Are mathematical articles on Wikipedia reliable?

I know that Wikipedia gets a bad rap, and it seems like some teachers of mine have nothing better to do in class than harp on about the Great Academic Pastime of calling Wikipedia untrustworthy, but let's face it - Wikipedia is probably the single best resource on the internet for getting quick introductions/reviews of new mathematical ideas. I have used it extensively, and I have seen links to its pages provided in hundreds of the questions on this site.

My main concern is: is Wikipedia really unreliable for mathematics? I realize that this may be true in general, but it doesn't seem like something mathematical could be posted "incorrectly" on the site insofar as mathematics is basically true (in an objective sense). I put quite a bit of trust in what I read on that site, and I assume that there will be no falsehoods - is this a justified presumption?

Please note that I personally love Wikipedia. I'm expecting the answer to be "yes" but I just wanted to make sure.

Solution 1:

In my personal experience, I've found Wikipedia tremendously useful and reliable both in my studies and in my research. Rarely are there ever mistakes. Anytime you get information, especially from the internet, you should always check with at least one other source, of course. I usually use wikipedia and another source to make sure they agree, but I don't know if I've ever found an error on Wikipedia. It can especially be very useful to get a broad overview of whatever it is you're researching, and can provide some links to some very reliable sources.

Solution 2:

Three days ago ---- Friday the 4th --- the speaker at the weekly probability seminar at the University of Minnesota was Larry Gray, who's been doing research in probability theory since the '70s. He began by saying that when he wanted to learn Markov-chain Monte Carlo methods, he began by going to the principal source of information on all things mathematical: Wikipedia.

I've edited Wikipedia math articles every day since 2002 and other articles as well, having done (I think) around 180,000 edits.

Sanath Devalapurkar's answer posted here is probably approximately correct.

Solution 3:

There are a few people on Wikipedia who are knowledgeable about their subjects. For example, in mathematics, concepts like Floer homology are probably edited by actual mathematicians. However, popular concepts like numbers are sure to have some rubbish in it (Disclaimer: I haven't read the article on numbers - that was the first topic that came to my mind with "popular"). Therefore, my answer to your question would be as follows: $$\text{Wikipedia is reliable for math?}=\begin{cases} \text{Most probably yes} & \text{if it's $\geq$ third/fourth year undergrad math} \\ \text{Most probably no} & \text{if it's $\leq$ third/fourth year undergrad math} \end{cases}$$ The requests in the comments have led me to finding this out: From this Wikipedia Page,

Adrian Riskin, a mathematician in Whittier College commented that while highly technical articles may be written by mathematicians for mathematicians, the more general maths topics, such as the article on polynomials are written in a very amateurish fashion with a number of obvious mistakes.

For an example, let me quote Riskin's example:

I’m going to take you through the lead section of the Wikipedia article on polynomials and try to explain some of what’s wrong with it.

In mathematics, a polynomial is an expression constructed from variables (also called indeterminates)

Variables are not the same as indeterminates! Even the linked articles acknowledge as much.

and constants (usually numbers, but not always),

Many more examples can be found in the link above.