No-one is disputing that mathematics can be useful. The question is, if we had slightly more advanced number theory slightly earlier in time, would that have been particularly useful? Answer - no.

You are missing the point in this context having the taboo against book burning is helpful because it is something one can use as a warning sign.

No, I am not missing the point. I am perfectly willing to concede that a taboo against book-burning might be helpful for that reason. But here we have an example where people were,at the same time as burning books, doing the exact worse stuff that book burning is allegedly a warning sign of. But no-one complains about the worse stuff, only the book burning. Which makes me disbelieve that people care about the taboo for that reason.

People say that keeping your lawn tidy keep the area looking well-maintained and so prevents crime. Let's say one guy in the area has a very messy lawn, and also goes around committing burglaries. Now suppose the Neighbourhood Watch shows no interest at all in the burglaries, but is shocked and appalled by the state of his lawn. We would have to conclude that these people don't care about crime, what they care about is lawns, and this story about lawns having an effect on crime is just a story they tell people because they can't justify their weird preference to others on its own terms.

Moreover, the sort of thing that Roth does is in the process of being more and more useful. His work allowing for organ donations for example not only saves lives now but will go on saving lives at least until we have cheap cloned organs.

Or, we could just allow a market for organ donations. Boom, done. Where's my Nobel?

Now, if you specify that we have to find the best fix while ignoring the obvious free-market solutions I don't deny that Alvin Roth has done good work. And I'm certainly not blaming Roth personally for the fact that academia exists as an adjunct to the state - although academics generally do bear the lions share of responsibility for that. But I am definitely questioning the value of this enterprise, compared to bringing cheap food, clothes, etc, to hundreds of millions of people like Sam Walton did.

This is wrong. His work with malaria saves lives. His work with selling computer software involved making mediocre products and making up for that by massive marketing along with anti-trust abuses. There's an argument to be made that economic productivity can be used as a very rough measure of utility, but that breaks down in a market where advertising, marketing, and network effects of specific product designs matter more than quality of product.

I don't see why "saves lives" is the metric, but I bet that Microsoft products have been involved in saving far more lives. Moreover, people are willing to pay for Microsoft products, despite your baseless claims of their inferiority. Gates's charities specifically go around doing things that people say they want but don't bother to do with their own money. I don't know much about the malaria program, but I do know the educational stuff has mostly been disastrous, and whole planks have been abandoned.

Yes, to the point where I have to wonder how drastically far off our unstated premises about the world are.

Obviously very far indeed.