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.
My answer is “probably yes”. Mathematics directly enables entire areas of science and engineering. Cathedrals and bridges are much easier to build if you know trigonometry. Electricity is a lot easier to harness if you know trigonometry and calculus, and easier still if you are aware of complex numbers. Optics—and therefore cameras and telescopes, among many other things—is a lot easier with linear algebra, and so are many other engineering applications. And, of course, modern electronics are practically impossible without some pretty advanced math and science, which in turn requires all these other things.
If we assume that technology is generally beneficial, then it’s best to develop the disciplines which enable it—i.e., science and mathematics—as early as possible.
He was talking about number theory specifically, not mathematics in general—in the first sentence you quoted he admitted it can be useful. (I doubt advanced number theory would have been that practically useful before the mid-20th century.)
My answer is “probably yes”. Mathematics directly enables entire areas of science and engineering. Cathedrals and bridges are much easier to build if you know trigonometry. Electricity is a lot easier to harness if you know trigonometry and calculus, and easier still if you are aware of complex numbers. Optics—and therefore cameras and telescopes, among many other things—is a lot easier with linear algebra, and so are many other engineering applications. And, of course, modern electronics are practically impossible without some pretty advanced math and science, which in turn requires all these other things.
If we assume that technology is generally beneficial, then it’s best to develop the disciplines which enable it—i.e., science and mathematics—as early as possible.
He was talking about number theory specifically, not mathematics in general—in the first sentence you quoted he admitted it can be useful. (I doubt advanced number theory would have been that practically useful before the mid-20th century.)