[amilein7minutes]

The author notes "Let us hope there are no real-world applications" when describing the Navier-Stokes regularity and smoothness problem. It looks like he meant to write the opposite and this was an error. However, in some sense, the statement may also be true. That is, people have been doing fluid experiments and numerical experiments (numerical fluid mechanics is a mature discipline) without relying on whether the conjecture is true. I mean, flight development was not waiting for an answer!

My point is engineering moved on without an answer to this particular question. At the same time, answering questions such as these (and the ones on number theory two of which were mentioned in the article) that occupy pure mathematicians provide more than artistic pleasure -- they provide the giant leaps that spur new technology. The often quoted example from Tao's research is compressed sensing but even bigger splashes like the idea of computers and the stored program, that can be traced back to Turing's seminal paper, comes from pure mathematics.

Charles Fefferman, mentioned in the article, makes 3 very cogent arguments[1] for the applicability of pure mathematics to the society, and in fact, says very pertinently that the line between pure and applied math is very blurry in the first place: [1]: https://www.youtube.com/watch?v=3LgjMjVA4sY

1. that unanticipated applications show up from purely theoretical questions

2. a rigourous study of math provides a way of thinking that prepares students to work in a range of fields that require quantitative or analytical thinking.

3. math is capable of revealing those ground breaking discoveries that happen rarely