> If the slowing growth continues, then eventually it will cross zero into the negative.

Err, no. The growth of log(x) is always decreasing and yet it always stays positive. This is true for a huge range of functions and one of the reasons limits are important.

Now, you can argue that the way human growth is slowing suggests it might possibly go negative at some point. But, that's less obvious.

You're trying to impress us with the maths. I already took all of the statistics, and differential equation classes twenty years ago. I get it. However, there are already countries experiencing negative population growth, and the trend is continuing in other Western countries.

I am not trying to impress with high school math, I defending someone that got down voted for an accurate statement.

At best we are predicting a peak human population 30+ years from now and those kind of predictions are never very accurate. Further, even if that's one peak it says very little about human population 100's or 1,000's of years from now.