The majority of people who hold just about any viewpoint are going to be uninformed, so arguing against the average holder of any idea is going to be pretty trivial as long as you know a bit of the subject matter. The value of an idea is surely roughly proportional instead to the strongest argument for it.

" In 1973, Jacques Morgenstern proved that you couldn’t get a Fourier transform faster than ½ n log n if you required that complex coefficients used in the computation had bounded magnitude"

I highly doubt this is going to somehow inspire people to make faster algorithms than the mathematical bound...

I have no problem with pure mathematics, my training was in it; but it seems very possible to me that most people funding theoretical computer science (as opposed to pure maths) probably assume the work has a more realistic computational model backing it up.

I've thought about it a fair bit, and I don't think there's really a very clear line between which religious beliefs people should politely decline to comment on, vs openly critisise. The cultural taboo that exists in much of the west against privately excluding people on the basis of religion has had some really positive effects (the marked decrease in religious violence of the past few hundred years is amazing), but it also leaves society somewhat vulnerable to the spread of some particularly cancerous ideas.