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"Mathematicians who make big claims are obligated both to be right and to make themselves understood." I spent most of this academic semester struggling with t

by mrdmnd 14y ago

"Mathematicians who make big claims are obligated both to be right and to make themselves understood." I spent most of this academic semester struggling with the material in MIT's 18.404 (Theory of Computation) class taught by Michael Sipser - at the end of one of his lectures, he mentioned that he keeps a large file of proofs on hand from people claiming to have resolved the P vs NP conjecture, but has little time or faith to read them... he calls this the "crank" file. It seems to me (and I'm just a lowly undergraduate math student, feel free to discount/discredit this) that 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. Then again, there is definitely something to be said for establishing credentials - there's only so much time in the schedule of someone capable of verifying claims to be spent on verification, and it seems obvious that they should spend that time on solutions that come from people who have a track record of competence.

crntaylor 14y ago
Scott Aaronson summarizes it well when he says, of papers that have signs of being by 'cranks' -- > If I read all such papers, I wouldn't have time for anything else. [1] Crank papers often take a long time to read, by virtue of some combination of (i) using non-standard notation and terminology, (ii) lack of familiarity with the established literature, (iii) tortured writing style. If you claim to have proved a big new result, and you don't already have the credentials that will ensure you get taken seriously, then it is up to you to write in such a way that makes it easy for other academics to verify your work. Part of being an academic is interacting with other academics. [1] http://www.scottaaronson.com/blog/?p=304 http://www.scottaaronson.com/blog/?p=304
- jseliger 14y ago
  If you claim to have proved a big new result, and you don't already have the credentials that will ensure you get taken seriously, then it is up to you to write in such a way that makes it easy for other academics to verify your work. Part of being an academic is interacting with other academics. This reminds me of the introduction to Thomas Kuhn's The Road Since Structure: "Kuhn develops further the theme, which again goes back to Structure, that science is fundamentally a social undertaking. This shows up especially in times of trouble, with the potential for more or less radical change. It is only because individuals working in a common research tradition are able to arrive at differing judgments concerning the degree of seriousness of the various difficulties they collectively face that some of them will be moved individually to explore alternative (often—as Kuhn likes to emphasize—seemingly nonsensical) possibilities, while others will attempt doggedly to resolve the problem within the current framework" {Conant and Haugeland "Road"@3}.
- raverbashing 14y ago
  Well, scan it and put it on the internet! The usenet groups will have fun with it.
Q6T46nT668w6i3m 14y ago
While correctness is preeminent, it isn't the only factor for the adoption of a proof. Coherence and intelligibility are essential. Typically, context is important too (i.e. a proof leverages a reasonable and translatable program). While I hate that Michael Sipser uses the phrase "crank file," he's expressing an important distinction between mathematicians, computer scientists, or philosophers and, for example physical scientists: humanistic attributes are important. P.S. You're an "undergraduate math student," not a "lowly undergraduate math student." Hang in there. :)
- michaelhoffman 14y ago
  Publications in the physical sciences need to be intelligible as well, and an elegant model is considered a plus.
losvedir 14y ago
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.
- ColinWright 14y ago
  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.

by mrdmnd 14y ago

crntaylor 14y ago

Scott Aaronson summarizes it well when he says, of papers that have signs of being by 'cranks' -- > If I read all such papers, I wouldn't have time for anything else. [1] Crank papers often take a long time to read, by virtue of some combination of (i) using non-standard notation and terminology, (ii) lack of familiarity with the established literature, (iii) tortured writing style. If you claim to have proved a big new result, and you don't already have the credentials that will ensure you get taken seriously, then it is up to you to write in such a way that makes it easy for other academics to verify your work. Part of being an academic is interacting with other academics. [1] http://www.scottaaronson.com/blog/?p=304 http://www.scottaaronson.com/blog/?p=304

jseliger 14y ago
If you claim to have proved a big new result, and you don't already have the credentials that will ensure you get taken seriously, then it is up to you to write in such a way that makes it easy for other academics to verify your work. Part of being an academic is interacting with other academics. This reminds me of the introduction to Thomas Kuhn's The Road Since Structure: "Kuhn develops further the theme, which again goes back to Structure, that science is fundamentally a social undertaking. This shows up especially in times of trouble, with the potential for more or less radical change. It is only because individuals working in a common research tradition are able to arrive at differing judgments concerning the degree of seriousness of the various difficulties they collectively face that some of them will be moved individually to explore alternative (often—as Kuhn likes to emphasize—seemingly nonsensical) possibilities, while others will attempt doggedly to resolve the problem within the current framework" {Conant and Haugeland "Road"@3}.
raverbashing 14y ago
Well, scan it and put it on the internet! The usenet groups will have fun with it.

Q6T46nT668w6i3m 14y ago

While correctness is preeminent, it isn't the only factor for the adoption of a proof. Coherence and intelligibility are essential. Typically, context is important too (i.e. a proof leverages a reasonable and translatable program). While I hate that Michael Sipser uses the phrase "crank file," he's expressing an important distinction between mathematicians, computer scientists, or philosophers and, for example physical scientists: humanistic attributes are important. P.S. You're an "undergraduate math student," not a "lowly undergraduate math student." Hang in there. :)

michaelhoffman 14y ago
Publications in the physical sciences need to be intelligible as well, and an elegant model is considered a plus.

losvedir 14y ago

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.

ColinWright 14y ago
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.