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There are folks who claim they proved Fermat's Last Theorem, Riemman Hypothesis offering no more than a half a dozen pages (sometimes one or two pages) of proof, very few if any citations of previous works (where are the giants whose shoulders they stepped in?), among other suspicious characteristics.

I am not suggesting the one can measure the quality of a work by their number of pages alone, but for problems like those I mentioned, common sense suggest that their proofs must be really very complex and probably very long because if they were so simple as to be solved in a few pages, then someone would have discovered how to solve them much before the genius of Wiles or Perelman.

I also have seen various things like functions, theorems, etc which carries the name of its discoverer and that are considered by some to be trivial or/and of dubious importance for Math.

It is easy for a professional mathematician to the faults in those works and sometimes it is not too difficult for someone like me, that have little knowledge of math to see some faults, for they are common outside math, like lack of references.

What worries me is that if some particular work deals with advanced Math, it is not obvious for almost everyone if the work has or has not value, more or less like the Bogdanov affair. The Bogdanovs write about something that has a jargon and concepts so complex/advanced that seemed esoteric or post-modern to almost anyone, so in the absence of another easily identifiable clues one cannot see the work's real value unless that one is very well-versed in whatever the work deals with and those are unfortunately few.

This being so, I can elaborate the question: has someone designed a baloney detection kit specific/optimized for math, that can help in identifying if not all, most of the Math works that have no value even if they seemed at first sight elaborate, serious and erudite?

I can risk some opinions: lack of formalism, non-trivial notions that are not properly explained/defined, incomplete reasoning which omits intermediate calculations/deductions that are also non-trivial. But that is not specific to Math but for other sciences too.

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  • $\begingroup$ Pick at random. Since most Math works have no value even if they seemed at first sight elaborate, serious and erudite. $\endgroup$
    – user119256
    Feb 1, 2014 at 20:02

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Behold, the Aaronson crank detector kit:

http://www.scottaaronson.com/blog/?p=304

This is directed at complexity theory (in CS) but that doesn't make a difference.

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Let me play the Devil's advocate here. It's my personal opinion that such a "kit" can't exist. Hardy almost threw Ramanujam's letter before he detected its value. Galois's work was not taken seriously by leading mathematicians. Also, sometimes there are genuine mistakes in proofs that can't be fixed- but we do get some insights into the problem, esp. if the work is by a leading mathematician. At least we know one more approach that looked promising, and yet was wrong. These are small but significant progresses.

Of course, cranks exists aplenty, but if a crank detector mechanically threw away Ramanujam's or Galois's works, then the world would be much poorer.

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    $\begingroup$ Agreed. Then it seems we must use time as judge too. If something remain undervalued, highly doubtful and without little/no progress for too long it probably has no value (I've Astrology in mind). Although I must admit that even this strategy is not 100% secure because there are those very few instances that an idea is too far off it's time or do not reach proper communication channels (not a problem anymore - we have the net) and are dismissed for a long time because of that. $\endgroup$ Feb 1, 2014 at 20:17
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In addition to the "crank detector" listed in Sam's answer, we also have a couple of "crackpot indices:"
http://primes.utm.edu/notes/crackpot.html
http://math.ucr.edu/home/baez/crackpot.html (for physics, but still applies)

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