If it is replaced by 'will make itself much smarter than us', that is enough.

Ok, but how much smarter ? Stephen Hawking is much smarter than me, for example, but I'm not worried about his existence, and in fact see it as a very good thing, though I'm not expecting him to invent "gray goo" anytime soon (or, in fact, ever).

I realize that quantifying intelligence is a tricky proposition, so let me put it this way: can you list some feats of intelligence, currently inaccessible to us, which you would expect a dangerously smart AI to be able to achieve ? And, segueing into #3, how do these feats of intelligence translate into operational capabilities ?

(Have you read Chalmer's paper?)

Probably not; which paper are you referring to ?

Which reasons would those be?

The ones I alluded to in my next paragraph:

If you took the ten smartest scientists alive in the world today, and transported them to Ancient Rome, they wouldn't be able to build an iPhone from scratch no matter how smart they were.

The problem here is that raw intelligence is not enough to achieve a tangible effect on the world. If your goal is to develop and deploy a specific technology, such as an iPhone, you need the infrastructure that would supply your raw materials and labor. This means that your technology can't be too far ahead of what everyone else in the world is already using.

Even if you were ten times smarter than any human, you still wouldn't be able to conjure a modern CPU (such as the one used in iPhones) out of thin air. You'd need (among other things) a factory, and a power supply to run it, and mines to extract the raw ores, and refineries to produce plastics, and the people to run them full-time, and the infrastructure to feed those people, and a government (or some other hegemony) to organize them, and so on and so forth... None of which existed in Ancient Rome (with the possible exception of the hegemony, and even that's a stretch). Sure, you could build all of that stuff from scratch, but then you wouldn't be going "FOOM", you'd be going "are we there yet" for a century or so (optimistically speaking).

the only way to cure your doubt if the prior history of humanity is not enough

Are you referring to some specific historical events ? If so, which ones ?