Something that everybody is either shooting for, or watching the shooters with great interest. Something that, “If only we can get this figured (or designed or built) we will be in fat city for life”.
Is there some thing or scheme or proof that would propel you to the top?
Me? Nah.
Well, in my field generally (computer programming)…
Sample proof that an NP-complete problem can be solved in polynomial time, complete with the algorithm. 
Yes, I know I’m a geek, but if I had that, I’m pretty sure I could be a geek as rich as Bill Gates.
I’m an archaeologist so I guess mine would be, well, I guess it would be the “Holy Grail.”
Barring that, I would settle for an undisturbed and deeply stratified site with an incontrovertible pre-Clovis occupation. I could probably get some people to take me out to dinner at next year’s SAA conference!
I’m in IT in health insurance. To me, the holy grail would be that all of the participants in our broken health care system would be communicating electronically in real time. Both the technology (encrypted XML) and the common data dictionary (HIPAA) exist today.
Imagine going to the doctor and having your health care claim completely adjudicated in real time while you’re checking out at the front desk. We (the health insurer) would part with the claims payment money more quickly, but the savings in overhead - resubmitted claims, paper/printing, dual data entry, phone calls to member services centers and doctor’s offices - would be tremendous.
Retail pharmacies have been doing this for years, but sadly it is still years away from being commonplace in my world.
As a film archivist, there are plenty of holy grails. This is a good place to start.
In public relations, the Holy Grail is a client in such desperate shape that they can’t possibly make it, and then the public relations firm helps them make it.
Chrysler in the early 1980s. Every good PR executive I knew would have killed to get the Chrysler account. It was a no lose situation. If Chrysler failed, well, they were bound to fail anyway. If they survived it would be because of brilliant PR.
When Firestone had all their trouble a few years ago, a huge PR firm agreed to take on the account. Firestone was so uncooperative the agency resigned after a month.
Telling a big client with a multi-million dollar budget to take their business elsewhere – that’s the REAL Holy Grail.
In mathematics each separate field has its own Holy Grail. Some get solved in each generation, others last for centuries. The Riemann hypothesis and the Goldbach conjecture are probably the biggest ones, along with the aforementioned P vs. NP hypothesis.
This would be great, but it would put me out of a job. I’m an insurance biller!
I have to ask you about this, as I have no clue. Would solving this problem win you a big prize, get you tenure somewhere, or allow you to develop some RW application that you could sell for big $$$?
Yes, yes, and yes. There’s a million dollar prize attached to it (and mathematicians/computer scientists don’t attach a prize to something unless it’s a Big Deal), you’d have solved a problem that the most brilliant minds of the 20th century couldn’t solve, and you’d bury most internet security standards.
Note that the first two also apply if you prove that NP-complete problems can’t be solved in polynomial time, if you come up with an impractical polynomial-time algorithm, or if you provide a non-constructive proof. Coming from a mathematical background, I’d very strongly prefer a non-constructive proof.
Surely the 30 odd reels of Greed top that list?
Seismic lithology, if determined to be reliable, would beat the crap out of a unified field theory for me.
Hope this answers your question!
I was under the impression that just in case anyone does ever prove P = NP, most network security software now takes an advantage of problems that are not NP. That’s just what a prof told me, so I could be wrong.
Wot, no Colin MacKenzie?
I was actually thinking about the last… there are about two or three dozen seperate problems which would suddenly be converted from ‘infeasable in a reasonable amount of time’ to ‘feasable and practical’ with the development of such an algorithm. Each of those seperate problems probably has up to four or five different real world applications, with varying amounts of $$ attached. At least one is probably worth ‘BIG big $$$$’ 
Of course, there’s probably no chance I’d ever figure out the code. (sigh)
Also in the Healthcare industry (hello tpayne!). To me, the Holy Grail is a system that aligns:
payer (whoever pays for care, be it the Government, a Health Insurance Co., an Employer or an Individual)
provider (whoever should be paid for delivering care, be it physician, hospital, therapist, provider of medical equipment, etc.)
patient / consumer (person who is receiving the care)
incentives, so everybody wins. In other words, it is in the payer’s, provider’s and patient’s best interests to make decisions in a similar direction, not in direct opposition to one another, as it typically the case now. There are some clear ways to do this in theory, but they are far from being implemented IRL.
Still, I’d expect him to be about as rich as say, Andrew Wiles, not Bill Gates.
Well, maybe I exxagerated a bit – it’s hard to really conceive of just how staggeringly rich billy is.
I think I’d be able to beat Andrew Wiles though - fermat’s last theorem has NOTHING on P=NP in terms of practical applications
As an aside… would you have to publish the algorithm to collect the prize?? I might be better off not collecting, in that case. You can’t patent an algorithm IIRC, so announcing it publicly would give everyone else an even footing on exploiting it.
Top of the line security does, but RSA is based on prime factorization, which is definitely in NP. I don’t know how widely used the better algorithms are.
Wiles didn’t do anything practical, though.