I don't think the essence is especially elusive. It's the ability to make novel, meaningful, and useful discoveries from precepts that don't immediately "obviously" lead to those discoveries. Observing the sky and nature leading to a mathematical formulation of gravity is an absolutely amazing leap. In part because of what was done, but perhaps even more so for even beginning to imagine it was something that could be done.
Imagine stargazing in a time prior to Newton, observing objects falling on Earth, and somehow managing to derive an accurate mathematical formulation of something you had no reason to imagine even existed. Man hadn't been to space, let alone the moon, and so for all we knew if you dropped an apple anywhere it would just as well fall. Perhaps how Newton may have began his discovery was by asking himself where it would fall, but that's a tangent.
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Humanity's entire existence has been but a blink of time on any sort of timescale, besides our own lives. And in that time we went from the bleeding edge of technology, perhaps pun intended, being 'poke them with the pointy end' to having men travel into space, voyage to other 'planets', land on them, and imminently live on them.
A truly intelligent machine, given its capacity for practically infinite storage, infinitely more accurate recall, and arbitrarily small 'generations' (in terms of self recursive evolutionary improvement) ought be able to not only match this, from a similar starting base of knowledge, but move rapidly beyond it at an extremely swift rate.
So I don't think it would be particularly ambiguous, or debatable. An intelligent machine would quickly advance nearly all fields of humanity by an unimaginable amount. Given the ability for a machine to also scale its own processing capacity to arbitrarily higher degrees (while we're, more or less stuck with fixed 'hardware') this should be able to continue for an exceptionally long period of time as well.
You would end up completely revolutionizing humanity to a degree we can't even really imagine today - repeatedly, and it would all happen within a matter of years. I'm even being somewhat generous here by allowing for a greater intelligence to remain mindless and servile, which seems quite antithetical to intelligence. But if we can "just" get to here, as described, I think that'd be pretty compelling, servility notwithstanding.