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I'm a postdoc in engineering who is interested in doing more "old school" mathematical theoretical research than computational research (i.e., running large simulations on a computer). Theory seems to get negligible funding in my area, but computational projects seem loaded with funding. I haven't seen any hard data on this, but my impression is that theory in engineering broadly seems to have been in decline since the 1970s or so.

The research project I'm working on right now is mostly computational, as were the vast majority of postdocs that I applied to. In the past few years I haven't seen any postdoc position in my area that was primarily theoretical.

How can one fund theoretical research these days? Am I wrong about getting funding for theory being difficult? It could be that few try to get funding for theoretical projects.


This is in my view irrelevant to the question but based on my experience talking to people, I know some will wonder. Why I'm interested in theory in short: Computational research in my area tends to produce very expensive pretty pictures of little value. Theory in contrast is cheap, and frequently of comparable accuracy to far more expensive computations. It also returns a lot of information that is uncommon (and often difficult to obtain) computationally like global trends and insight into the structure of the problem.

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    Research in string theory is very mathematical, but gets a lot of funding from private donors who look for some meaning in that theory. They also get funding because they tackle "big questions" like the formation of the universe. So, if I were you, I'd look for areas of theoretical math that are well funded compared to yours and see what is it they do differently. Or you could just pair up with some computational counterparts on projects you do the theoretical stuff.
    – Magicsowon
    Jan 6 at 21:36
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    Where is this? Funding differs in different places.
    – Buffy
    Jan 6 at 22:06
  • @Buffy: US, but I'm interested in advice relevant to anywhere in the world. Jan 6 at 22:28
  • You say theory gets little funding even though it is cheap. Funding agencies say theory gets little funding because it is very cheap. It produces results without funding. Jan 6 at 22:45
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    About two-thirds of papers in the Journal of Engineering Mathematics are "mathematical" in the sense you mean. You could try scanning those to see what funding sources they acknowledge. Jan 7 at 13:55
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The cynical ---but probably correct--- answer is that you camouflage the research you want to do inside a grant application that focuses on the research they want you to do. So in the situation you describe, where computational projects get loads of funding and theory-work gets negligible funding, you could construct a theory-based project, add a computational element to it, but then write up the application in a way that makes it look like the computational element is the major part. In fact, given the situation you describe, you are probably lucky that your existing work is in the hot area, and it would be best not to squander that advantage.

When I worked in a school of physical sciences in Australia, there was a running joke among the academics there that if you wanted funding for your project in mathematics, physics, chemistry, biology, oceanography, etc., all you had to do was add something about climate-change into it. So if you gave a talk on your research, sometimes one of the academics in the audience would use the question period to (jokingly) ask if you could connect this to climate-change, even if your topic had nothing to do with it. This was because the funding preference at that time (and still now I think) gave high priority to research on climate change, but low priority to much other scientific research.

Now, this is just the cynical answer, and I'm not sure if the academics in my department actually acted on this kind of reasoning, or if it was just the running joke around the traps. Similarly, this is not something I've done myself. In any case, I've seen this attitude around and seen anecdotal evidence of it being applied to secure funding. It shows a recognition that it is much easier to get funding for some things than others, and the strategic response that this provokes.

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  • This answer might be both cynical and true: identifying eventual applications of theory requires a wide knowledge of the field. The problem with many theoretical projects/papers is not that they are theoretical, but the fact that the authors do not bother to learn anything beyond a very narrow topic.
    – Miguel
    Jan 7 at 11:44
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This is a technical answer for the US. As a research administrator, I have submitted more than 100 applications for Computer Scientists at a world-class university in the last 6 years. I have successfully justified tens of millions of dollars across various fields of CS-- data science, AI, HCI, CNS, theory, etc. I have applied for funding to about 15 federal sponsors and dozens of non-federal ones including Silicon Valley. I hope to draw some distinctions between the CS and more classical math tracks, but please know that some of what applies to CS applies to math too; however my direct experience is mostly with CS and not math (which does have less funding overall). Lessons that I impart among all new faculty (and even some senior folks):

  1. Applications to federal sponsors are no longer based on one person's research. Teams and centers are the new normal. If you want to go solo, there are still some options, e.g., NSF has the CISE Core Programs (our theory folks tend to fall under CCF, primarily under AF "Algorithmic Foundations"). However, NIH has nearly eliminated the solo R01 project--interdisciplinary teams are nearly always more compelling unless you are applying for a small project (R03), or a class like DP2 that focuses on a single PI's research. The average age of getting an R01 as the PI (the basic independent research grant) is famously old -- mean 44 y.o., median 42 y.o. So this all being said, I find that my current CS folks (mostly AI and HCI at present) are always part of teams. They can cobble together millions of dollars over 5-10 funding sources as part of these teams. It's all about taking a small to middling chunk out a large project. It is possible that you have to contribute to a topic that you are less interested in, but often my folks work with hospitals who have may get 75% of the budget on the application. For us, 25% of a multi-million dollar application is still a lot of money for one project. My folks are almost always subcontracts or non-lead collaborators (i.e. "Co-PI" for NSF). I have someone who is a sub on DOD MURIs -- that is a lot of funding for the individual, but only a small percentage of a huge application. You have to figure out your niche; find people who will plug you into their projects. A junior PI can be very well-funded by playing a small role on other people's projects. In my institution, it is customary for senior faculty to give their name to a junior PI's project (i.e., senior PI is lead PI helping fund junior PI's work), and the senior PI prioritizes 1 month of supplemental salary for the junior PI as well as giving them a graduate student or postdoc.

  2. Be sponsor independent. CS faculty tend to apply to NSF of course, but they also find ways to hook into various DOD sponsors, NIH, DOE, Census Bureau, really any agency with a solicitation, their skills are probably valued in some small way. Again, $50k here, $300k there, it all adds up. You have to figure out which agencies fund basic research and through what mechanisms. You can search for open solicitations across all of the US government on grants.gov. If you are interested in US gov't contracts, you want sam.gov. I suggest finding PIs in your institution who can tell you what they submit to. You can also look them up online to see some of what they have been awarded (often on their own websites). Funding is a relationships game. I know folks who are friendly with the Program Officer/Program Manager, and this is how they get their funding. They know when to apply; they know what the agency wants to see in applications. They write for this relationship and they get the funding. This is very common with DOD, DOE, and NASA; somewhat with NSF.

  3. Unlike in the wet labs, funding in CS is based on paying higher salaries and low to no "other direct costs". We generally don't put computers on grants because too many projects run on them to spend time allocating percentages. Some faculty get cloud computing resources donated. We instead write $500k grants to fund our very large indirect cost rate as well as postdocs starting in the $70-75k range plus about 25% in fringe. That doesn't go very far. We want to compete with Silicon Valley, but we can't. This is the best we can do. This is actually about $20k above the NIH minimum for postdocs.

  4. When considering building a lab, I tell my faculty to consider two types of resources in particular: money and their time/patience. I have a PI (HCI is the focus) right now with over a million dollars (NSF funding split over about 5 grants, non-lead on 4 of them). I have to help them figure out how to spend in two years. This PI has less than 5 years as an assistant professor, with 2 years under COVID. Their postdoc just got a new job; they have two graduate students in their lab, one is 90% funded by a fellowship. What are we going to do? I have told them to hire at least 2 postdocs, but I won't let them hire just anyone. The reason is that CS labs tend to be small, especially ones bent on theory. At my institution, the theory labs like intimate groups and PIs do not expand them even when they are funded. So I ask my PI how they handle bad relationships -- if they are willing to part ways with a bad hire. If they hire someone who is just passable, they will have mediocre results for two years (possibly a third), and will end up feeling drained by having to support a postdoc who is supposed to be helping relieve the leadership role. So what can we do then if we don't hire a middling postdoc? I ask them if they have colleagues with students or postdocs who they can support on their project. Maybe a graduate student in a theory group, perhaps an ML person, etc. We chip away at that funding with small percentages on different projects, and this is the essence of successful resource sharing in CS and theory groups that I have found.

So what I would do is go to NSF's award search and look into what projects are funded for what you are interested in. Look up the PI's websites and see if their proposals are released on their site (not super common, but happens). If you really want to look at a successful application, you can submit a FOIA request to read the proposal that was funded. [ETA: Some folks feel you should contact the PI first and ask if they will share the proposal. If they say no, then you can submit the FOIA. Many PIs will share when asked.] Pay attention to the directorate. Are your people applying to the traditional MPS (Mathematical and Physical Sciences) or are they getting their funding through CISE (Computer and Information Science and Engineering)? If you are interested in total dollars each directorate and program awards, that information is available as well. Hint: DMS (Division of Mathematical Sciences) is not where the money is at. I highly suggest finding a person whose work you admire, looking them up in the NSF award system and seeing if you can find someone on a big center (e.g., AI Institutes, STC) and do a FOIA request to see how that person was written into the application.

Try to strike a balance between doing what you love, which may come without a lot of funding, and being willing to do something you don't want to do for much more funding. Find a research administrator at your organization and ask for advice. To your point about theory being cheap; that's a lot of your problem. IHE's (institutions of higher education) fund 9-month appointments for the PIs; they do their thing during the year; maybe in time hire a grad or two with startup funds, and they don't need a lot more than that. A bio-engineering PI would fail within months with a setup like that. The CS/math world is a much lower-stakes game (no judgement there; it just is). You don't have to deal with buying consumables, user fees, animals, human subjects, capital equipment, etc. etc.

Best of luck. The funding road is hard for everyone; even the top PIs. They spend more time thinking about funding their lab than you can possibly imagine. You are never "set".

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I'm not sure how the situation is in your particular area, but the usual life cycle is of a particular research direction is: people get spectacular results - get famous - get funding for students, postdoc etc. - get even more results - get into funding panels, editorial boards etc. - even more funding flows - ... - Lee Smolin and Peter Woit write books about them the direction is exhausted and people move elsewhere.

Theory in contrast is cheap, and frequently of comparable accuracy to far more expensive computations - if so, then there should be recent high-profile breakthroughs in your area with theoretical methods, recognized by the community. Someone who just made a breakthroughs would not be short on funding. Why not apply for postdocs with them?

If there are no such recognized breakthroughs, then it seems that the community sees the importance of theoretical methods in your area differently from you. Likely there is a reason for that. But it might also be that you are right and they are wrong; a way to convince them is to start publishing strong results obtained with theoretical methods by yourself.

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A lot hinges upon how correct you are about the greater accuracy of theoretical results. If theory is demonstrably more accurate/insightful, an idea would be to create a comparative investigation. Ask for computational resources in the grant, keep some money aside for theoretical work, and use the study to highlight the superiority of theory.

The problem could well be that many in engineering do not actually believe that theory can efficiently solve real-world problems faster than numerical simulations. Changing that perspective would be key to you being able to follow your chosen direction.

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Fund is a harder question than to be applicable to. Plenty of new mathematics has been invented in the process of helping undergird and understand the techniques of approximating simulation techniques first invented by engineers and physicists without a great understanding of the fundamentals first. Having the aide of mathematicians may speed up or make more trustworthy the results of new and experimental techniques in computing and simulation.

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