Short answer: nobody knows. Slightly longer answer:
In 2013, 549 AI experts were asked at what year they thought there was a 10% chance of human level machine intelligence existing, at what year they though there was a 50% chance of it existing, and what year they thought there was 90% chance. Of the 170 responses, the median year for a 10% chance was 2022, the median year for a 50% chance was 2040, and the median year for a 90% chance was 2075.1
Let me point out that human-level AI has been forecasted many times before, and people have consistently underestimated the difficulty of the problem. On the one hand, this might make us want to push back the dates on these estimates. On the other hand, the people making these estimates know as well as we do that AI has consistently been predicted to be right around the corner, so many of them probably corrected for that themselves.
If for some reason you value my opinion more than the hundreds of surveyed experts, I would, in fact, say that those dates are too early. I’d say there’s a 10% chance by 2030, a 50% chance by 2050, and a 90% chance by 2200. I don’t know why so many people are so confident we’ll have human-level AI figured out by 2075.
If that didn’t satisfy you, this paper has a good section on forecasting AI. One final thing though: not knowing when AI will reach human-level intelligence is not an excuse to tacitly assume it will be a long time from now.