Consider that the advances here were mostly in the realm of numerical methods and PDE's rather than a brand new area of mathematics. The heavy computation necessary to design quiet (non-cavitating) propellers and hulls was simply unavailable until quite recently.
> Unsurprsingly, most of the work was done in the name
> of transporting large heavy objects in the direction
> of people you don't like.
It's much easier to justify that much expensive research when directed towards a practical, rather than an abstract goal. The urgency of the goal matters, too, and what is more urgent than war? It is an excellent justification for research funding in any discipline. Perhaps a morally suspect one as well.
> But if your fundamental theorems of calculus are
> developed to solve viscous flow problems, you're going
> to end up with a calculus that looks very different
> notationally from Newton's.
Are you sure that the notation matters significantly in this case? I don't believe that it does.
> Perhaps one in which it
> would be very difficult to plot cannonball
> trajectories.
I would consider that almost impossible, given that the mathematics of fluid flow (pde's, vector analysis) rely directly on a pre-existing mathematics of flying cannonballs. For that matter, the mathematics of flying cannonballs can be derived empirically, without significant use of calculus; not so for fluid flow.
I can see that perhaps there would be emphasis on different fields of mathematics if mathematical research was not important to the military-industrial complex (as unlikely as that appears), but we're dealing with very fundamental mathematical problems here which have wide-ranging import. Engineering is much more important to military applications, and engineers tend to know fundamentals but not advanced mathematics.
IANAE, as usual.
Marco
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> Marco Anglesio | What upsets me is not that you <
> mpa at the-wire.com | lied to me, but that from now <
> http://www.the-wire.com/~mpa | on I can no longer believe you. <
> | --Nietzsche <
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