| (Adapted from an
index for Physics Claims by John Baez.)
A simple guide to the evaluation of contribution to the PrimeNumbers list. Though this index is formed partly as a joke, in it are serious signs that one can use to recognize a crack-pot. Some novice and mathematically unsophisticated members on the list can be taken in by crack-pot claims. We'd like to stop such posts and claims from spreading like a virus.
When you do recognize such claims, it is usually best not to respond. When you do respond, do so with gentleness and respect. A flame war is as much an annoyance on the list as a crack-pot's droning.
Credits (evidence of reasonableness)
Debits (evidence of 'crackpot'ness)
I have tried to place the highest penalties on those behaviors which most directly contradict the methods of mathematics. In mathematics we seek to communicate and share. This starts by studying the literature to see what others have done (first via the standard textbooks and texts, then by MathSciNet). Because of this study, we then know: the proper way (notation and context) with which to express our new discoveries; the key researchers in our area; and the proper journals for submitting our results. We learn the proper language for sharing, namely "mathematical proof." Crackpots are those who seek to share without knowing the language they are speaking. They seek to join into a conversation without first listening to what the conversation is about.
Mathematical communication then continues by listening. Mathematicians share their results as preprints and at meetings so that others can see what they are doing and so that the authors might gain from the feedback. Mathematical disagreements and times arise but they are addressed in the time honored way: put up or shut up. That is, either present a proof of your position or admit it is just a guess (often called a conjecture or heuristics). Mathematical journals are refereed. Referees read to see if the mathematics is new, correct, and appropriately presented. They often ask questions and make suggestions that help authors improve their articles. Mathematics is a conversation, not a soliloquy. Crackpots are unable to listen, unable to join into this conversation. In fact most crackpots set themselves in direct opposition to the dialog of mathematics.
How do mathematicians establish claim to their ideas? They publish. Eventually in a journal, but usually first by e-mail, preprints and at mathematical conventions. Many mathematicians point out if you just read the journals, then you are already several years behind the key researchers. Most mathematicians have had ideas that they have failed to publish, and so when others published those ideas first, the others appropriately got the credit. Ironically, some crackpots keep their "discovery" secret. Should they (by some great stroke of luck) be correct, the crackpots own claim to the idea may be lost. In mathematics you establish your claim by sharing your proof (correctly, concisely, in the appropriate locations).
Some of the behaviors attributed to crackpots are also present in the elder statesmen of mathematics. For example, Paul Erdös famously offered prizes for proofs (and disproofs) of those things he thought true. Before his death he paid on many of these offers (and others maintain a fund to continue to pay on most of his offers). But Erdös' mathematical saneness is well established by the 1500+ papers he wrote or coauthored. Indeed it is these articles that established his right to offer prizes.
Another excellent example is Andre Wiles who proved Fermat's Last Theorem
though Wiles was exceptionally well established as a mathematician, he hesitated
to state publicly what he was working on. Not because he thought his
work might be stolen, but because merely claiming to have proven something
thousands of the best minds in history have failed at, brings your work under
grave suspicion. So
what did he do? What all mathematicians do: he shared his ideas! First
he shared with a colleague in a course at his school. Then with hundreds
of colleagues at a mathematical meeting. Only
at the end of that meeting did he actually make his claim. Why? First,
because his work was important whether or not it could be used to prove FLT. But
perhaps more importantly to allow errors in his work to be pointed out before
making a grandiose claim as FLT.
Another prime page by Chris K. Caldwell <email@example.com>