The PrimePages' Crackpot index
By Chris Caldwell
(Adapted from an indexfor 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)
- Subtract 5 points for each refereed publication in a closely related area of mathematics.
- Subtract 1 point for quick and concise admission that a previous claim was false.
Debits (evidence of 'crackpot'ness)
- 1 point for each word in all capital letters.
- 5 points for every statement that is clearly vacuous, logically inconsistent, or widely agreed on to be false.
- 10 points for each such statement that is adhered to despite careful correction.
- 10 points for not knowing (or not using) standard mathematical notation.
- 10 points for each new term you invent or use without properly defining it.
- 5 points for offering prize money to anyone who proves and/or finds any flaws in your theory. (*)
- 10 points for stating that your ideas are of great financial, theoretical and/or spiritual value.
- 20 points for each of the following conjectures that you purport to have solved: Goldbach's conjecture; twin prime conjecture; Riemann Hypothesis, GRH; Fermat's Last Theorem (*); infinitely many Mersennes, Fermats, primes of the form n2+1...; or finding new patterns in the primes.
- 20 points for talking about how great your theory is, but never actually explaining it.
- 40 points for claiming to have a "proof" of an important
result but not knowing what established mathematicians have done on
- 10 points for pointing out that you have gone to school, as if this were evidence of sanity.
- 15 points for pointing out that you have gone to school in an area unrelated to mathematics.
- 10 points for beginning the description of your work by saying how long you have been working on it.
- 10 points for claiming that your work is revolutionary, a "paradigm shift," or a simple idea missed by all but you.
- 10 points for each favorable comparison of yourself to established experts such as Einstein, Erdös, ...
- 20 points for naming something after yourself. (E.g., talking about the "Caldwell primes" or "the Caldwell factorizer" when your name happens to be Caldwell.)
- 10 points for expecting others to disprove your result(s) rather than providing the proof yourself.
- 10 points for citing an impressive sounding, but irrelevant, result. (Typical example: Gödel's theorem.)
- 30 points for not knowing how or where to submit their major discovery for publication.
- 30 points for confusing examples and/or heuristics with mathematical proof.
- 30 points for eliciting support from, or expressing support for, well established crackpots.
- 50 points for failing to respond to appropriate corrections, questions and challenges.
- 10 points for expressing fear that your ideas will be stolen.
- 15 points for complaining about the existence of this crackpot index. (E.g., saying that it "suppresses original thinkers" or saying some item on the index is personally directed at you.)
- 20 points for defending yourself by bringing up (real or imagined) ridicule accorded to your past theories.
- 20 points for each complaint that the list moderators are out to get you or are blocking your substantial and useful posts. (Note: the list moderators allow unmoderated posts by 99 44/100 % of the list members).
- 40 points for comparing those who argue against your ideas to members of hate groups.
- 40 points for claiming that the others (e.g., the list moderators) are engaged in a "conspiracy" to prevent your work from gaining its well-deserved recognition or fame.
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 meetingsso 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.
Wiles then sent out his preprints and submitted to a journal. His work was circulated on the Internet. And as would be expected in a work of this size, errors were found. Most were trivial and immediately fixed, but one stopped the proof dead in its tracks. Eventually, with the help of another mathematician, Wiles circumvented the major error, and the proof was published. His work will be continue to be questioned, examined, modified (and even doubted) for many years, but it is out there for all to see. Mathematicians publish.