Where did the military money go?

Question

In older papers, one sometimes finds references to sources of funding directly linked to or overseen by military agencies. For example, I have memories of seeing acknowledgments to DARPA funding in a pure mathematics article - much to my surprise, as it didn't seem to have any relevant applications. (However, I haven't been able to track down said paper in my personal collection, nor indeed any which contain said references; this might suggest that such support was rare even in the past.)

In more recent papers - at least those I encounter - such attributions are conspicuously absent. Instead those written at American institutions overwhelmingly thank NSF grants for their support.

Question. Is my impression accurate? Namely, did the US military fund pure research with little real-world upshot in the past; and has it become more reticent in recent years? If yes, when and for what reason did this shift occur?

• I would be interested in a historical explanation just as much as a personal account.
• To be sure it is only natural that the defense sector still has a keen interest in certain parts of mathematics, say cryptography or data science. I am specifically interested in (past and present) support for projects where the payoffs seem far-fetched.

Answer 1

This question is rather old, but never got an answer (though it did have some useful comments), so I'll try to answer it.

First, yes, I think it's fair to say that the military funding for pure math research in the USA has dried up relative to the Cold War Era. Back then, there was a huge surge of funding for higher education. The GI bill meant that tons of military veterans were able to get a college degree, and that meant a surge in hiring professors and funding their research. The article Who Picks Up the Tab for Science? points out that, before 1940, a lot of funding for research came from the private sector (more on this here), but then President FDR created the National Defense Research Committee and the OSRD, which started to funnel federal dollars into supporting scientific research, including mathematics. Then, with the Cold War and the "space race," even more federal funding went to math, including very pure math, because there was plenty of money to go around and no one was quite sure what would be useful. Data on the explosion of funding during the Cold War is presented in the first linked article above. There's also a graph showing the increase in funding in math over those years. Even very pure mathematicians like Saunders MacLane were tapped to help with applied math problems. It's also worth noting that during that era, mathematics departments often contained statistics, applied math, and computer science.

Now, from the 1940s through the present, we've had more mathematicians every year. So, even if funding levels didn't go down, and even if they kept pace with inflation, still the net effect was that it is harder for a mathematician today to win a grant, because funding has not kept pace with the growth in math PhDs. You can get data on federal funding for the sciences from AAAS, and you can see that the number of new PhDs outpaced funding to math. For more history, check out A Brief History of Federal Involvement in University-Based Research.

Around the 1980s, funding began to dry up. For example, President Reagan's budgets had big reductions to NSF, and around the same time, there were corresponding drops in funding from military sources. This is discussed in the Science Policy Committee Recommendations from 1987, linked in the comments. Then, with the fall of the Soviet Union, funding shrank again, down 30% more, as pointed out in the article Declining Mathematics Funding at the DoD linked in the comments.

Lastly, over the years from 1940 till today, many applied mathematicians, statisticians, and computer scientists (many who were PhD mathematicians) split off from pure math departments to form new departments in their areas of specialization. So, again, there was less funding for pure math as it was being "pulled" to these areas where the connection to military applications was clearer. There actually are databases listing all DARPA/DoD/ONR/NASA/AFOSR grant awards (see also this and this). In recent years, these organizations often put out calls for proposals, seeking to fund research on narrow topics. They can do this because there's so many more mathematicians today, with specialized research, and comparatively fewer dollars to spread around (once you adjust for inflation and the sheer number of mathematicians today). Here are some examples: 1, 2, 3, 4. They also fund young mathematicians hoping to pivot towards research that DARPA wants. Finally, even today, they do fund some pretty pure math research, as long as the grant writer can convincingly make the connection to applications that the military care about. Great examples include David Spivak, Mike Shulman, and Steve Awodey. They also funded work related to geometric representation theory in 2004.

I hope this helps a bit with both the historical context, references for the various moments that funding dropped relative to the number of mathematicians, and also with concrete examples of pretty pure math that has been funded by the military, without the expectation for immediate applications.