Have you heard any buzz from your mathematical collegues on the alleged disproof of the Riemann Hypothesis.Later comments indicated that the mathematician was not that good. When should you believe a math announcement? Which of the following would you believe? Would you bother downloading the paper?
- Karp claims to have shown P = NP. P \ne NP.
- Shelah claims to have shown P=NP. P\ne NP.
- Widgerson claims to have shown P=BPP. P\ne BPP.
- Bill Gates claims his group has shown P=NP and the binaries are available but not the source code.
- The Free Software Foundation claims to have shown P=NP and of course the source code is available.
- An undergraduate math major who is really sharp claims to have solved the the Collatz Conjecture) (also called the 3x+1 conjecture).
- G: How good is the person who claims to have solved it. Hard to measure. (number of STOC/FOCS papers :-) ) For someone new this might be even harder to access.
- B: How believable is the result? We'd believe P\ne NP more than P=NP. But we may believe that if a proof was found now it would be that P=NP. I've heard that Riemann Hypothesis will probably be solved in the next 50 years.
- H: How hard is the problem?
- W: How good is the writeup? Is there one?
- If the problem is outside of your area then you may have to take other people's word for some of G,B,H, or W. How good are the people telling you about the problem? This may lead to a recursive formula.
If G*B*W/H > C then the result is worth looking into.If you claimed to prove Green's Conjecture then I could use Green's Conjecture to to see if your proof is worth downloading.