tl；dr what Singularity means：
Three different ideas go by the name singularity.
- Vernor Vinge in 1993 meant the point where machines outthink us and human forecasting stops working， an event horizon you cannot see past. -I. J. Good in 1965 meant something more mechanical： a machine that designs a better machine， which designs a better one， until it runs away from us. -Ray Kurzweil meant a smooth exponential curve arriving around 2045.
Science has no collective position on this， because it was never a research programme with a standard model or a measurement， so the best available evidence is surveys and economics： ask a few thousand publishing AI researchers when machines reach human level and the aggregate lands near 2047 with enormous disagreement underneath， while a majority doubt that scaling current methods gets there at all.
Nordhaus went looking for an economic singularity in the productivity data and found no sign of one， and the standard objections are that intelligence is not a single dial you turn up， and that thinking faster does not build chip fabs or run physical experiments any quicker.
To make a long story short： it would be good to know what Sam Altman means. But I suspect something like self-improving AI， exponential development， and possibly abundance. In any case， those are the terms from his blog post.