solutions to many of the large, imposing academic challenges of our era might be found in the depths of other such professor's "crank" files.
Interesting, because I feel as time goes on the reverse trend will hold true. It seems to me more and more of the "easy" proofs will be discovered, leaving only those that require more sophisticated mathematical machinery. And to obtain that you will have to, at the very least, have a PhD which will leave some track record of your ability. And the better credentialed you are the less likely you'll end up in a crank file.
I took 18.404 and really enjoyed it. I remember one lecture that Professor Sipser talked about the many years he wasted battling against P vs NP. He seemed pretty cynical about it getting solved without a lot of new groundwork being laid first, and this might contribute to why he so easily tosses proposed proofs into that crank file.
As new proofs are distilled, understood, enhanced, and internalised, so conjectures that were previously thought out-of-reach become more reasonable. "Easy" is a relative term - many things now presented at undergraduate level were once post-doctoral work. The "more sophisticated mathematical machinery" becomes an everyday tool for the working mathematician.
Interesting, because I feel as time goes on the reverse trend will hold true. It seems to me more and more of the "easy" proofs will be discovered, leaving only those that require more sophisticated mathematical machinery. And to obtain that you will have to, at the very least, have a PhD which will leave some track record of your ability. And the better credentialed you are the less likely you'll end up in a crank file.
I took 18.404 and really enjoyed it. I remember one lecture that Professor Sipser talked about the many years he wasted battling against P vs NP. He seemed pretty cynical about it getting solved without a lot of new groundwork being laid first, and this might contribute to why he so easily tosses proposed proofs into that crank file.