It's amazing how similar this is to my experiences answering the correspondence for https://www.eff.org/awards/coop https://www.eff.org/awards/coop However, I

It's amazing how similar this is to my experiences answering the correspondence for https://www.eff.org/awards/coop https://www.eff.org/awards/coop However, I'm at a big disadvantage there because while general-form compass-and-straightedge angle trisections have been proven to be impossible, primality testing is known to be possible and we are actively soliciting solutions. (And even worse, we—like the Clay Mathematics Institute with its much more intellectually-important problems—actually do have prize money available, unlike the trisection problem.) It's just that several people per month refuse to believe that the problem is difficult and computationally intensive and was selected for precisely those reasons! Instead, they believe that they can solve it by pure reasoning, by finding a formula that generates prime numbers. https://en.wikipedia.org/wiki/Formula_for_primes https://en.wikipedia.org/wiki/Formula_for_primes It's even possible that this is the computer age's equivalent of the trisection and cube-duplication problems... People I've corresponded with have exhibited all of the characteristics that Dudley describes here. :-( The worst part is that (rather like the angle trisectors) a majority believe that mathematical results are tested experimentally and observationally, by trying them out and seeing if the results look right. For example, a lot of people have submitted formulas for primes which allowed them to find two or three or four primes (or simply two or three or four numbers that they didn't know how to factor, even though the factor program from coreutils can do it). Also, like Dudley's correspondents who "think that the trisection is important" and even suspect it may lead to "practical alchemy" with transmutation of elements, we get claims from people who have found theories of everything, often including new physics theories and complete reinterpretations of mathematics and the foundations of mathematics, which they believe will be very important to society. One recent correspondent insisted that "10 is not a number, it is a concept". Dudley described being sad that people have in some cases spent years of effort pursuing a mathematical impossibility. I often feel the same way because you can see people who are very, very passionate about mathematics and yet refuse to believe that mathematicians know anything about their subject or that one should study mathematics in order to make progress in it.