Using first person or third person in papers?
@earthling's accepted answer -- to use the passive voice -- is perhaps the convention in certain disciplines, but it is crucial to note that the active voice is the convention in others. Using the passive voice will make a paper sound daft and amateurishly pompous in certain communities.
My preference is very much for the active voice, first person (plural in almost all cases). This is also the most prevalent convention in my community (applied CS).
The strongest argument (and it is a very strong one!) against passive voice is that it removes all responsibility from the doer: it leaves ambiguity as to who did what, which is crucial for proper attribution in scientific writing.
For example:
The methods of Franklin et. al. were taken. The software was implemented in Java.
Who implemented the methods? The authors of the current paper or Franklin and his pals? Who should be contacted if there's errors in the software? Who's to credit and who's to blame?
Even aside from ambiguity, in the hands of a deceptive author, the passive voice could be used to subtly claim credit for others' work.
The methods of Franklin et. al. were taken. These methods were extended to incorporate the inputs previously described.
... the authors make it sound a bit like they did the extending, but maybe they didn't?
The second argument against the omnipresent passive voice is more subjective: that for many people (including me), it sucks to read, it sucks all humanity from the writing, any modesty it provides is entirely false, and it just generally sounds pompous.
So if using the active voice, which person to use? Again this is convention, but talking about yourself in the third person is again considered silly in many communities (although mandatory in some journals!). Also using the third-person can introduce the same ambiguities regarding what was your work and what was the work of others:
The methods of Franklin et. al. were taken. The authors extended these methods to incorporate the inputs previously described.
Leaving convention aside, first person is the only voice with a clear objective argument in favour of it: it avoids ambiguity as to who did what!
All arguments for passive voice refer to subjective matters of style or (false) modesty. (Aside from which, I feel that first person active voice is a more natural style!)
However, you should follow the convention of the venue you are submitting the paper to!
See these letters to Nature, for more on the debate. (The second author sounds ridiculously pompous to me.)
In mathematics, we is used in a few subtly different ways:
To mean the author(s): "We are not aware of any previous work on reticulated splines." (But maybe we just didn't look hard enough.)
To mean the author(s) and the reader: "We see from Theorem 5 that every snark is a boojum." (You are supposed to be able to see it too.)
To mean the mathematical community: "We lack a complete classification of cromulent blobs." (No such classification exists, but it sure would be nice if it did.)
Usually it is clear from context which meaning is intended. But occasionally third-person phrasing like the authors will be used to emphasize or clarify that the sentence is only referring to the authors, and not anyone else. "We cannot prove Conjecture 6 using these techniques" could be ambiguous: is it an absolute claim that it is impossible to do so, or merely an admission of failure by the authors? "The authors cannot prove Conjecture 6 using these techniques" resolves it in one direction. To make an absolute claim, you might use the passive voice: "Conjecture 6 cannot be proved using these techniques."
The link provided in the first comment above has a VERY useful answer but I will add a little bit as to the why part of your question.
In writing research papers, the reader's focus should be on the idea, not the author. Yes, you did the research but the point is not "Everyone! Look what I did. I am so great!"
The research paper should be more along the lines of "Everyone! Look what is new and interesting. This information is really great!"
So, the purpose of the research report is not "I did this" but rather "This was done." For this reason, it is quite common to use the passive voice (this was done) rather than the active voice (I did this).
Personally, I disagree that removing the use of the word "I" prevents writing readable English. I do agree that is makes the writing more difficult but lots of things are more difficult when they are done the proper way. That doesn't mean we give up and do it the wrong way because it is easier.