Thanks! That first link is a good summary. (I already had read the wikipedia page and looked through von Mises' paper... so I wasn't being too lazy there. ;)
It's weird to look at this debate, as part of my day job is to be aware of the efficiency of the processes people use. Like, if you were to sort a big list of names alphabetically, there's slow naive ways which'd take forever, and more clever fast ways which you might stumble upon.
The literature of my field is full of people arguing that some process can't be done with a certain fastness, but then one day someone figures out how to do it.
And those people arguing against the fast method's existence often aren't being jerks; these were just conjectures which happened to be wrong. (I'm sure some are jerks of course.)
Tayssir