(UPDATE- 17x17 and even 18x18 was solved. See my arXiv paper on grid colorng and/or Feb 8, 2012 post.)
(Reminder: NYU-IBM-COLUMBIA-THEORY DAY: see here.)
Anon 9 on comments on 17x17 post writes about my 17x17 post:
This is just like when teachers ask their students to model or code parts of a system that will be used in the teachers own research eventually. this is really bad for academia in general. Never again propose such things, please.I will take this comment as the starting point in an intellectually honest discussion. I reply to it after this paragraph. I then URGE the poster to reply with either: (1) Yes, GASARCH you are correct, or (2) Yes, GASARCH you are correct, but its still bad for academia because ..., or (3) No, GASARCH you are wrong because ... . Doing either would be intellectually honest. Doing neither would be intellectually dishonest. You need not use capitals or use my phrases, but you get the idea.
- When a teacher assigns students to write code for a system the students are forced to do it in order to get a good grade. I am not forcing anyone to work on the 17x17 challenge.
- When a teacher assigns students to write code for a system and the students do not get a co-authorship then this could be bad (this might depend on the situation). I stated explicitly that whoever cracks 17x17 can publish it themselves, or, if they do enough other stuff, with me. In any case the terms are out in the open. Also note that whatever I do will get much scrutiny because I posted it on a public blog rather than a private classroom.
- When a teacher assigns students to write code for a system the students might get nothing for his efforts. If a student cracks my problem they will get $289.00. If they try and fail they may learn things of interest (to be fair, this may be true for student-code-writer as well).
- The 17x17 challenge has already stimulated discussion on three blog and might get some people interested on the math end (Ramsey Theory) or the computer end. How is this bad for academia?
- As Michael pointed out what I am doing is similar to what Erdos did, though my problem is not deep mathematics. Do you think that when Erdos offered money for problems, this was bad?
- If I had posted about the problem WITHOUT the cash prize would you still object to it? (One point: if I offered it without a cash prize I would have asked to RESOLVE the problem rather than to GIVE ME a verifiable coloring). If I had offered ALOT MORE money would you object? Is it a U-shaped curve: offer either less than 10 or more than 2000 and you are okay with it? I am not being funny--- I look forward to your intelligent to comment on this.)