A colleague and I recently had a bit of argument concerning the style in which mathematics papers are written. Research papers in mathematics are usually written in the third person plural (“we prove the following”; “we need to show”; “we use the following lemma” etc) whilst papers written in most other scientific disciplins are largely written in the first person singular (“I did the following experiment”; “I performed the following test”; “I found that” etc). My colleague thoroughly dislikes this ’stylistic’ point and avoids this ‘convention’ whenever possible.
I would like to argue that this ‘convention’ is not only NOT a convention, but actually an inherently necessary part of writing mathematics. You see, in almost any other scientific discipline, it is not the case that simply reading about an experiment recreates it. If I do an experiment and YOU read the results it is not the case that YOU are redoing the experiment.
Mathematics is different. Its objects are purely abstract, existing only in the mind - its ‘experiments’ are proofs run through only in the mind. If you discover a proof of a result, I try to understand your proof when I read it. I may do this by filling in little arguments to get myself from one line to the next which may not be the same as how you saw it. I may try to apply your argumnt to my favorite example that may be diferent to yours. I may simply have a very different perseption of the objects we are dealing with. Ultimately, however, the basic form of the argument was constructed by you.
In short, if I read YOUR proof, the form it takes in MY mind is somthing that WE constructed together and it is for that reason that it is genuinly the case that WE prove results.
(The title of this entry is a bastardization of a quote said by the great early twentieth century mathematician David Hilbert “Wir müssen wissen, wir werden wissen ” ie “We must know, we will know”)
July 17, 2008 at 7:19 pm |
The objection I have to the ‘we’ convention is that if you write
‘we have shown that…’
I can be read as
‘we have shown ….., because we’re clever, and you haven’t because you’re not’
That’s possibly a bit strong, but I think that ‘we’ can often be read as ‘we the authors’ rather than ‘we the authors and the reader’ and so the convention is exclusive rather than inclusive.
Admittedly I read and write physics papers rather than mathematics ones, so possibly the emphasis is different
August 7, 2008 at 8:57 am |
My PhD supervisor was quite strict about when to use “we” and when “I”. “We observe that” versus “I would like to thank X, Y and Z for useful comments”.
“we deduce X” as opposed to “The second-named author first made this observation when thinking about quandles in 1998″.
August 7, 2008 at 9:45 am |
I suppose we agree that “I would like to thank X, Y and Z for useful comments” is correct and that if we must refer to the authors then it is either “the suthors” or the “the nth author”.