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December 13, 2020

The Lie of “It’s Just Math”

Posted by Tom Leinster

Jade Master at Riverside has written a short, important and lucid article about military funding of math, The Lie of “It’s Just Math”, accompanied by a call to action:

Fellow mathematicians, it’s time to stop letting the military benefit from our work.

Military involvement in math is particularly an issue in applied category theory, and particularly an issue in the USA. But the principles that Jade pithily expresses are universal:

  • The [US Department of Defense’s] real goal is not just the math you produce, they want to gain access to your mathematical community.

  • Your math is not too abstract to be useful.

  • The DoD wants to normalize themselves in your non-mathematical communities.

  • The DoD will lie to you.

Mathematicians are generally highly reluctant to talk about the human impact of what we do and the choices we make. For that reason, we’re not very practised at it. But Jade’s article deserves wide discussion, and I hope it gets it.

Posted at December 13, 2020 5:23 PM UTC

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Re: The Lie of “It’s Just Math”

Thank you for sharing this article. Here is an article I wrote on this topic that the readers of this blog might find interesting:

Doing Math in Jest: Reflections on Useless Math, the Unreasonable Effectiveness of Mathematics, and the Ethical Obligations of Mathematicians available on the arViv at

Posted by: Gizem Karaali on December 13, 2020 6:32 PM | Permalink

Re: The Lie of “It’s Just Math”

It’s also worth remembering that plenty of mathematicians regard this kind of work as perfectly ethical and even patriotic (the NSA has claimed to be the largest employer of mathematicians in the US, for example).

Posted by: Ryan Wisnesky on December 13, 2020 6:44 PM | Permalink

Re: The Lie of “It’s Just Math”

Yes, some mathematicians regard this kind of work as ethical and patriotic (and also regard patriotism as a good thing). There are mathematicians who believe that by and large, the US military has a positive effect on the world. Personally I find that position extraordinary, but people have all sorts of opinions.

But independently of one’s position on that, I think every mathematician should agree that this is an important conversation to be having.

It’s just a fact that the US military has been, and continues to be, the agent of a very large number of deaths and life-ruining injuries around the world. And it’s just a fact, not a judgement, that US military actions to change other countries’ governments have profoundly affected the lives of millions of people.

And these are extremely serious things. They could scarcely be more serious. However one judges the moral value of the US military’s actions, what it does is important, in the sense of radically changing human lives. And so when mathematicians get involved with the military, and the military gets involved in mathematics, that puts a heavy responsibility on us. Not to consider the human implications would be psychopathic.

Posted by: Tom Leinster on December 13, 2020 8:46 PM | Permalink

Re: The Lie of “It’s Just Math”

This is very well said Tom. I don’t want to tell anyone what decisions to make. I just hope that when we make a decision, we’ve made peace with its full moral implication.

Posted by: Jade Master on December 13, 2020 11:15 PM | Permalink

Re: The Lie of “It’s Just Math”

Another aspect of this discussion that I do not think gets as much attention as it deserves is the fact that in general, mathematicians can make a decent living by working for private corporations. This is contrasted with the fact that many jobs in acedemia are adjunct positions.

Posted by: Ana N Mouse on December 13, 2020 7:54 PM | Permalink

Re: The Lie of “It’s Just Math”

This is a serious problem, and it’s perpetuated by the fact that we professors don’t know much about jobs outside academia. We steer our students toward academic careers merely because we don’t know enough about the alternatives.

Posted by: John Baez on December 13, 2020 9:55 PM | Permalink

Re: The Lie of “It’s Just Math”

This is a good point and navigating the ethics of that sort of job can also be very difficult :)

Posted by: Jade on December 13, 2020 10:50 PM | Permalink

Re: The Lie of “It’s Just Math”

I don’t really like getting grants, and I’ve managed to survive most of my academic career without them. The pressure to get them has been building, but luckily I’m about to retire.

I’ve gotten a few to help out my grad students. The only military-funded one was not actually a grant, but a ‘subcontract’ from Metron Scientific Solutions, who got money from DARPA to work on their CASCADE (Complex Adaptive System Composition and Design Environment) project. I used this to support my student Blake Pollard and Joe Moeller, and got money from it myself. This project was directly responsible for the discovery of network models, and indirectly for the discovery of the monoidal Grothendieck construction, which we needed for network models. And of course a hefty chunk of the money went straight into the coffers of U. C. Riverside, which is one reason they want faculty to get external funding.

The project started out focused on an innocuous maritime search and rescue mission—saving sailors who went overboard in a yacht race. This is one reason I joined it. But later the focus changed to ‘combat search and rescue’, which made me unhappy. I wouldn’t be surprised if this sort of ‘bait and switch’ is routine.

In the end I quit. One reason was that Joe Moeller pulled out: he wasn’t comfortable working for the military and he actually missed being a teaching assistant. Another reason was my own discomfort with the military. But perhaps the main reason was that I was frustrated. This general kind of DARPA project is aimed at getting results quickly: there was a ‘challenge team’ posing problems to Metron, which had to be solved in months or sometimes hours, and there were software people at Metron whose job was to quickly crank out code to solve these problems. The CASCADE project in particular seemed to be premised on the idea that because David Spivak had written about practical applications of operads, we could just grab those ideas off the shelf and use them to solve complicated problems. In fact the ideas weren’t ready for such complex applications. I wasn’t able to get many people to put time into my own ideas for designing systems using operads. Quite possibly these ideas were impractical, but certainly they were too abstract to apply without some serious work. Everybody except one person, John Foley, was too busy to really think about them. No venue was proposed to get a group of people talking about them and muscling. them into concrete form, and I didn’t have the energy to create such a venue. I’m used to being able to describe something in a very abstract way and be done with it, letting someone else take it from there.

In short, I was a bad match for this line of work, completely independent of whether it involved the military.

It was very interesting nonetheless, and I can’t say I regret it even though it made me ‘lose my purity’ as far as military funding goes. In fact, losing my purity may have been a good thing. It’s very easy to harshly denounce things you’ve never had much contact with yourself, and this applies not just to working with the military but also going to gay bars, or attending a bible study class or a madrassa, or joining the Communist Party or a gun club, or listening to death metal, or becoming a Mormon, or doing various kinds of drugs, or marrying someone of a different ethnic group. Everything seems much more obviously disreputable and scandalous when you associate only with people who don’t do it, and shun those who do. But the conversation is more interesting, to me at least, when you have people with significantly different opinions involved, and not just scolding each other but actually trying to think things through.

Posted by: John Baez on December 13, 2020 9:35 PM | Permalink

Re: The Lie of “It’s Just Math”

My intent is not to shame people who took military funding in the past, just try to convince them not to take it in the future. There are lots of DoD funded mathematicians whose work I value very highly and I don’t think we should cut them out of our community. I would be very happy to work with them as soon as they find another source of funding. I understand there are shades of gray in this, to a certain extent we are all complicit, but even in “shades of gray” situations you have to draw the line somewhere. I think that too many mathematicians realize the moral ambiguity and decide not to draw a line at all.

Posted by: Jade Master on December 13, 2020 11:11 PM | Permalink

Re: The Lie of “It’s Just Math”

I think your post may be persuasive to those who are already somewhat suspicious of the military. But apparently the US military is the second most trusted institution among US citizens. 72% of respondents reported that they had a “great deal” or “quite a lot” of confidence in the military. Of course, academics are probably quite different—that would be interesting to check! But there are probably thousands of mathematicians who think the military is fine and would be utterly unmoved by your arguments. Persuading them would be a much bigger challenge.

By the way, in 2020 the number who had a “great deal” or “quite a lot” of confidence in the military greatly surpasses those who expressed that much confidence in the medical system (51%), public schools (41%), organized labor (31%), newspapers (24%), big business (19%), television news (18%), or Congress (13%). Only “small businesses” ranked higher, at 75%.

Unfortunately they did not ask about university professors.

Posted by: John Baez on December 13, 2020 11:49 PM | Permalink

Re: The Lie of “It’s Just Math”

One point that I think is hard for non-Americans to fully digest (and I include myself in that) is quite how gigantic, how truly enormous, the US military budget is. There’s a widely cited statistic that the US spends more on its military than the next ten countries put together:

graphic showing "defense" spending of top 11 countries

That’s absolutely extraordinary, especially for a country with only 5% of the world’s population.

When your budget is that vast, and you’re so thoroughly woven into the establishment, perhaps it’s not surprising that public trust is so high. (Within the US, of course. Outside is another story altogether.) The US military is an incredibly powerful force politically and culturally, as well as militarily. But that’s not to say that resistance is futile — it isn’t.

Posted by: Tom Leinster on December 14, 2020 12:31 AM | Permalink

Re: The Lie of “It’s Just Math”

Perhaps, at a minimum

This research was sponsored by the National Science Foundation under grant numbers CCF-XXXXXX and Air Force Office of Scientific Research under grant numbers FA-XXXXXX and FA-XXXXXX. The views and conclusions contained in this document are those of the author and should not be interpreted as representing the official policies, either expressed or implied, of any sponsoring institution, the U.S. government or any other entity.

could be supplemented by

Conversely, the views and aims of the Air Force Office of Scientific Research [or insert other appropriate body here] are those of the U.S. government and should not be interpreted as representing the position or opinions, either expressed or implied, of the author(s).

Posted by: David Roberts on December 13, 2020 10:59 PM | Permalink

Re: The Lie of “It’s Just Math”

The DoD is a department of the executive branch of the US government, and the actions of the DoD are ultimately actions of the US government. So how can a mathematician morally justify accepting funding from the US government but not the DoD? Where do we draw the line?

Posted by: Advocatus Diaboli on December 14, 2020 12:41 AM | Permalink

Re: The Lie of “It’s Just Math”

I don’t find personal morality, line-drawing, purity, etc., to be useful ways of thinking about all this. What matters — I mean what actually matters in human terms — is the predictable consequences of your actions. That’s a phrase of Chomsky’s:

You’re responsible for the predictable consequences of your actions. […] The most important thing for me and for you is to think about the consequences of your actions. What can you effect? These are the things to keep in mind. These are not just academic exercises. We’re not analyzing the media on Mars or in the 18th century or something like that. We’re dealing with real human beings who are suffering and dying and being tortured and starving because of policies that we are involved in.

I do appreciate that in the US, a lot of government funding is channelled through the military. And I appreciate that this presents many of my US friends and colleagues with difficult situations. But the ultimate question is “what are the predictable consequences of my actions?”

Any serious, thoughtful answer to that has to go beyond “it’s just math” and consider, for instance, the four points highlighted in Jade’s article.

Posted by: Tom Leinster on December 14, 2020 12:58 AM | Permalink

Re: The Lie of “It’s Just Math”

Interestingly, Chomsky worked in a military funded lab for much of his early career (and to some extent his later career). At some point he considered leaving MIT because of the ties to the government, but ultimately decided against it. These days he seems to think that the practice of military funding of abstract academic research should not happen, but it doesn’t seem like he thinks researchers should not take the funding. (Side note, he also thinks private funding of academic research is a problem. He even thinks that NIH funding is a problem, though for other reasons). The problem is the system, which we have an obligation to organize against and produce change. To me, it seems unlikely that not taking DARPA grants is going to do much, but I applaud the discussion. It’s important to not let these issues dissapear from our minds.

Posted by: Adam on December 14, 2020 5:30 PM | Permalink

Re: The Lie of “It’s Just Math”

Yes, Chomsky has often taken positions that have surprised people. As far as I can tell, that’s generally because he informs himself about the details of a situation then asks himself that same question — what are the predictable consequences of this action?

For example, some were surprised when he opposed Trump’s withdrawal of some troops from Syria. The famous leftist Chomsky, supporting US military presence in another country? Why?

Because the, from the left at least, the call for withdrawal was based on anti-imperialist principles. But principles have to be understood in connection with the human reality of the existing circumstances. A small, U.S. contingent with the sole mission of deterring a planned Turkish invasion, which was obvious, is not imperialism. It’s protecting the Kurds from an expansion of the atrocities and massacres that Erdogan has been carrying out both within Turkey itself and in the areas of Syria that he’s already conquered.

People often view Chomsky and others on the left as naive utopians disconnected from the harsh realities of the world we actually live in. Nice in theory, impossible in practice. And in Chomsky’s case at least, that’s the opposite of the truth. I don’t agree with him on everything, but he’s phenomenally well-informed and bases his positions on the real world. The guiding principle is to consider the “human reality”.


Why am I bothering to talk about Chomsky? Because I see the same criticisms being made of Jade’s position, or mine, and those criticisms are equally inaccurate here. John’s comment could be read as suggesting that what we care about is “purity” and “scolding” and that we’re not “actually trying to think things through”. Henry said “It all sounds nice to be above the fray, but we should really consider exactly what we are really doing” (as if we aren’t). Steve H thought Jade’s article “naive”. John seemed to suggest that some people’s aim is “just ‘avoiding evil’” rather than trying to “create positive outcomes”, and Steve A used “politically incorrect, morally suspect, ethically challenged” to summarize the problems of working with the military.

Those are all mischaracterizations. I don’t care about morality or purity. I care entirely about practical real-world consequences.

(Obviously I only speak for myself, not Jade.)

For example, if I could click my fingers and make the US military vanish entirely — or even just instantly scale it down to a size proportionate to the US population — I wouldn’t. Why? Because much as I’d like to see it gradually reduced, the reality is that right now, it’s so enmeshed in so many places around the world that instantly removing it would create terrible conflicts and a great deal of human misery. Those would be the practical real-world consequences. Of course that’s a hypothetical that has 0% chance of happening, so it’s not a serious question. I only use it because Mike talked about “imagining a world without the US military”, to illustrate the point about always considering the human reality.

For mathematicians, most consequences are long-term. That’s the case for both the mathematics itself and the social effects of normalizing military presence within academic commmunities. I think one reason why mathematicians talk so little about the real-world consequences of our actions is that they’re so indirect. That makes everything more diffuse, less visceral.

No specific deaths can ever be laid at your door. You will never look at TV footage of someone’s leg blown off by a US drone and know that you did that. You can read about the world’s largest humanitarian crisis, in Yemen, a result of the US- and UK-backed Saudi onslaught (and I highly recommend that last link), and tell yourself that although you work with the US or UK military, none of the suffering is directly caused by you. And maybe you don’t know whether your mathematical contributions were ever even put to use.

Modern warfare is increasingly indirect, and mathematical contributions to it are less direct still. So it’s more challenging to think about. But it’s a truism that anyone conscientious contemplating working with a violent armed organization has to do their best to think through the consequences first. Real-world consequences, real-world consequences, real-world consequences: that’s all that matters.

Posted by: Tom Leinster on December 15, 2020 11:54 AM | Permalink

Re: The Lie of “It’s Just Math”

The war in Yemen is being fought between the Saudi, UAE, and US-backed government of Yemen on the one hand, and a group whose slogan is “Death to America, Death to Israel, Curses on the Jews, Victory to Islam” on the other (see here.).

The attempt to try to end US support in Yemen is really an attempt to have the Houthis take over. It’s propaganda, and it’s not even good propaganda.

We’ve been hearing that Yemen was on the brink of complete starvation for what, five years now?

Posted by: Henry on December 15, 2020 7:10 PM | Permalink

Re: The Lie of “It’s Just Math”

In case I wasn’t clear enough about this, the reason I suggested imagining a world without the US military was because you (Tom) said

There are mathematicians who believe that by and large, the US military has a positive effect on the world. Personally I find that position extraordinary…

It seemed to me that if the question is whether “by and large, the US military has a positive effect on the world”, then imagining a world entirely without it is the appropriate comparison to make.

But this is, certainly, quite a different question from (1) whether the US military should be smaller, (2) whether the US military should be used less, and (3) whether the US military should improve its technological capabilities, and moreover these other three questions are quite distinct from each other. I didn’t, and don’t, intend to express any opinion on (1) and (2). My opinion on (3), which is I feel probably the one of most direct relevance to accepting military funding for mathematics, is that in order to continue having its net positive effect on the world, it must, because its adversaries are certainly doing so.

Posted by: Mike Shulman on December 16, 2020 4:48 AM | Permalink

Re: The Lie of “It’s Just Math”

Tom wrote:

Military involvement in math is particularly an issue in applied category theory, and particularly an issue in the USA.

Maybe all of category theory? For example:

Or in the introduction to Mac Lane’s 1963 book Homology:

For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science.

Or in the introduction to the 1971 edition of his Categories for the Working Mathematician:

I have profited much from a succession of visitors to Chicago (made possible by effective support from the Air Force Office of Scientific Research, the Office of Naval Research, and the National Science Foundation): M. André, J. Bénabou, E. Dubuc, F. W. Lawvere, and F. E. J. Linton.

Or in 2014, on the Homotopy Type Theory blog:

We are pleased to announce that a research team based at Carnegie Mellon University has received a $7.5 million, five-year grant from the US Air Force Office of Scientific Research, as part of the highly competitive, DoD Multidisciplinary University Research Initiative (MURI) program. The MURI program supports teams of researchers that intersect more than one traditional technical discipline, and our effort will focus on mathematical and computational aspects of HoTT. The team consists of Jeremy Avigad, Steve Awodey (PI), and Robert Harper at CMU, Dan Licata at Wesleyan University, Michael Shulman at the University of San Diego, and Vladimir Voevodsky at the Institute for Advanced Study. External collaborators are Andrej Bauer (University of Ljubljana), Thierry Coquand (University of Gothenburg), Nicola Gambino (University of Leeds), and David Spivak (Massachusetts Institute of Technology).

In order to encourage collaboration and development, the funds will be used to provide support for students, postdoctoral researchers, visiting junior and senior researchers, meetings, and conferences. We are delighted about the opportunities that the grant provides to build infrastructure and lay the foundations for this exciting research program.

The technical portion of the grant proposal can be found here: MURI proposal (public).

In 2017, an Army Research Office Broad Agency Announcement for Fundamental Research wrote:

Modeling frameworks are desired that are able to eschew the usual computational simplification assumptions and realistically capture … complexities of real world environments and phenomena, while still maintaining some degree of computational tractability. Of specific interest are causal and predictive modeling frameworks, hybrid model frameworks that capture both causal and predictive features, statistical modeling frameworks, and abstract categorical models (cf. Homotopy Type Theory).

and later:

Homotopy Type Theory and its applications are such an area that is of significant interest in military applications.

The examples could be multiplied.

Posted by: John Baez on December 14, 2020 1:58 AM | Permalink

Re: The Lie of “It’s Just Math”

I take your point, and I hadn’t seen those last two quotes before — thanks.

I still think this is more an issue in applied category theory than category theory as a whole; e.g. consider the issue of sponsorship of ACT2020 by weapons manufacturers, or the question of how the Topos Institute will be funded, and other examples to do with specific applied category theorists who I won’t mention by name here. But it’s not really an important point.

Posted by: Tom Leinster on December 14, 2020 11:35 AM | Permalink

Re: The Lie of “It’s Just Math”

I agree that we should expect the DoD and military contractors to have the good sense to fund applied category theory more than “pure” category theory… making the moral challenges greater in this area. But as their memo shows, they consider homotopy type theory to be “applied” category theory. Among other things, it’s bringing a lot of very smart mathematicians into the project of developing computer-verified proofs — breaking down the walls between math and computer science. And as Jade pointed out elsewhere, formal proof verification has lots of applications:

Posted by: John Baez on December 14, 2020 4:44 PM | Permalink

Re: The Lie of “It’s Just Math”

The DoD does not need help to fight against low-tech adversaries from mathematicians. Mathematicians might be useful in dealing with highly sophisticated threats from authoritarian highly sophisticated countries like China and Russia.

As bad as one thinks the US military has been, I don’t think it’s defensible to refuse to cooperate against hostile authoritarian adversaries. It all sounds nice to try to be above the fray, but we should really consider exactly what we are really doing when we try to lock the military out from mathematics.

Posted by: Henry on December 14, 2020 2:03 AM | Permalink

Re: The Lie of “It’s Just Math”

This is not relevant to your main point, which is worth a careful discussion, but:

I’m pretty sure the US Department of Defense, CIA and NSA use fancy math almost as much against low-tech adversaries as against high-tech ones. The amount of math required to locate a guy riding in a car in Somalia and obliterate him from afar with an AGM-114 Hellfire is, I think, significant.

Posted by: John Baez on December 14, 2020 3:21 AM | Permalink

Re: The Lie of “It’s Just Math”

I dunno, is it a bad thing that we got that guy (an enemy of the USA and Somalia) with the consent of the government of Somalia? Do you reckon that we found where he was with math or with traditional intelligence gathering?

Posted by: Henry on December 14, 2020 5:27 AM | Permalink

Re: The Lie of “It’s Just Math”

““I saw my son die, burnt in the rubble in front of me,” said one bereaved woman from Raqqa. “I’ve lost everyone who was dear to me. My four children, my husband, my mother, my sister, my whole family. Wasn’t the goal to free the civilians? They were supposed to save us, to save our children.”

From this article:

Posted by: Jade Master on December 14, 2020 4:00 PM | Permalink

Re: The Lie of “It’s Just Math”

I dunno, is it a bad thing that we got that guy (an enemy of the USA and Somalia) with the consent of the government of Somalia?

My comment here didn’t say anything about anything being good or bad. I was simply saying that the US uses lots of fancy math even against relatively low-tech adversaries.

Do you reckon that we found where he was with math or with traditional intelligence gathering?

Try to get a missile to fly hundreds of miles and blow up at a specific moving target without using math.

I don’t know how the intelligence gathering worked in this specific case, but these days counter-terrorists use lot of cryptanalysis, traffic analysis and the like, as well as old-fashioned spycraft. There’s a lot of math involved.

The 22 chapter titles are pretty interesting.

Posted by: John Baez on December 14, 2020 6:27 AM | Permalink

Re: The Lie of “It’s Just Math”

It all sounds nice to try to be above the fray

Again, I don’t think purity is a helpful way of thinking about this. I agree with the rest of your sentence:

we should really consider exactly what we are really doing when we try to lock the military out from mathematics.

We should absolutely consider this. We should face up to the likely real-world consequences of working with the military, or weapons manufacturers, or the NSA, etc., or not. We should consider the predictable consequences of our actions.

Some people will conclude that US military might is good for the world and want to boost it further. Others won’t. Much of humanity regards the US itself as a hostile adversary, and, as polls repeatedly show, the greatest threat to world peace. Everyone has their own opinion about this. But no one should take it lightly.

Posted by: Tom Leinster on December 14, 2020 11:45 AM | Permalink

Re: The Lie of Its Just Math

Thanks for sharing!

One topic that hasn’t been brought up– at least I didn’t see it– is the secretivity of the US Military.

If your work, which we will assume is open to the public, is used by the US government in applications that are top secret, then any new findings will be top secret as well.

Thus, not only can your work be used to do bad things, it can also be advanced in an anti-scientific way, that is, in secrete! Thus preventing science from being a product for all.

In fact, there are entire secrete government journals.

This is one of many big reasons I will not work with the US military. I feel our work belongs to the world not to my government.

I do take money from the NSF, but I don’t see this as directly working with the US military.

Posted by: Harley Eades III on December 14, 2020 3:31 PM | Permalink

Re: The Lie of Its Just Math

Thank you for sharing your experiences and I very much appreciate your support Harley.

Posted by: Jade Master on December 14, 2020 3:55 PM | Permalink

Re: The Lie of “It’s Just Math”

The article is ridiculous and naive.

The DoD doesn’t _care_ about gaining access to your mathematical community. A very few people like me see promise in “applied applied” category theory and struggle to get others in our orbits to drink the Kool-Aid. Like me, they are in the von Neumann camp, not the Grothendieck one. If y’all want to lecture in the forests to prove a point then go for it. Your perceived adversaries in DoD have nothing to lose from your disengagement because you’ll have produced nothing of value to them.

Your math _is_ too abstract to be useful. Your ideas will not be “applied applied” until they are mature, and they are uniformly not yet. People like me make them mature enough, with considerable effort, given a good enough reason. But I have had enough trouble applying my own very specific and concrete forays into ACT. If you want anyone to make your ideas mature enough to be applied, then you should come to terms with the fact that applications will inevitably be out of your hands, for better or worse. I believe it will mostly be for the better. Grothendieck left IHES and became a hermit. Are any of you glad that he did? Von Neumann helped usher in computer science and much of modern economics. I for one am glad that he did. I know which of these two had a bigger net positive impact on the world (and even more certainly in their own productive span).

The DoD doesn’t care about normalizing themselves. The DoD is normal: you are not. You can decry it, but I don’t think you can honestly deny it: it is a fact. And I’m sure that some of those who have met me can vouch for my utter lack of concern about what others think of me personally. There is no conspiracy at NSA or DARPA about seducing applied category theorists. I have been in closed door funding meetings (mostly for quantum computing) as a government participant. There is no man behind the curtain. There are only other mathematicians with different research interests and ethical stances than yours, and I have never encountered a Teichmuller. (If any of you think I am one, I suggest you ask me privately about my positions and actions outside of mathematics: you will be quickly disabused of this notion.)

The DoD will not lie to you. But neither will they assume that you are naive enough to think that you have an exclusive right to ideas that you put into the open, or to think that they are not actually a military organization that is necessary in some form (for sad but inevitable reasons) so long as humans are just slightly evolved chimps. DoD funding agencies frequently dual-track applications: I’ve seen many examples of this and produced slightly nontrivial mathematics of my own this way. But again, I’ve been in the funding meetings. I’ve never known anyone to lie. The idea that people like me live on a different moral plane from “you” is ultimately false and self-defeating. Many of you are collectively arguing from the privilege of a position (whether youth or tenure) that frees you from the obligation to actually grapple with work that might actually be useful out of the box.

PS–for those who have been concerned about my personal involvement in your orbit, I am no longer at BAE, but at another DoD contractor (that I am not naming, much less representing here) doing the same sort of stuff. I look forward to engaging many of you in conversations in the flesh down the road.

Posted by: Steve Huntsman on December 14, 2020 3:42 PM | Permalink

Re: The Lie of “It’s Just Math”

Grothendieck left IHES and became a hermit. Are any of you glad that he did?

Yes: he set an example showing that even his incredible contributions to mathematics were not as important to him as human lives. If Grothendieck can draw the line and say “I won’t do mathematics if it crosses here”, then it makes me realise that I certainly can, because my mathematics certainly aren’t even comparable to his.

Posted by: Tim H on December 14, 2020 4:16 PM | Permalink

Re: The Lie of “It’s Just Math”

Continuing in my practice here of making tiny nitpicky comments that aren’t aimed at defeating or promoting anyone’s argument: it’s a bit misleading to say “Grothendieck left IHES and became a hermit”. They were, in fact, two separate acts.

Grothendieck left IHES around 1970 when he discovered that it was receiving military funding. (Some have commented on his naivety for not having known this all along.) He became a temporary professor at Collège de France for two years. He then became a professor at the University of Montpellier, where he worked until his retirement in 1988. In 1991 he moved to an undisclosed location in the Pyrenees—that’s when he “became a hermit”, though as far as I can tell he was still perfectly friendly to his neighbors.

In the period from 1970 to 1991 he did a lot of important mathematics. Around 1983 he wrote À la Poursuite des Champs, a massive letter that introduced nn-categories and nn-stacks. In 1984, he wrote Esquisse d’un Programme, actually as part of applying for a position at the Centre National de la Recherche Scientifique (CNRS). This initiated the study of dessins d’enfant (a new approach to Riemann surfaces) and anabelian geometry (a bunch of questions involving étale fundamental groups). In 1991 he finished a 2000-page book Les Derivateurs, which introduced derivators (an approach to nonabelian homological algebra).

And then he disappeared from view.

Posted by: John Baez on December 14, 2020 5:06 PM | Permalink

Re: The Lie of “It’s Just Math”

Steve, you say that our math is “too abstract to be useful” to the DoD, and that the DoD also doesn’t care about buying status in the mathematical community. In your opinion, why does it fund mathematics?

Posted by: Tom Leinster on December 14, 2020 5:57 PM | Permalink

Re: The Lie of Its Just Math


DoD funding is usually to invest in a) specific mathematics for the medium-to-long term (like DARPA helping to bootstrap topological data analysis ~15 years ago), and b) for the general practice of mathematics, since a rising tide lifts all boats. Maybe also some other reasons that don’t immediately spring to mind.

Frequently there will be someone like me (but in the government) who sees where things could lead and makes a small investment in the public domain. Behind closed doors, there will be some parallel effort to demonstrate or at least outline the utility. More often than not this is just a program manager impedance matching between stuff on arXiv and higher-ups. But sometimes there are actual substantive technical efforts in parallel. Usually these are not secret, just not advertised (that much). Very rarely, this results in some actual capability that gets used.

One good reason for DoD to fund ACT would be that it catalyzed the development of UMAP (by folks who work for the Canadian version of Heilbronn, no less).

PS- the autopopulation of the “subject” line on this website is really annoying!

Posted by: Steve Huntsman on December 14, 2020 6:10 PM | Permalink

Re: The Lie of Its Just Math

One other aside: not mathematics, but DARPA funding of Moderna led directly to its COVID-19 vaccine. There are many other instances of social good coming from military funding, but few are unalloyed from a purely anti-DoD perspective.

On the other hand, what’s the difference between taking funding from NSF and NSA or DARPA? I have news for folks who want to draw that line: those program managers talk to each other, and even move back and forth between organizations and give funding advice to each other.

Posted by: Steve Huntsman on December 14, 2020 6:19 PM | Permalink

Re: The Lie of It’s Just Math

PS - the autopopulation of the “subject” line on this website is really annoying!

It’s really easy to change the subject line or blank it out in your comment: there’s a gray box that says “Subject” next to it. I just used this to correct a missing apostrophe.

Usually people change the subject by accident, typing in their name, and get embarrassed when their own name appears as the subject of their comment! It looks so egotistical!

There is, alas, no way for the moderators to fix this retroactively.

Posted by: John Baez on December 14, 2020 6:53 PM | Permalink

Re: The Lie of Its Just Math

Chrome does this on its own when I try to autopopulate my name and email, and so much as clicking on the required email field brings up the autopopulate option. I have to manually un-autopopulate the subject line each time. First world problem.

Posted by: Steve Huntsman on December 14, 2020 7:05 PM | Permalink

Re: The Lie of “It’s Just Math”

The idea that people like me live on a different moral plane from “you” is ultimately false and self-defeating.

I don’t know what a moral plane is, and as I seem to keep saying, I don’t find the language of morality very useful. However, there is a difference between those who work with the US military and those who don’t. It’s that those who do have chosen to help a group that habitually inflicts violent death, maiming, and psychological trauma on a massive scale.

I’m not arguing that that’s a bad thing, at least not now. I mean it as a factual statement only. One can make the judgement that all this is outweighed by positive effects. But whatever “moral” means, making this judgement is a truly massive moral weight. Those who have decided that all the horrors and the human suffering are worth it, and are willing to join with those who inflict them, are in a genuinely different position from those who have not.

One might hope that everyone who works with the military or for arms manufacturers would first have weighed up the human consequences carefully, looking at photos of the corpses and gruesome injuries caused by the organizations they’re joining, listening to the stories of those who’ve had husbands or daughters killed by American missiles, learning about the human cost of the chaos and misery that have often followed US military interventions in other countries. I’m sure some have done that, maybe including some people in this conversation, weighing it all up and coming to the conclusion that the pros outweigh the cons.

However, I guess most people who work with or for the military — including most mathematicians who do — just kind of go along with it, because the military is a part of the establishment, or because they see people they respect doing it, or because of some patriotic values, or because they don’t like thinking about “politics”, or because they trust the wisdom of their political leaders.

I’m sure most of your colleagues, Steve, have been pleasant people who love their families and would help a friend in need and say “who’s a good boy?” to their dog in that same silly voice we all use — all the things that make us ordinary humans. I’m sure the mathematicians make the same corny math jokes and know some people I also know and would blend right in at a math conference. I don’t think anyone’s imagining moustache-twirling Hollywood villains. But in choosing to work for the DoD and BAE etc., you really have made an extraordinarily weighty decision that most of us haven’t.

Posted by: Tom Leinster on December 14, 2020 9:18 PM | Permalink

Re: The Lie of Its Just Math


Posted by: Steve Huntsman on December 14, 2020 9:50 PM | Permalink

Re: The Lie of “It’s Just Math”

Thank you Jade for raising such an interesting issue, and thank you Tom for inviting everyone to reflect about it.

I posted my two cents on the issue on my blog.

Posted by: Matteo Capucci on December 14, 2020 4:50 PM | Permalink

Re: The Lie of “It’s Just Math”

Nice blog article. I especially like this part:

Strive to work for things likely to have a positive impact on humanity. The idea is to have a good endgame in mind, so that, hopefully, your net impact will be more positive than negative. However, for the same reason pointed out above, this is hard unless you happen to work quite close to applications.

Nonetheless, I find it a good exercise to try to see in the distant future and look at what your work is doing (a kind of ‘where do you see yourself in 10 years?’ question). Moreover, you have the power to frame your work in a specific narrative and that can be extremely effective to steer the people engaging with it in the right direction, or even to just attract the ‘right’ people and repel the ‘wrong’ ones.

Indeed, taking action to create positive outcomes is a much more interesting challenge — and I hope also more effective — than just “avoiding evil”. Mathematicians should probably talk more about this side of the equation: how to get people interested in the good applications of our work.

Posted by: John Baez on December 14, 2020 11:17 PM | Permalink

Re: The Lie of “It’s Just Math”

Let me ask a very simple question to those of you who think it’s just math: would you feel the same if I go and present in North Korea, Iran, and other sanctioned countries work that is just pure category theory, or even ACT? What about if that conference was sponsored by the Iranian intelligence service? Or the North Korean military? Is it then just a matter of me presenting useless information to disinterested but generous funders?

Posted by: Juan Sebastian lozano on December 14, 2020 5:19 PM | Permalink


This made me smile. I have literally used the example of “it’s OK for the [insert country X military] to see this” when clearing work for public release.

In the other direction, I once brought the work of a person in [country Y quite friendly to the US] to the attention of folks in DoD who were doing something similar. It actually helped advance the at-the-time-classified (soon thereafter declassified) US research effort (i.e., money appeared soon after), and along the way resulted in a technology transfer to a startup that got put into an actual network security product. That company ended up getting acquired by a tech giant for nine figures, so it must have been doing something right in helping to keep the internet slightly less unsafe. I did a startup of my own to try to get the actual tech right (but failed as a businessperson).

Posted by: Steve Huntsman on December 14, 2020 5:50 PM | Permalink

Re: Steve

Wonderful, so if this sort of work is definitely important enough to have serious classification review and export controls (which apply to non-clasified technical expertise, even that produced in academia unrelated to the DoD or even NSF), specifically targeted to prevent foreign militaries from obtaining them, then why exactly is it that the work of mathematicians isn’t actually important to the DoD? And why exactly are NSA, DoD, NGA, etc just funding a set of work that amounts to useless research.

I actually agree with your earlier post, there is no boogyman behind the screen, it’s just a bunch of scientists and military or intelligence bureaucrats funding basic research and translations into applications which might or might not pan out to be useful for the US. It’s not a matter of a Machiavellian takeover of math by those who wish to kill Pakistani kids for the fun of it. But isn’t that worse? That somehow absent true evil we manage to create the hardware and software of occupation and slaughter? And that to push back against that is just a difference of research interests? And I understand very well the relationship between the abstract and the applied (I spend most of my day programming, after all) but to say it’s okay if the government pays you to perfect the process of enriching the uranium, just not create schematics for the bomb, doesn’t make much sense to me.

And the idea that “The DoD is already normal, you’re not” is precisely the problem. The defense-industrial complex runs deep in every way into academia (and here I am making an observation against my own interests), and should our government start doing things we find objectionable how are we as a society to continue doing math without supporting them? If they’re so normal, and so deeply embedded in our research processes, then it seems they’ve created a world where that’s impossible. Where those of us who find drone strikes’ civilian casualties largely unconscionable cannot eat and continue to do math. In a way, the world you paint is much much worse than the world Jade posits in her original post.

Of course good things come from military funding, the very medium I’m writing this on has billions of dollars of public funding, much of the early funding military, to make it possible. And sometimes the military and intelligence agancies even fund things that make oppression harder, like encryption and TOR. But, the question is not “is the military good”? Eisenhower, knowing full well the strength and importance of the military to defeating Hitler, was the one that coined the term military-industrial complex precisely because it’s not a matter of doing good sometimes, it’s a matter of protecting a certain kind of freedom from the monopolization of our government, of our academy, of our lives, by those who profit from war.

Posted by: Juan Sebastian lozano on December 14, 2020 7:11 PM | Permalink

Re: The Lie of “It’s Just Math”

I am proud that my work is funded by the US military, and I am happy if it can be of use to them. I believe that despite its many failings and mistakes (which include some truly terrible ones, and all of which we can and should criticize and work to reform), the US military is one of the greatest forces for good in the world today, and has been for most of the past century. Often this is less because of what it does than because of what it prevents others from doing. I find it extraordinary that anyone could spend a few minutes imagining a world without the US military and not conclude that by and large, its effect on the world is positive. Note, for instance, that after the US, China spends more on its military than the next four countries put together — and two of those next four are Russia and Saudi Arabia.

I do not want to have an argument here about the military, and I will do my best not to respond to further discussion on that subject. But given how difficult it can be for academics (especially younger ones) to dissent from progressive orthodoxy, I don’t want any readers to get the impression that there is unanimity among Cafe hosts on this issue.

Posted by: Mike Shulman on December 14, 2020 6:39 PM | Permalink

Re: The Lie of “It’s Just Math”

Mike wrote:

I don’t want any readers to get the impression that there is unanimity among Cafe hosts on this issue.

By the way, it should have been clear from my comments that I don’t think in at all the same way about this stuff as Tom or Jade—or Mike, for that matter. I have complicated feelings about this stuff. Since I don’t really feel like writing a massive screed speckled with comments like “on the other hand”, I’m mainly preferring to throw more facts into the discussion.

Posted by: John Baez on December 14, 2020 7:00 PM | Permalink

Re: The Lie of “It’s Just Math”

Respect for Mike for taking an unpopular position. Since HoTT was mentioned as an example of DoD funding I’ll state my own view, which is a bit different from Mike’s, but still compatible: not “it’s just math”, but rather “it’s math!”. That is to say, mathematics is important enough in it’s own right that we should take our funding wherever we can get it. Politically incorrect, morally suspect, ethically challenged - it’s still math, and it’s worth it. A good theorem will outlast the politics of the day - or the century. We should not loose sight of the intrinsic value of mathematics as one of the highest forms of human intellectual output. We’re not talking about building some better vacuum tubes.

Posted by: Steve Awodey on December 15, 2020 3:55 AM | Permalink

Re: The Lie of “It’s Just Math”

I too am glad that we’re hearing from people with different viewpoints. And I’m glad to hear from Steve A, because I always wondered how he felt about the massive DoD funding for homotopy type theory.

There’s a persistent mischaracterization of people with views similar to mine, or Jade’s, that I address up here. It comes from people who have chosen to work with the military, and implicitly makes the claim that they’re the ones in touch with the real world, unlike us naive utopians who only care about lofty principles, unmoored from messy reality.

Personally, I haven’t suggested that anyone else in this conversation is naive, blindly idealistic or ill-informed about facts on the ground, whatever I might sometimes suspect. Maybe the conversation would be more productive if everyone avoided doing that.

Posted by: Tom Leinster on December 15, 2020 1:06 PM | Permalink

Re: The Lie of “It’s Just Math”

Really appreciated this comment. This kind of thing needs to be said more often.

Posted by: Henry on December 15, 2020 7:14 PM | Permalink

Re: The Lie of “It’s Just Math”

Really pleased to see this excellent post of Jade Master promoted on here. I don’t intend to comment much on the topic for reasons that may be more or less obvious to at least some of the people on this thread (so I will not be responding further to the thread), but I will just say the following:

1) I want it on the record that while I have immense respect and regard for my colleague Mike Shulman, I disagree almost entirely with what he has said in this thread and find it shocking & disturbing in some respects. I do appreciate the welcoming attitude to dissenting points of view, however — something I frequently must take advantage of.

2) I think that while it is admirable to want to disengage from military funding, there may be some who underestimate the level of integration in the imperialist system: almost any source of grant funding in advanced capitalist-imperialist countries, whether it is private or public, is in essence tainted in the same way (and I am not referring to morals or purity, but rather in the sense of contributing materially to the evil imperialist project).

The military is only but one weapon wielded by imperialism to sow misery and cause trouble around the world, and works hand-in-hand with finance capital (that quant job some people planned to take when they get burned out of the academy), large corporations (Facebook, etc.), the charity/philanthropy sector, NGO industrial complex. Not to mention the destruction of human living environments by large industry — a trend that disproportionately affects the masses of countries under the boot of imperialism.

I applaud Jade’s post and much of Tom’s discussion of it. But I think we need to move toward a discussion of what scientists in mathematics can do to actively attack the foundations of imperialism, this demon that enslaves humanity for the sake of super-profits, and veer away from too much emphasis on individual actions that may have less factual impact than intended.

Posted by: Jonathan Sterling on December 15, 2020 1:58 PM | Permalink

Re: The Lie of “It’s Just Math”

What are you even talking about? Which countries are currently under the boot of (implicitly Anglo-American) imperialism? Why are you talking like a robot?

Anyway, I prefer the current system to whatever you’re advocating.

Posted by: Henry on December 15, 2020 7:27 PM | Permalink

Re: The Lie of “It’s Just Math”

Why are you talking like a robot?

Feelings run high on this topic, but insults are out of bounds. If there’s more like this, I’ll delete it.

Posted by: Tom Leinster on December 15, 2020 11:45 PM | Permalink

Re: The Lie of “It’s Just Math”

I’ve deleted a comment here. However much you might disagree with some of the views expressed here, let’s try to treat what others write with seriousness and respect.

Posted by: Tom Leinster on December 16, 2020 9:44 AM | Permalink

Re: The Lie of “It’s Just Math”

Well, that’s fair, because despite my reciprocal great respect and regard for you, I also find some of your political views shocking and disturbing. (-:

I’m glad you appreciate the freedom to express dissenting points of view, though. For what it’s worth, safeguarding that freedom is, in my opinion, part of the net positive effect of the US military.

Posted by: Mike Shulman on December 16, 2020 4:55 AM | Permalink

Re: The Lie of “It’s Just Math”

About military exploitation of mathematical result, I recommend Roger Godement’s preface in his first book on analysis : Analysis I Convergence, Elementary Functions. For example this ferocious judgment : “And I do not see why being opposed to the military exploitation of mathematics and science should be considered as a more political stand than for instance, helping Los Alamos or Arzamas to develop their “weapons of genocide” was.” But not only, the preface (and other parts in the treatise) is about relations between science - in particular mathematics - and weaponry.

Grothendieck’s decision was also motivated by other issues than the military ones. He talks about it in his conference at Cern in 1972 : “Je voudrais préciser la raison pour laquelle au début j’ai interrompu mon activité de recherche : c’était parce que je me rendais compte qu’il y avait des problèmes si urgents à résoudre concernant la crise de la survie que ça me semblait de la folie de gaspiller des forces à faire de la recherche scientifique pure” (Excuse my french..)

Posted by: Alexis de Saint-Ours on December 15, 2020 10:01 PM | Permalink

Re: The Lie of “It’s Just Math”

Excuse my French

Always a pleasure :-)

My amateur translation of what Grothendieck said:

“I would like to detail the reason why I initially interrupted my research activity: it is because I realized that there were such urgent prolems to solve concerning the crisis of survival that is seemed folly to me to waste strength on pure scientific research.”

And I very much agree with Godement’s point that you quote.

Posted by: Tom Leinster on December 15, 2020 11:53 PM | Permalink

Re: The Lie of Its Just Math

I’m unclear what this discussion is hoping to achieve. Presumably the logic behind disengagement with DoD has the form:

The political situation is X. If the political situation is X, then you should do Y and refrain from Z. Therefore, you should do Y and refrain from Z.

I very much doubt anyone’s value of X is going to be changed by a blog discussion such as this, and that’s surely where the variation of opinion will be. The hypothetical seems straightforward enough.

One point to raise: It’s very difficult to find a permanent job in the academic field of your choice. Foregoing certain funding sources may lessen your already slight chances. But, then, who didn’t realise this?

Posted by: David Corfield on December 16, 2020 8:13 AM | Permalink

Re: The Lie of Its Just Math

I’m unclear what this discussion is hoping to achieve.

The use of military force is an extremely serious undertaking. Some military groups like to hire mathematicians or pay them to do math. That leaves mathematicians with a very serious question, of which we’re now having a general discussion. I for one have learned quite a lot from it.

The hypothetical seems straightforward enough

If I understand correctly, you mean it’s straightforward enough that if I, a mathematician, am generally opposed to the actions of the armed forces, then I should never accept their money or any other kind of involvement with them.

That’s not straightforward enough, in the sense that very many mathematicians disagree. Opinions like “they’re paying me to do research that’s useless to them (suckers!)” or “good, less money for the bomb makers” or “it’s my only way to carry on doing math” (career first) are very common indeed. And we’ve seen some of those views expressed here.

Posted by: Tom Leinster on December 16, 2020 10:10 AM | Permalink

Re: The Lie of “It’s Just Math”

This thread has required some active moderation and there are other things I need to pay attention to for a while, so I’m closing comments now. Thank you, everyone, for the discussion.

Posted by: Tom Leinster on December 16, 2020 10:25 AM | Permalink