progress. Some of our articles are highly polished, while others are in a rougher state. The Wikipedia model relies on volunteers to edit articles, and you're invited to help.
Particular points
Studying mathematics from a reference source is not ideal. Unless you consult Wikipedia to answer a specific question, it is not reasonable to expect instant results.
Mathematics textbooks are conventionally built up carefully one chapter at a time, explaining what mathematicians would call the prerequisites before moving to a new topic. For example, you may think you can study Chapter 10 of a book before Chapter 9, but reading a few pages may then show you that you are wrong. Because Wikipedia's pages are not ordered in the same way, it may be less clear what the prerequisites are, and where to find them, if you are struggling with a new concept.
There is no quick way round the need for prerequisite knowledge, as Euclid is said to have replied to King Ptolemy's request for an easier way of learning mathematics, "there is no Royal Road to geometry". Be prepared for a few moves to get round such blocks, by getting more context. What different readers need by way of introduction will differ widely. Therefore
- follow wikilinks to pages on unfamiliar terms, to orient yourself;
- look at related pages, either under the "See also" section or using the article's categories.
Absences from the encyclopedia
Mathematics is something that is done rather than read. A mathematics textbook will contain many problems, and solving them is an essential part of learning mathematics. Wikipedia does not have these; by design, Wikipedia is an encyclopedic reference, not a textbook.
When it comes to more advanced topics, mathematics is developed, and largely hangs together, by means of the large body of quite formal proofs that exist in the mathematical literature. Wikipedia does not attempt to condense this material into encyclopedic form, for reasons that are discussed at length in another essay. Wikipedia assembles the facts uncovered by mathematical investigation, and the definitions underlying the abstract theories. In common with other mathematical encyclopedias, it omits most proofs.
Although learning mathematics involves memorization of such factual knowledge concerning the content of mathematical theories, memorization is not enough. To become a mathematician you must acquire the skills of creating proofs and doing calculations for yourself, to internalize the material. Therefore you must go beyond the outlines a Wikipedia article can supply.
Caveats
Remember that every source potentially contains errors, so do not put too much trust into a single account. Verify proofs and calculations yourself.
Ways to use Wikipedia
- Talk pages (the "Discussion" tab at the top of article pages) are the best way to raise particular queries about the content of an article.
- The mathematics reference desk is useful if you have a question and don't know where to look up the answer.
- Explore the category system.
- The mathematics portal is a good "way in" to mathematics articles on Wikipedia.
If you doubt, ask at the mathematics reference desk. No one on Wikipedia is going to do your maths homework for you... but if you ask the right question they might point you to some information that will enable you to do it for yourself.
Sister projects
For those engaged in self-study, some of Wikipedia's sister projects may help. These have different and definite purposes:
- Wikibooks is a collection of collectively-written textbooks;
- Wikisource is a repository of free texts of all sorts;
- Wikiversity is a collection of teaching materials;
- Simple English Wikipedia is a version of Wikipedia that is more accessible for both children and adults who are learning English.