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I'm applying for a fellowship wherein they ask for a long proposal about what I'm working on (a PhD thesis in pure math). Then they advise me that some of those evaluating me will be from non-math departments, so the proposal "should be jargon-free."

Right off the bat I guess [PSL2(Od):Γ] < ∞ is out of the question... I could explain what a manifold is to a mixed audience, but I think they'd need to do some homework before they followed what it might have to do with finite index subgroups of Bianchi groups (or whatever topic you might be studying). Without the "jargon" I feel like my whole language for it is gone. Afterall the reason we have so many definitions is because each one refers to a distinctly defined thing that we previously had no name for!

I can see that I could take a more historical, conceptual perspective, but I'd still be dancing around what I'm actually doing. It's especially hard to summarize something that is not even fully developed. I think that for people who don't study math, the only reference point is science applications, but those don't really exist here because then it would be applied math and not pure math.

I'm coming up short looking for anyone addressing this online. There are multidisciplinary tips about writing proposals, but I think the accessibility problem is at its biggest with pure math.

migrated from mathoverflow.net Jan 6 '15 at 12:32

This question came from our site for professional mathematicians.

  • 2
    You might find this recent blog post interesting or semi-relevant: golem.ph.utexas.edu/category/2014/12/… – Yuichiro Fujiwara Jan 6 '15 at 8:27
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    have a look at popular books about modern maths, e.g. on Fermat last theorem. Then, in the proposals you are allowed to write a bit of sci-fi... – Dima Pasechnik Jan 6 '15 at 9:42
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    Insist your proposal will promote synergy? No, wait... – BrianH Jan 6 '15 at 15:23
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    It's a shame that this question was migrated so that the OP may not see the comments. I would be interested to know what the fellowship actually is. This helps to figure out who is reading it, which seems at least very helpful and perhaps necessary in properly calibrating the level of technicality. – Pete L. Clark Jan 6 '15 at 15:46
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    I'm a little annoyed that this couldn't stay on Mathoverflow. Before deciding to post it I had noticed for instance these: mathoverflow.net/questions/39242/… mathoverflow.net/questions/39168/… – j0equ1nn Jan 6 '15 at 22:44
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What I did in that position:

  1. Explain some "motivation", even if it is far-fetched, from physics, economics, computer science ... for the general field of study.
  2. Try to paint some geometric picture of some (very simplified) version of your field.
  3. Make sure you stress that there are unsolved questions and that the solution would contribute to a general picture.
  4. Give some "hard" mathematical details at the end, coming with some disclaimer, to convince any mathematicians on the committee.

Generally, I would try to give an overview of the general aim and direction of the field and stress that there are "important problems in it".

  • I think this speaks the most to my concerns. If you don't mind my asking, did you have success with the strategy you suggest? – j0equ1nn Jan 6 '15 at 22:49
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    I tried twice and won once. – J. Fabian Meier Jan 7 '15 at 8:54
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I think that the key idea here is that they want to know why you are doing what you are doing more than what you are doing.

Let's say you're diligently working towards establishing an isomorphism between soliton elves and the christmas-tree singularity. That's all well and good, but:

  • There are lots of properties in the world. Why is isomorphism between soliton elves and the christmas-tree singularity an interesting property to try to establish?
  • Is there a higher-level strategy to your approach than "just do lots of math until the problem is solved"?
  • Why is the approach that you are taking a good one?
  • If you establish this property, what are the consequences, and what comes next?

A really good and clearly written proposal should be able to have its logic grasped by pretty much any scientist, whether or not they are capable of judging its originality, plausibility, and significance in detail.

  • 1
    What about the question of why I might be successful? Obviously they don't want to give the money to someone who isn't cut out for the project they proposed, but should I be including anything about how I've prepared myself to study the particular topic? Or is the transcript supposed to take care of that entirely? – j0equ1nn Jan 8 '15 at 1:15
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    @j0equ1nn In general, it is the combination of the CV (showing a track record of success) and the explanation of approach (showing why this is a good bet too) that is used for judging likelihood of success. – jakebeal Jan 8 '15 at 5:57
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Hint: what you are doing is "non-Euclidean crystallography". Then explain somewhat aspects of those two concepts, and why there is still research to do. I.e. Euclidean crystallography was all worked out long ago, but ...

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    Hint: if it's a hint and not an answer, it's not an answer and should belong in the comment section. – Yuichiro Fujiwara Jan 6 '15 at 9:49
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    That's actually a good tip. I mean I know it's non-Euclidean crystallography but we don't usually call it that in my particular niche -- but what an enticing thing to call it for this purpose. – j0equ1nn Jan 6 '15 at 22:47
  • @YuichiroFujiwara The OP left a message for you as an edit (see the edit history of the post). The message was: "Yuichiro I choose not to edit out the "Hint". Sometimes being helpful should trump being literal; see the other comments. MO, where this question originates, may see that otherwise, and I have departed." – ff524 Jan 9 '15 at 2:21
1

I'm adding a different answer based on the advice I got from my adviser, which is the method I ended up going with since after all he is my adviser. If I do end up getting the fellowship I will most likely change my selected answer to this one (though as you'll see the other strategies suggested are actually a part of this one). Here's what he told me:

Mainly, don't worry about the idea of it being accessible to people from other departments. When they say to write it that way and keep it "jargon-free" it really is kind of misleading compared to what they're actually looking for.

The important thing is that it look serious and professional, and writing in a more friendly tone can give the impression that the project is elementary. The evaluators (especially those not from the math department) will pay the most attention to the introductory portion of the proposal, so that is really the place to include the type of content suggested in the other answers. In particular, @J._Fabian_Meier's itemized list would end up with the first 3 items done quickly at the beginning, and the 4th item would take up the remaining majority.

After setting up the general motivation and context in the first couple of pages, go ahead and get into the mathematical details as though writing for a mathematician to read it. The other people on the evaluating committee will be looking for the math representative to confirm that what you are proposing is well considered and properly formulated. Moreover the more complicated and confusing the explanation looks to them the better. After all most people not in the math world gauge mathematical sophistication by their own inability to understand it, so just go ahead and scare them!

I will add though that I think the process of trying to explain my research to a mixed audience was really good for me in developing a broader perspective, even though my adviser had me start over again after that. I think that in the future, even if I don't end up using it (like what happened this time) I might take some time to write an outreach-style exposition of my project first, just to get that farther-reaching view of things.

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    "...after all most people not in the math world gauge mathematical sophistication by their own inability to understand it, so just go ahead and scare them..." And I get down voted?!?!? – Inquisitive Jan 20 '15 at 4:23
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    I respect your dissent and that is not a philosophy I live by, but it is a real and very common tactic (though perhaps unspoken). Most of the time I strive to combat people's tendency to respect something just because it's confusing. But if doing the opposite is what it takes to get the fellowship, well you have to choose your battles in this life, and I won't get very far with anything else if I can't get funding. – j0equ1nn Jan 20 '15 at 8:19
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My only suggestion would be to describe how the work you do could eventually be applied to improve the human condition. I simply don't accept that pure mathematics can't be of benefit to humankind.

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    By nature, it is unknown how pure mathematics will effect anything other than mathematics. My favorite example would be the fact that the imaginary number (so-named as an insult) was discovered in the 1700s and remained an intellectual curiosity until we found out that it models electricity and aerodynamics. I absolutely believe pure math benefits mankind, and that it's extremely important, but the moment you project to applications is the moment pure math becomes applied math. – j0equ1nn Jan 20 '15 at 8:22

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