Wikipedia and Math

I am a relatively big fan of Wikipedia. It tends to be my go-to source for things I want to know that are of a general nature - for instance, when I finished Bleak House the other day, I read/skimmed the Wikipedia articles on Charles Dickens, Bleak House, and the Chancery court that is such a big feature of that book.

But for professors in many disciplines, Wikipedia is a kind of sore spot, because students will often try to cite it. Not only is it generally inappropriate to cite an encyclopedia in a college class, Wikipedia is extra-suspect since anyone can edit it, and so it may or may not be rife with errors. (Everything in life is full of errors, really, but at least published encyclopedias have editors.)

But in math, people seem to like Wikipedia a lot. Several of my professors have referred to looking up things in Wikipedia themselves before presenting them in class, or to using it in general.

In fact, a few weeks ago, we had a visitor from the NSA who came to talk about careers there. It came up that of course (for security reasons) they don't have Internet access at their workstations there. I asked the woman how they did math without Wikipedia, and she immediately replied, "Oh, we have our own copy of Wikipedia." She didn't seem to find the question bizarre (like if I'd asked, "Oh, how do you do math without Facebook?")

I think there are some legitimate reasons why Wikipedia is different for math than for other subjects.

First of all, I imagine that when, say, history professors read Wikipedia, they find errors that irritate them. (This is probably true of many encyclopedias as well, but I doubt it comes up much that professors read encyclopedias.) You can make a lot of factual errors in history, or you can simply write an article that is unbalanced - that goes into a lot of detail on one small point and completely fails to include other major points. This is especially likely if the topic is controversial.

In math, on the other hand, there are not so many facts. When you look up a math topic in Wikipedia, you want to answer questions like

• How is this thing defined?
• What areas is it used in?
• What are some theorems about it?
• What are the different notations or ways that it is conceptualized?

You might think of definitions as being akin to facts, but actually they're quite flexible. It's true that some things are simply NOT the definition of an algebraic group, for instance, but there are several different definitions to choose from, and you can do math from a lot of different standpoints or bases.

I commented to Ed the other day that, unlike in other fields, in math it's the facts (definitions and axioms) that are matters of taste or opinion, and the conclusions drawn from those facts (theorems, etc.) that are either right or wrong.

The second reason I think Wikipedia is different for math is that, honestly, it's difficult to abuse it. You can't read and understand a Wikipedia math article unless you actually know enough math that any errors are probably not going to be dangerous to you. Is there a proof that is erroneous? You should be able to tell. (Nobody sophisticated enough to read proofs in Wikipedia should be foolish enough to treat any proof as authoritative.)

So if you were going to write a paper about Hausdorff spaces and you looked up the Wikipedia article and started there, it wouldn't really hurt you any. Either the definition in the article would work for you as a starting point in your research or it wouldn't. Once you know generally what's being discussed, you can make up your own definition if you want (though of course if it's not roughly equivalent to a commonly-used one, you'll only confuse your audience by calling it "Hausdorff"). You don't need a source for a mathematical definition, so you're not likely to mistakenly cite Wikipedia.

So, math Wikipedia - all upside, no drawbacks (if you can read it at all).

As a side note, my ability to read Wikipedia articles in math has absolutely skyrocketed since I started grad school. I'm actually starting to get enough background in the various general areas of mathematics for these things to make sense.

Academic Fields

The other night in Prob/Stats, before class, some of the students were discussing graduate school. Specifically, they were talking about whether master's programs in math and/or stats involve writing a thesis. I commented that some do and some do not, from what I've seen, and it partly depends on the purpose of the master's.

"Why would you ever write a thesis in math?" asked one woman. "That's weird."

It made me think about how math isn't what people think it is. When I repeated her question to Ed, he asked, "What, does she think math is a solved problem?" But I don't think it's so much that she thinks everything in math is already known as that her conception of math is probably that it is about learning how to solve different kinds of problems.

A lot of fields are not about what you naively think when you have barely any knowledge of them. Psychology is not, as Sally mentioned, all about why people are crazy (or, alternately, about how to make people like you and do what you want by understanding the inner workings of the mind). History is not about learning the timeline of events. English Lit is, for all I know, probably not about writing papers about how the three rooms in the house in a novel represent the holy trinity or whatever. Computer science is not about learning programming languages (much less, as a coworker once asked me, learning how to use Power Point). Even GIS, which was my major at one point, is not about using software to make maps.

However, I'm pretty sure anthropology is about squatting in the dirt with some unknown natives and keeping a diary about their ways, and paleontology is about carefully excavating big dinosaur fossiles, and archaeology is about looking for ancient cities like Troy. Must be.

Can't Be Much To It

Ed has a friend (who I guess by now is my friend too) who is very down on software engineering. Software engineering isn't about how to write code - it's more about how to manage and run software projects. So it is partly about how to write code, but it's more about the general procedural aspects of how to write code (e.g., is it better to code in pairs? what kind of coding standards should be in place? how does a group manage working on code together? how can we make sure we're building what the client wanted?) than on things like how to craft the perfect algorithm.

Anyway, Adam basically thinks software engineering, at least as currently taught/practiced is full of shit. He had one course in it in college and what he learned was, he felt, a lot of "buzzwords." He later had to regurgitate these in interviews, and found that basically doing some reading on Wikipedia was enough to satisfy the demands of this process. ("Oh, I'm supposed to know what 'agile' means, fine...")

There are a lot of buzzwords, you could say, in business in general, but there are also stark differences in methodologies. I'm sure (as Ed pointed out to me) that "assembly line" was once a buzz word. It's also a significant, radical way to manufacture things. And if you're going to make up new ways of doing things, then assigning words to them enables discussion, right? So if I've decided that these five or so factors are key to the way I want to work in a team to program something, and I name that style "Extreme Programming" (or XP) then is that wrong?

And if I wanted to go to work for a company that practiced XP, it's reasonable to think I should know the term, right? And have an opinion about it? Or concerns and questions about the actual implementation. I should know whether I love or hate or am curious to try pair programming, for instance.

I feel like Adam's dismissal of "buzzwords" in software engineering is related to a general tendency that some people have to assume that, if they don't know much about something, there must not be much to it. Some things, like brain surgery, seem intrinsically complicated and aren't subject to this phenomenon, but other things, like sociology, get no respect. What, don't they just write papers about how people act just like anyone with any common sense would think they'd act?

I imagine most fields have their bullshitty elements. There are probably buzzwords in reinforced concrete structure design. But I try really hard not to assume that academic disciplines have nothing to them, just because I know nothing about them, because I've found that usually, the more you learn about a field, the more you see it expand before you into something deep and rich with detail.