Wouldn't it be better for mankind ... if as many people like these kids as possible pursued math and science more vigorously ??? Especially kids like these, who have what I would term "creative" intelligence.
Why would we want those people in law ??? That gives us far less than having them in math and science. And we will get the MOST by having them in art AND math and science. Then we'd really get their creativity going as they look for solutions to problems.
That's not to say funding such things is necessarily a waste, just the focus on STEM education may be excessive. Russia for example ended up with a lot of highly educated security guards.
Another cool application is the superconductors in the NMR devices. They can see what is inside your head and even do something equivalent to a chemical analysis (with NRM spectroscopy) without opening it. The first superconductors experiments used Helium at 4K, so they were only a laboratory curiosity.
For everyday use, I like the giant magnetoresistance. This is my favorite case to explain that strange quantum effects have real world direct applications. Just start talking about the spin in electrons. Then explain that some magnetic conductors have a different value of the current with spin up and the currents with spin down. Then add the sandwich with non-magnetic conductors. At this moment it looks like a weird laboratory experiment. Then suddenly explain how it is used in hard disks heads: http://en.wikipedia.org/wiki/Giant_magnetoresistance
Don't get me wrong, QM for example was ridiculously useful. But, pointing to past and saying these tiny particle accelerators where useful let's make a multi billion dollar one feels like cargo cult science for the lack of a better phrase. We just keep piling higher and deeper without a clear reason to do so other than we can afford to do so.
String theory is another example where lot's of effort from seemingly smart people with no practical basis.
Dumping all of LHC's money into say a large ITER style fusion project would have also been cutting edge, but there would have at least had the possibility of useful results. Hell, even ISS would qualify as vaguely useful.
How about a self sustaining bio-dome in Antarctica. Now that's probably harder and possibly more expensive, but would have real useful applications if we ever want to try and colonize Mars.
PS: Not that the 13+Billion for the LHC was all that expensive, but there are a lot of similar projects out there.
Consider, we know the first five digits of the gravitational constant. So, while it might seem like the diminishing returns are a long way off. Yet, each extra digit becomes exponentially more expensive and less useful. So, actually learning g out just 9 digits is probably a huge waste of resources.
Or in the words of a physicist, in 1920 second rate physicists where doing first rate research. Now, first rate physicistare doing second rate research.
In number theory, what's considered 'elementary' now was cutting edge in the times of Diophantus, all the way to Fermat, to Euler, to Gauss (etc). The fact that children are now routinely conversant in it, I think, is another point in favor of the importance of making such discoveries in the first place.
My point is that applications that were never envisioned for these (at the time) centuries-old-facts, are now commonplace and indispensable.
I think that there is a bit of survivorship bias that warps our understanding of old science. We remember only the great discoveries because those are the most likely to be republished and read.
Also, in the case of math, it is my impression that an amazing amount of very significant progress is being made in the present era.
As to survivorship bias, that's huge but it's not just based on good ideas. Copernicus was ~4,500 years late to proposing the sun was the center of the solar system. But, the pop story looks better when Darwin is breaking new ground instead of simply collecting more evidence in support of an old theory.
As to Amazing progress, I would hope the ~1,000,000 active mathematicians are not all wasting their time. But again, the point is we don't need to maximizing the number of Mathematicians, we are well into diminishing returns.