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Topic: Announcement of bet on the settlement of the problem concerning P and NP
Replies: 1   Last Post: Dec 2, 2012 9:02 PM

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Posts: 1
Registered: 12/2/12
Announcement of bet on the settlement of the problem concerning P and NP
Posted: Dec 2, 2012 4:03 PM
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Dear colleagues,

I here announce the proffer of a bet on the settlement of the mathematical problem concerning P and NP.

This problem is better known as the "P vs. NP" problem, and the settlement of it is referred to hereafter as SETTLEMENT.

To be precise, SETTLEMENT is the existence of a proof of the "P vs. NP" problem and hereafter, whenever 'proof' is mentioned in this announcement, it refers to proof of the "P vs. NP" problem (not of any other problem). As far as the bet proposed here is concerned, a false "proof" does not count, and a proof dependent on the model of computation, e.g. precluding the possibility of (the feasibility of) quantum computing, does not count, either.

If any reader sees fit, please pass my announcement (of the bet) around so some people may make some easy money or may easily lose some hard-earned money.

In the past I have tried pretty hard, to no avail, to get people who proclaimed to (want to) bet on SETTLEMENT to bet on SETTLEMENT. A most recent attempt generated not even a reply, which made me wonder. But I just realized, browsing on the internet, that there is a person by the name of Vinay Deolalikar to have claimed to have solved the problem. That may be the reason that this less brave person, fearing he/she might lose the bet, is swallowing his/her words hard and is shying away. What an unfortunate coincidence!

I am now laying out the bet (but in a much taller order due to Vinay Deolalikar's announcement).

First, of course, the bet amount is proposed to be ten thousand US dollars (US$10000). But there can be flexibility. If somebody is really serious and would like the amount to be less, another amount can be discussed and agreed upon.

To avoid the inconvenience of the announcement by Vinay Deolalikar, I will go out on a limb to bet in addition for that US$10000 that a proof existed prior to the claim by Vinay Deolalikar, even though I still do not know the exact date on which Vinay Deolalikar first proclaimed. Actually, there is an even stronger version of this, which I will pronounce toward the end of this announcement in the form of a 'paradoxical' statement.

What if people want to bet more? Here is something additional. I will challenge with an additional US$9999 that the proof will only contain math no higher than undergraduate level (keeping in mind that the proof will have to be prior to Vinay Deolalikar's announcement as promised),

If people still think the amount too low, I can make a further bet that a proof, when written out in the format of a refereed publication agreeing with the general requirements of margin, font size, etc., will be no more than 6 pages, even with preamble and (the redundancy of) relevant, well-known basic formal definitions. For this I am willing to bet one hundred thousand US dollars (US$100000).

I do not want the bet to drag out for long, so the completion will be in half a year (or shorter) after the monies are deposited. A little more time, if requested, can be agreed on beforehand, but I do not see the necessity.

Jokingly, a piece of caution. I am not likely to lose on the US$100000, since I might be able to time-travel and tell the author to alter the proof such that it would guaranteed to be within 6 pages in length. When shortened, undergrad level math might fail to do the trick, and I could lose on the other bets, but surely not the US$100000 one in such a TT case. (Smileys).

In fact, I suspect that one version of the proof could fit in one page, or even in any margin on a page of any textbook!

When SETTLEMENT has come out, some minor problem may be exposed for the current (practice of) mathematics. Therefore, we have to adopt a precise definition of the "P vs. NP" problem, even though SETTLEMENT, as I see, should be immune to which definition we adopt. Besides, they (i.e. the definitions of NP) are claimed to be equivalent, anyway.

Nevertheless, we need to be precise without ambiguity. The definition we use will be the 'certificate' version by S. A. Cook, one at http://www.claymath.org/millennium/P_vs_NP/pvsnp.pdf as appeared on December 2, 2012.

When SETTLEMENT has come out, it might say, or might not say, something along the line of Ramsay Theorem and Rice Theorem, about Tarski's discovery and the true semantics of the 'paradoxical' Incomplete Theorem. It might even compliment the infinitely lower quality on the CERN saga about superluminum; it could be highly sociological and deeply philosophical. (Smileys, Smileys). It is in this spirit, I make the following 'paradoxical' statement (not part of the bet):

For any proof known to the world, there exists another proof predating the former.
(NOTE: proof here is always the proof of the "P vs. NP" problem).

I feel, lastly, I still stand a chance of not losing a penny even when SETTLEMENT never comes out, since this might be a less brave stale world after all and there might not be one who is really daring enough to bet with me. (Smileys, Smileys, and more Smileys)



Of the three bets offered here, one does not need take them all, but the first bet of US$10000 is a must for it to be a bet at all.

Should the bet be on (with anybody), we would have to find an escrow. If anybody in the academic field would like to act in such capacity, please let me know. I thank you in advance for the existence of a Brave New World!

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