Can Singularity movement’s goal “greater than human intelligence” be reached? The answer is no.
The problem with the idea of “greater than human intelligence” is that in the intelligence that manifest as the thing we call a human, there are many kinds of intelligence.
Long ago the single cell organisms came really good at something. Then eventually they combined to form new more complex lifeforms. This went on for the few billion years. Not to mention the intelligence that led to proteins, or the way the planet was created, or the way the sun nurtures us. All of that and everything we can’t name, is within “human intelligence”.
That is not the right problem to solve in the first place. As “JCR” said already in the sixties, the problem (goal) is to have the machine functioning in such a way that allows us to augment our intelligence with the machine’s capabilities.