> A better argument for advanced math: it's not always clear in advance what math will be useful. A popular example is Riemannian geometry, which had no clear real-world value when developed, but ended up being used for General Relativity a few decades later.

This is the classical argument, but I don't think it is plausible. It seems even less likely that, say, transfinite set theory will ever become remotely useful than string theory ever becoming useful.

The argument "it might be useful in the future" can justify research in any theory whatsoever, no matter how esoteric. It's like defending an outlandish conspiracy theory by pointing out that it is possible that it is true. That's technicality correct, but what matters here is the probability that it is true, which might well be close to zero. Similarly, while we can't rule out that transfinite set theory might have a useful application someday, this probability is so small as to not being worth discussing.

I think people should admit that they are interested in theoretical math (as opposed to applied math) for its own sake, like people who are interested in cosmology or string theory or theoretical philosophy or whatnot. Pointing to the technical possibility of future usefulness seems to be a dishonest fig leaf.

>noone bashed string theory for failing to make useful predictions

That stuck out for me. Lots of people have criticized string theory for exactly that reason. A theory that makes not testable predictions is not a scientific theory.

Mathematics doesn't have to have real word applications. But science has to make predictions that can be tested experimentally.

Just to quibble a little bit, but the entire effort of string theory (et al) was to find a testable theory. It's not that they weren't interested in useful predictions, but just that they didn't find any. It wasn't that they weren't making the effort, but that the effort has so far failed.

But the day is young, as they say. It took humanity 1000 years to figure out how to solve quadratic equations. Physics theory has had a lot of quick successes, but you still never know when the next one will arrive. We might figure it out in a year, or a decade, or a century, or we might never figure it out.

Will probably edit it, as many people complained. The focus here is useful predictions, in the sense of predictions that have utilitarian value, but string theory doesn't make any predictions at all, which is another issue altogether.

Even in the late 90s when I was studying Topology there was a bit of furor over the lack of application...

Until, suddenly, it was quite applicable in evolutionary biology and knot theory in context of D?NA enzymes.

When I think of string theory, the first thing that pops into my head is "mathematically sophisticated theory that sucked in a generation of physicists but is dead now because it doesn't make any testable predictions".