I don't think the question is, "What happens when they equal us?" It's, "What happens when they greatly surpass us?"
Another framing of singularity theory is one made popular by Ray Kurzweil, who talks about exactly what Heradel said: that technology has already transformed the world many times, including several transformations in the last century, and that those world-changing advances are coming faster and faster. If the acceleration of technological development continues, then sometime within the next couple of decades we'll hit a point where the world becomes unrecognizable from one day to the next
Of course, human minds are completely unable to cope with such rapid change. So either the pace of development has to flatten out before that happens, or
the inhabitants who function in that world comfortably will have to have minds with capabilities greater than what we today call "human."
That's the singularity.