Written: June 29, 2011
Mathematics and Science is a communal enterprise, and it is very important that people share their ideas. Unfortunately, it is very hard to get the big picture. The number of good expository articles is, unfortunately, very small. (People who write them should be rewarded! A good expository article is worth one thousand mediocre (and even good) technical papers.)
People are at their expository best when they are begging for money, and in the case of mathematicians and scientists, this means writing a grant proposal. The scientific community would benefit a lot if people would publicly post their funded grants, and be generous with their ideas. If you are naturally generous, then this would be the right thing to do anyway, and if someone solves "your" problem, you should be happy. If you are ungenerous by nature and/or paranoid (like Bill L. (see below)) then it is also good. Once you posted a problem it is "yours", and whoever solves it should reference it, and by publicly posting it you establish priority (for what's it worth). This way you are safe. After all, if you are paranoid, then you may be afraid that those who reviewed your grant, and the panel members, may "steal" your problems, and not even acknowledge you!
Ideally, people should publicly post their funded grant proposals, for example, like in this page (Added July 10, 2011: another great example is Jim Propp's homepage). If you are being funded by the tax-payer, it is your duty to share your ideas. Don't worry, mathematics (and science) is so specialized, and there are so many different problems, that it is very unlikely that someone would "steal" your ideas, but the scientific public can benefit from the general part and background. There is another very good reason why one should make their funded grant proposals public. Our distorted academic system (in the so-called "top" schools) is "get-funded-or-perish". In order for young people to get tenure, and for older people to get promoted, they need to get "funded", or else you are nothing. It is a bad and unfair system, but granted (pun intended) that this is the system, one should give a chance to everyone. For not-yet-funded people (or for people who plan to apply for a special type of grant, like a CAREER award) it is important to have samples of successful grants. We all know that success in getting funded is only partly mathematical talent. A large component is being a talented sales-person and PR agent. Knowing how to concoct the optimal cocktail of buzz-words that would impress and intimidate the reviewers and panelists. Also know how to put just the right kind of hype for the "broader impact". If you are too honest, then you will get screwed, but if you are too dishonest you would also get screwed, you have to know how to do it just right, and walk the tightrope between under-hype and over-hype. So it is OK to say that your mathematics has potential broader impact for eliminating traffic jams and understanding deep water waves, even if it is a big stretch (that combinatorics, for example, could contribute to problems that are probably best handled by simulation), but it is probably not OK to say that your mathematics will completely solve the global warming problem. So, especially if you are young, and you care about other young people who are not yet funded, and would like to give them a fair chance, please, post your funded grant proposal.
If you are not yet comfortable doing it, at least you should be "comfortable" enough to Email a .pdf file of your funded grant proposal to any one who requests it. That much is obvious. Unfortunately, about a month ago, I had a rude awakening. A good friend of mine told me that he looked up, in NSF award search people who are close to his field who recently got a grant, and asked one of them let's call him Bill L. (Note: This is a made-up name, as much as I detest that Bill, it wouldn't be right to break, because of him, the ad hominem taboo, and reveal his (or her) real name). Bill L. replied that he does not feel "comfortable" doing it. This got me very mad. How piggy can one get! This is only mathematics, not Finance! Mathematics is infinitely wide and infinitely deep, and sharing your ideas (both mathematical and how to sell it) should be a must.
Luckily there is a way, that very few people know about, and even less people use. There is something called the Freedom of Information Act. I decided to exercise my rights, and followed the NSF's directions. After a week, Bill L. sent me a .pdf file of his grant and begged me to withdraw my request, that I kindly did. Apparently, it was easier for him to do it directly.
So here is my suggested algorithm for procuring a funded NSF grant.
And If and when you would get your own funded grant, please don't be like Bill L., and share your ideas. If possible, post your funded proposal in your website, but at least send it to anyone who requests it.