Since people are commenting on the dichotomy between "Bill Johnson" and "Bugs Bunny", let me add my opinion on the matter.

When Bill Johnson first appeared on MO, I didn't know him from Bugs Bunny. But because he uses his real name, I have with almost no effort learned a fair bit about him. People like Yemon Choi gave him a warm welcome and dropped hints on the meta site that he was a leading mathematician in the field of functional analysis. This has been confirmed by his answers on MO up to the best of my own knowledge: i.e., I know so little functional analysis as to be unable to tell the difference between a leading functional analyst and a decent functional analyst, but Professor Johnson is certainly decent enough for me. Moreover I began to notice and remember that certain theorems in functional analysis bear his name. Just now I went to MathSciNet and immediately found a William B. Johnson who has 118 papers in functional analysis and related areas, which have been cited 992 times. So it's pretty clear who and what he is. If I had a specific question about something that appeared in one of his papers (again, I am not at present up to that task, but I have been in the mathematics business long enough not to rule out the possibility that this could happen in the future) I could ask it here thinking that he would probably respond. Or perhaps I would feel bold enough to email him personally about the question, since he probably has at least some vague awareness of who I am as well. If some day our paths cross at some conference or other event, we will probably stop and talk to each other because of our MO connection. (Such has been the case, at least, with dozens of other mathematicians over the last 16 months.)

Now try out any of these things with Bugs Bunny...it doesn't work. Maybe he is someone that I already know, and maybe he isn't. (Maybe he's a she...) He certainly seems to be a knowledgeable and interesting person to the extent that I would benefit and enjoy out-of-MO interactions with him. So it seems a bit of a shame that I don't know his actual identity: without that he exists only as an MO character, whereas Bill Johnson and I exist also -- and let me go so far as to say primarily -- in REAL LIFE. I don't remember exactly what Mr. Bunny's justification for his anonymity is, but if I am being honest it strikes me as an eccentric and mildly antisocial choice. (It is, of course, his choice: I am not disputing that.) I wonder what he is gaining to give up all the pleasant human interaction that could come from identifying himself as a real person.

Picking banks and paypal to bestow one's online trust on is somewhat funny :)

@Qiaochu: One also doesn't put one's money in the care of Math Overflow (one is, I assume welcome to do so.. but MO does not guarantee that one's deposit will not be spent on a magnificent party and/or a spaceship).

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But, for example, let's consider an undergradute student that newly arrives to the site.
His/her name in all likelihood won't tell you anything whatsoever, and also might not help you to find any information (assuming the person has no/little online presence). How in such a case it still makes any difference for you whether it says Smith, Chen, Sanchez, Mueller,..., or something that is not a real name is really difficult to understand for me.
>>
I disagree. Knowing a poster is an undergraduate student gives information on how to formulate an answer. If a new poster gives a name and I click on the thread, I immediately click on the name to see if the poster gives information about himself or herself and sometimes also Google the name.

an_mo_user: Please understand that I am not trying to construct a logical, reasoned argument. I am trying to explain what it is like for me - that's the only reliable data that I can bring to this discussion. In particular, I don't know why I am the way that I am! All I can say, is that a name helps. As I've said, I have no knowledge of Bill outside MO, yet my knowledge of him is far greater than for, say, Bugs Bunny. The fact that I can link the various small bits of information that I have about Bill but can't about Bugs is something that I attribute to the names.

I could have picked graduates, I might have had more trouble picking undergraduates simply because I don't know many just from MO. I don't think that it has anything to do with status, just that the higher status users are more noticeable. I have certainly noticed both Bill and Bugs, but one stuck and the other ... eats carrots.

I'm also not trying to say that my behaviour is ideal; just that if I'm typical then that information should be taken into account when someone chooses to be anonymous or pseudonymous.

Incidentally, this does suggest a strategy for someone wanting to be anonymous: choose something that could actually be a real name. Just don't choose Abel (and don't choose a gravatar of a famous mathematician).

Actually, talking of gravatars, the same goes for people that don't put pictures of themselves but choose something silly ... like the cheshire cat! Again, it's information that helps me build up a picture of who they are. I feel that I would know David Speyer at a conference, but I could be talking to Pete Clark for half an hour before realising who he was. (Actually, it would probably take about 2 minutes before he reminded me that I've offered to buy him quite a large number of pints by now.)

But I don't want to up the ante. I'll keep the discussion on names for now.

Bill Johnson, perhaps I did not describe carefully enough the scenario I mean. I believe there is no disagreement regarding this point; certainly I agree it is helpful to know somebody is an undergraduate. Let me make my example a bit more explicit and extreme (originally I meant both leave About Me blank).

Pseudonym-User:
Name: Donald Duck; and in the About Me box it says, eg: 3rd year undergrad at a mid-level US institution, presently mainly interested in Real and Complex Analysis.

Realname-User:
Name: John Smith. No further information. [And assume this is also an undergraduate without webpage or other significant online presence, so no real hope of finding this John Smith with Google.]

I think, leaving psycologiacal issues aside, the first, while in violation of the realnames-policy, provides more useful information when it comes to answering his questions.

Andrew Stacey (and also Mariano), thank you for taking the time to repeteadly explain me what you mean. I believe I finally understood it. Sorry it took so long for me to understand, but regarding this we apparently think/feel very very differently.

I can't speak for Andrew, but at the conferences I go to nametags are provided but frequently not worn.

I do not religiously wear nametags, but my social skills are so high that if I meet you for the first time, there is a very good chance that one of the first things I'll say is, "Hi, I'm Pete Clark. I don't think we've met: you are...?"

Now I know that you cannot count on just any mathematician to do this, but what can I say? I'm a pretty exceptional guy.

As an aside: I do religiously wear name tags. So if you see a waterfowl not wearing name-tags at a conference, that's probably not me.

@Andrew: a propos garments, are you talking about sticky name-tags? Plastic sleeves with a clip on the back works wonders with a shirt with breast-pockets.

@Andrew: I find it curious that you consider a conference in which the organizers decided that participants shouldn't be trusted with safety pins is "higher class" :)

While we are on the subject, I think we as an Organization should also promote name tags with the names on the two sides, specially when it is one of those worn around the neck.

Wow. There is patent material there, Willie!

Dear Angelo,

By random chance, I happened to notice that you answered the question

http://mathoverflow.net/questions/83949/the-composition-of-derived-functors-commutation-fails-hazardly

from a user "sasha" who seems to me to be, for all intents and purposes, anonymous. I'm wondering what it is about this case that prompted your reply. Of course, being an anonymous questioner myself, perhaps I have no reasonable expectation of a reply here!

Best, Storkle

Edit: There is also your relatively recent answer to the user "36min", but I have to admit that I don't see a pattern so I'm still curious.

Sorry to revive a long dormant thread, but I read through the history with interest and it seemed to me the most important reason for anonymity was neglected: avoidance of persecution.

It is not likely someone would be persecuted for contributing to mathoverflow specifically, but if I live in a country with an oppressive government and use the same computer for activities that are considered subversive, having any activity on this computer tied to my name could put me in jeopardy. Even those of you living in "liberal western democracies" could have reasons to fear your own internal securities agencies if you were to use the same computer for participating in islamic forums, or researching certain types of physics or chemistry that could be used in explosives. Or more innocuously, if you used the same computer to surf pornography, you might not want your real name tied to that activity.

Even if you do not use the same computer for anything that might be considered subversive by anyone, if it is a public or semi-public computer used by other people, *their* activity could put you at risk. Say I log on to mathoverflow from this public computer, and someone who is involved in such activities also uses this computer for their activities at other times. The government determines this undesirable activity is coming from this particular internet cafe or whatever, seizes the machine, and tries to figure out who was using it. My name comes up as having visited a mathematics site immediately before or after someone visited a forum and participated in some illicit discussion. My government's police may well decide I am worthy of investigation or interrogation or worse.

There are very good reasons for the protection of people's anonymity. It is an important issue that should not be trivialized. You'll recall many Chinese dissidents are still in prison today because Yahoo! revealed their identities to the Chinese government. This was not an isolated incident, and even in "free" countries, security agencies are certainly working around the clock to tie user activity on some sites to people's real names. I am not sure that I trust them to do so in an error-free way (even though I am not involved in anything remotely illicit.)

Ryan, while I sympathise with your broad point, I feel the wording of your response comes over - I'm sure unintendedly - as dismissive towards the points raised in horus's 3rd and 4th paragraphs. The whole point is that in certain places, it is remarkably easy to be found engaging in what the Powers That Be deem to be subversive activity. It is perfectly justifiable to worry about being flagged for "subversive activity" even if one is not intending to be "subversive in one's home country".

"If you've done nothing wrong, you have little to worry about" is a dangerous line, which I hope we're not espousing.

That said: I personally I think MO should discourage anonymity, on the grounds that it isn't the place to fix the many and varied non-mathematical iniquities of the world.

Regarding the personal-safety problem mentioned by Horus: Fear becomes internalized.

I will explain using a personal anecdote. In city X, there had been a number of physical attacks against Jews. Person A was a religious Jew, who sat next to me in synagogue every morning. But when I saw him in the university, he pretended not to know who I was. When I would come into his office, he would pull down the blinds. Why? Because I wear a kippa in public, and he was afraid he would be identified as Jewish. There was no objective danger inside the university or inside his office, and it was triviality itself to figure out that he was Jewish- yet the fear had become internalized, and was no longer correlated with a rational risk-assessment process.

This is how I interpret Horus's comment. It seems a fair point. But I don't think it should have any influence on MO policy- basically I agree with Ryan and with Yemon.

Interesting stuff!

I'm still pretty steadfast in my plan to encourage people to use their real names, but I think we're doing this in a fashion that is completely compatible with allowing access for people who are worried about their online identity.

We've never restricted access to good-faith anonymous users. I really do need to say "good-faith"; when an anonymous user misbehaves we usually have very little patience. But for this, anonymous also means not providing an email address visible only to the moderators. When an email address is available, we nearly always try to write an email explaining our concerns, if it's not obvious trolling.

If you're really worried about participating in online mathematics because of your repressive local government, drop me a line. (PGP public key on my website, along with other contact details.) I might well be happy to set up a very respectable looking tunnel for you, if I'm convinced you're kosher.

@Daniel, allow me to quote Futurama on that:

Bender: Please, I'm scared.
Sal: We're all scared, it's the human condition. Why do you thinks I put on this tough-guy façade?