How many humans were born since beginning of humanity?

One proposed approach

1. Define when the humanity began, how long ago. 

2. Divide the period between when the humanity began until today in more periods based on the total population, assuming each period had a constant total population. (here you should mainly pay attention to what happened after the middle ages, before that it doesn't really mater for the final result because the world total population was much much smaller than until the middle ages)

3. For each period determine the average life expectancy. 

4. Having the average life expectancy use the replacement principle to get how many people were born within that period.

5. Sum up results from every period. 

Any comment or another method is welcomed. ​

Stefan

Great analysis! Except for one minor problem, I think the global population burst since the discovery of antibiotics, which is around 1940s. I assume the change after middle ages is not that substancial compared to what happened after 1940s.