Q: Is the number of "breakthroughs" in mathematics decreasing?
To get some quantitative feel for the question I considered the Timeline of mathematics on Wikipedia. Not all entries are "breakthroughs", but most could be considered as such. Here is a plot of the cumulative number of entries since 1900. I do notice a kink in the slope around 1965, so based on this evidence on might conclude that, indeed, the rate of discovery has decreased, but it's a relative small change in slope.
