I have been wondering recently if we can now come up with a better answer to the question of how many orders of birds should be recognized.
It is a question I wondered for some time, but never had time to work.
Groups in taxonomy like 'order' 'family' 'class' were first created artificially by Linnaeus and later taxonomists. However, there are methods to check objectively whether variation of birds (or any other organisms) really falls into groups of different sizes like orders, rather than just say: lets call it an order, because I like it. There is a sub-branch of math officially called data clustering which does it. It is used from playing on a stock market to diagnosis of diseases, but did not make it yet into ornithology.
This would answer objectively: whether there are groups of species of some size, which are more similar than groups of different size. So, whether differences between birds go smoothly from most similar to least similar species, with no steps in between, or there form objective groups of different size coming in hierarchy, which can be then called 'orders' 'families' etc., or perhaps new names would need to be invented.
Second question would be, if these differences are shared between groups of birds and birds and mammals or other organisms (so, whether an 'order' of birds is so similar as 'order' of mammals, or 'family' of passerines is as similar to each other and dissimilar from another family of passerines, as are 'families' of say, waders.
The third question is naturally, what belongs where and how many these groups are (if they turn to be real).
It would require making a matrix of bird characters (visual or DNA sequences) and applying methods like clustering.
If some birder has mathematics/programming knack, this would be an interesting project. Another question would be, who will supply the data (matrix of differences between birds).
BTW, I consider what I wrote above an original research idea. If somebody wants to follow it, please contact me privately and don't steal ideas without attribution.