> It could very well pass for a modest PhD thesis in a smaller university :)
This may be a bit far-fetched. Some might even say disrespectful to the bulk of PhDs out there, who typically worked several years (not weeks) to complete their dissertations.
From properly relating to current state of the art, to actually developing multiple (not just a single one) techniques improving it, and finishing by properly presenting all that work in a scientific manner: your nice trick has a long way to passing as a PhD.
A common standard for a Ph.D. dissertation is "an original contribution to knowledge worthy of publication", and the usual standard for publication is "new, correct, and significant". The length of time devoted is not part of the criteria. Maybe can do the work in a weekend; maybe take years.
When I was a grad student, at one point I took a 'reading course'. A paper was required, maybe just expository and not necessarily original. I started with a problem seen but not solved in a course. I hit the library and saw no solution. In an evening I got some rough ideas for a solution and then proposed solving the problem as my 'course'. A prof looked at the problem for a weekend, didn't see a solution, and agreed that the problem was significant enough. We shook hands. Then immediately I outlined my first cut solution.
Then in some pleasant evenings for two weeks, sitting with my wife on our bed as she watched TV, I found a
good, clean, solid solution. In addition I discovered
a new theorem comparable with the famous Whitney extension
theorem and applied it to solve my problem and, also, produce some curious additional, new results. I also found that I'd solved a problem stated but not solved in a famous paper in mathematical economics by Arrow, Hurwicz, and Uzawa. Poor Uzawa -- apparently so far he has yet to
get his Prize! I published the paper in JOTA, right away, with no significant revisions. So, about four weeks of pleasant, not very hard, work, and I'd met the formal requirement for a Ph.D. dissertation. I used another piece of work I'd done for my Ph.D. dissertation, but that paper did 'polish my halo' in the department.
Yes, I know how doctorate degrees work and what they mean. It was a joke (as indicated by a smiley) and as with every joke there's a grain of joke in it. Not all PhDs are created equal.
This may be a bit far-fetched. Some might even say disrespectful to the bulk of PhDs out there, who typically worked several years (not weeks) to complete their dissertations.
From properly relating to current state of the art, to actually developing multiple (not just a single one) techniques improving it, and finishing by properly presenting all that work in a scientific manner: your nice trick has a long way to passing as a PhD.
EDIT: Ok, I didn't get the playful tone. Sorry.