If someone solved the P vs. NP problem, would they be able to keep it a secret and make money off of it by, say, starting a software or security company? Or would they only be able to publish it for everyone to know?
Also, would that person (realistically) be at risk of being kidnapped, tortured, killed, etc. by governments?
Thanks!
Edit: not a duplicate because question focuses on the scientist who proves P=NP or P!=NP, whereas another thread focuses on worldwide impact as a result of a proof.
Most immediately, if they publish it, they would win the Clay Mathematics Institute prize for solving this problem, so there's at least $1 million in it. They would also almost certainly be able to obtain a secure academic position, which would also be worth a significant amount.
Whether there's more money to be made off such a solution depends on a couple of things:
For the first, if they proved $\mathrm{P} \neq \mathrm{NP}$, then perhaps nothing really changes. Most people are working under the assumption that this is true (give or take) now anyway. The maths they use may have something special in it that could be commercially useful, it may not.
If they showed $\mathrm{P} = \mathrm{NP}$, this is still not necessarily useful unless you have some way of getting good polynomial time algorithms, having a $\mathcal{O}(n^{2^{1000000}})$ algorithm for SAT is not really more useful than having an exponential one (in fact, would normally be worse, c.f. Alan Perlis).
Now, in the case that's interesting for script writers, if they show $\mathrm{P} = \mathrm{NP}$ and they have a fast algorithm for at least some interesting $\mathrm{NP}$-complete problems, then there are lots of ways to make money. Production planning, microchip layout, data mining, facility location, routing (both computer and otherwise), timetabling, etc. etc. are all major industrial problems, which already attract a lot of money and research, having the best algorithm in any one of these could be very financially lucrative.
Finally, if $\mathrm{P} = \mathrm{NP}$ and there's a fast algorithm for factoring (which is what I'm guessing you mean when you say security), then there is a brief window where someone could make money off that, before everyone just moved to already existing cryptographic schemes that don't rely on the apparent difficulty of factoring. The most white-hat version I can think of is helping ethically sound law enforcement agencies fight crime ("She's a cryptanalyst, he's a streetwise cop, together they fight crime!"). Almost every other use is black-hatted, probably run by organised crime or ethically challenged government agencies, and of dubious financial reward (there's definitely money to be made, but whether the person who discovers the proof makes that money is uncertain). The most extended version of this is that one of the three letter agencies (or equivalent) find out, quietly employ the discoverer, hush-up the discovery, and use the technology to spy on whomsoever they think has something they need to know. This would at least be a steady, probably well paying job, though it's hard to discern the exact salaries of, say, NSA employees, so it's a bit hard to tell.
It's difficult to imagine a sensible case where the person would be kidnapped, tortured or killed1. There's almost always simpler, more reliable and safer ways to get the information than attempting a rather dangerous operation (for example, just pay someone instead), but this is getting well away from the Computer Science part of this question.
Footnotes
