Then came the public defense. The student started by stating his theorem. The afore-mentioned famous graph theorist raised his hand and pointed out a simple counter-example that extinguished in one stroke both the theorem and all of the consequences that filled out the dissertation.

The sad thing is that the student’s committee and adviser invented a face-saving way to “amend” the dissertation and pass the student. Essentially the result wound up saying “This theorem is provably false, but if it were true then we could do all of these things”. The ultimate result was that the student substantially decreased the value of the paper he printed his dissertation on by the simple act of printing it. This guy actually got an academic job and then proceeded to terrorize students for many years with unanswerable questions collected into non-sensical exams.

The moral for students is to ask your peers and professors for feedback. And the moral for committees and advisers is to force your students to ask for feedback. And the moral for all of us is that we shouldn’t give PhD’s to people just to get them to leave.

Getting back to the subject in hand, I think there are interesting possibilities in using social networking software in science. There have been conferences where attendees tweet, and I’ve heard of technical questions coming up in grant panel discussions which have been answered in 10 seconds through Twitter. At some conferences, attendees have done real-time ADS searches to address questions from the floor or even refute a speaker. Peer review in seconds! Wow, buzzy. But astronomy, at least as I’ve experienced it, thrives on collaboration. Can we do more with web 2.0? (Academia reclaiming the web! For me, the main obstacle isn’t pride, it’s trust. I like interacting with other researchers and being free with ideas, but (mentioning no names) there have been a couple of times when I’ve felt an idea of mine has been taken without attribution or collaboration – nothing earth-shattering, but enough to feel a bit burnt and cross. You can be careful who you talk to in a corridor, but Craigslist talks to anyone and everyone. So I think people would need to be a bit guarded on a Craigslist-type scientific match-up listing. Still, I think thales has an interesting point that we could make more of web 2.0 social networking in science. What do other people think?

This reminds me of someone else’s even much worse experience. A graduate student once told me that he had gotten half way through typing up his thesis (yes, I come from pre-computer days, and typing math was painfully tedious back then) and discovered that a lemma that he and his advisor had assumed was obvious was in fact false. He had to start a thesis all over again from scratch.

However, such collaborations do sometimes happen. Example I’m aware of: an astronomer working with a computer scientist, because both skill sets are needed to solve the problem.

Example: you’ve spent a frustrating month trying to solve a network of partial differential equations. So you go to, say, Hawkingslist.com and post your problem, promising the first person who can solve it to be credited as a collaborator. Maybe you promise a small cash payment as well.

My hunch is that such a system hasn’t already been put in place because there’s too much pride at stake for the researcher/scientist to risk. Or perhaps there is such a system and I am simply unaware of it.

The famous maths collaborators G H Hardy and J E Littlewood had differing opinions on how to leave things after the initial “AHA!”. Hardy liked to sleep on it, with a glow of satisfaction that his idea or result was probably right even if his hopes might be dashed the next day, whereas Littlewood preferred double checking immediately to be absolutely sure.

Regrettably, reality is usually best described by these sorts of equations. The upside is that it keeps anybody who has to do fluids (for example) employed