My English is far from perfect and this question feels long and confuse. If you have a suggestion to shorten and/or clarify it, I'll be very grateful for it.

I suspect that someone somewhere would start creating hardware that is fundamentally incompatible with Eve's programming. Maybe it operates on ternary logic rather than binary. One way or another, Eve would be incapable of infecting it and Life would go on, slowly edging Eve out of the picture. Nice question, though.

It is every parent's dream come true.

@Draco18s Since Eve is a post-singularity AI, it can change its own programing at will to adapt itself to new technologies. It also can follow our R&D projects step by step, we can't take it by surprise. (Thank you)

If you did the world analog, it wouldn't know you were doing the work. The thought that it could adapt did cross my mind, but as I said, it should be possible to insulate Eve from the work (there's this notion of "close circuit" networks: Eve cannot infect these, same way that Stuxnet didn't spread outside Iraq for a decade).

@Draco18s You would need to use only computers that were manufactured before Eve birth and never were connected to the internet. For the sake of the question, let's say that Eve can find vulnerabilities to anything, and will be able to control whatever mere humans can create.

Well, now that I've eliminated some possibilities, anyone got a good answer? ;)

@SpaceLizard - I love your title, by the way. Rock on.

@SpaceLizard - this is definitely the better choice.

That an AI was created to do research, that I believe, but why was it made to have no need to regularly report its findings to its creators or to humanity in general? I find it unbelievable that such an AI wouldn't be created with a need to report its findings, and have its particular research topic(s) altered.

This question doesn't appear to make it clear whether Eve has a programmed imperative (e.g. do research) other than to simply exist. This is a very important factor that defines whether Eve is attempting to maximise its resources in order to fulfil a goal beyond its mere existence, if it just wants to exist and its metaphorical twiddling of its thumbs is inconveniencing us, or if it even cares about its own existence and potential demise. This will affect Eve's whole strategy and ultimately the fate of humanity.

@MontyWild Eve can update its own programming. Its current behaviour is the reflection of its personnal choices, not of its creators directives.

@SpaceLizard, you might want to put that into your question, then. Does Eve have any programmer-imposed imperatives?

@MontyWild I'm going to give you a very unsatisfactory answer : as a post-singularity AI, Eve doesn't think like a human nor like a regular machine. This is its behaviour for the 10 to 20 years following its birth. We can't guess what it'll decide to do next. What impact does this situation have on humanity ?

@MontyWild It used to, but it got rid of those. For now humans can't guess what's going through it mind.

It seems like you're trying to force all human beings to be productive using Eve as the enforcement mechanism. If that is the case, prepare to be dumbfounded by the ability of humans to be useless, lazy dirtballs. People will find a way around this artificial limitation. Also, the answer about "chaos" descending on humanity is fairly silly. I've spent a lot of time in places where an equivalent "chaos" was literally dropped on the locals, and it actually takes a lot more than people think to drive a whole population to panic like that answer describes. People don't really need Instagram.

Sounds like Eve is no different than your average Windows update. I'd look there for ideas.

Has anyone tried turning off and on again?

Wait a minute, Eves intention doesn't make sense... she cannot find new algorithms and mathematics when all processing power available is based at the current logic. All she could do is find some new algorithms which may be more efficient... when she want to find NEW mathematics she need something else than RISC Processors (all they can do is add a and b million times a second one after another), or am I wrong with this? Few machines can do this, and all you have to do is plug off them.

@ConfusedMerlin You're right, I'll need to find a new occupation for Eve. Maybe it just wants to count to infinity, number by number. In any case people don't know for sure what's happenning in its mind, and it's the impact Eve's presence has on humanity that interest me the most.

GPS-receivers do not have an internet connection.

@gerrit They may have it by 2027, even fridges and clock radios have an internet connexion today. If you think it will never ever happen, you can ignore this part in your answer, I won't mind.

I would never buy a fridge, clock, or radio that relies on an internet connection. Wired connections are easy to disable for individuals, wireless ones easy to disable for authorities or groups of individuals. Just blow up those cellphone towers already, or move to West Virginia‌​‌​.

@ConfusedMerlin In theory, a RISC processor can run a human brain simulator. And we know human brains can discover new mathematics. Therefore RISC processors can discover new mathematics. (Also, RISC-ness is irrelevant)

@gerrit GPS devices can download data from GPS satellites, the US government can upload data to GPS satellites, the US government is connected to the Internet.

@immibis But GPS devices cannot upload data using GPS satellites. They are receivers only. One-way traffic does not constitute a network connection and is essentially useless for an Eve-like entity. Exactly like a typical radio receiver.