> The Kelley, General Topology pure math book acknowledges NSF and Office of Naval Research support in years 1950-1952. Same financial supporters for Luenberger, Optimization by Vector Space Methods -- fun with the Hahn-Banach theorem.

So what if they did? Your original claim was "NSF funds (1), and does not fund (2)". Symbolically, we can represent this as "A and (not B)", where A is "NSF funds (1)" and B is "NSF funds (2)". To refute that, we need to show the negation, i.e. "(not A) or B" (This is, of course, just a De Morgan's law)

If I were going for "not A", then Kelley would destroy that line of argument, but in fact I was going for "B", and neither Kelley nor Luenberger bear on that.

> Good to hear that the NSF has supported some computing hardware -- my guess was that that was done mostly by the US Department of Energy. E.g., as I recall LINPACK was developed at Oak Ridge.

"In 1985, NSF began funding the creation of five new supercomputing centers"
https://en.wikipedia.org/wiki/National_Science_Foundation_Ne...

> At one time I was teaching computer science at Georgetown U., and some colleagues wanted to work in speech recognition, asked for NSF support, and were told that the NSF did not support "software development" or some such.

Sounds to me like they wrote the grant for the wrong thing, or spun it incorrectly. NSF turns down grants all the time (more than they fund, in fact), and if they didn't make it clear that there was actual research being conducted, then of course they'd get turned down.

In fact, when it comes to speech recognition, NSF says they funded a lot of it back when:
https://www.nsf.gov/od/lpa/nsf50/nsfoutreach/htm/n50_z2/page...

"""Much of the initial research, performed with NSF funding, was conducted in the 1980s. This research led to further product development from Dragon, AT&T, IBM and other companies. """

(And presumably your colleagues would have had a reasonable expectation of having had a shot at NSF money, otherwise they wouldn't have wasted their time)

> Most of numerical analysis I saw was good definition, theorem, proof math. But recently I saw that the Formula 1 auto racing teams have been using CFD (computational fluid dynamics) for detailed design of the shape, wings, downforce, etc. of their cars. That's a lot of progress in fluid flow since I was working with the Navier-Stokes equations. So, apparently numerical methods for fluid flow have made a LOT of progress. As I recall, at times there was some such work at Courant Institute. I hope the NSF supported some of that progress.

See, this claim, to me, is bizarre, as a sizable portion of HPC use has historically been doing CFD and of course the NSF was heavily involved.

For example : https://nsf.gov/pubs/1996/nsf9646/nsf9646.pdf and https://www.nsf.gov/od/lpa/news/03/tip031113_topsupercompute...

> For NSF support of "applying mathematics to biological problems" very good to hear, but my guess would be that that came under NSF support of biology instead of applied math.

I went and checked, and the grant was via DMS, which stands for "Division of Mathematical Sciences" and not, as one might have thought, "DNA, Metabolism, and Snakes".

> Here is more what I had in mind: Daily the many US research-teaching hospitals take in sick people and make them well. There is good research, but the actual patient care is clinical, that is, serving people, and professional, e.g., with apprenticeship training, code of ethics, and liability and for professional practice. In the US I don't see anything similar for applied math or computer science, with or without NSF support.

This is an entirely different kettle of fish and also irrelevant.

>Since the research universities don't much like math applications outside of academics

.... What? https://www.pacm.princeton.edu/about ??? https://amath.washington.edu/history ???

> E.g., university math departments have lots of talks by professors presenting their solutions without known non-academic problems but nearly no talks from non-academic people with problems looking for solutions.

Non-academics usually use back channels and personal communication instead of formal presentations. Maybe in a better world it'd be different.

> When I was a B-school prof, I was shocked to discover that B-schools were fine with some quite pure math research but wanted nothing to do with education or practice as in the law school, medical school, school of pharmacy, or agricultural college.

I used to teach math to business school students, and in the interest of decorum I will say no further on the matter.